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BITSAT-MOCK TEST 11, SOLUTION OF MOCK TEST, CONDUCTED ON DOUBTNUT APP, , Download Doubtnut Now, , Q-1 - BITSAT-MOCK TEST 11-MATHS, , If z, , √3 + i, =, , z, , , then z, , 69, , is equal to, , (A) − i, (B) i, (C) 1, (D) − 1, Correct Option : A, , SOLUTION, 69, , Z, , 69, , 69, , √3 + i, = (, , ), 2, , − 1 + √5(3i), , 1, = [, , (, 1, , 2, , 69, , w, )], , = (, , ), i, , 1, =, , =, i
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ATTEMPT FREE TEST ON DOUBTNUT, , Q-2 - BITSAT-MOCK TEST 11-MATHS, , If 2, , < x < 3, , , then, , (A) |x, , − 3| < |x − 2|, , (B) (x, , − 3) > (x − 2), , (C) (x, , − 3)(x − 2) < 0, , (D), , x − 3, > 0, x − 2, , Correct Option : C, , SOLUTION, If a, b, , ∈ R, a < b, , , then a, , ⇔ (x − a)(x − b) < 0, , Alternatively, 2, , ,, , < x < 3, , < x < b
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⇒ x − 2 > 0, , ⇒ (x − 2), , and (x − 3), , < 0, , and (x − 3) are of opposite sign, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-3 - BITSAT-MOCK TEST 11-MATHS, , If z is a complex number, then |3z − 1|, , = 3|z − 2|, , (A) y-axis, (B) a circle, (C) x-axis, (D) a line parallel to y axis, Correct Option : D, , SOLUTION, |3z − 1| = 3|z − 2|, z = x + yi, x, y ∈ R, , √(3x − 1), , 2, , + (3y), , 2, , = 9x, , 2, , + 9y, , 2, , − 36x, , represents
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⇔ 30x = 35, 7, ⇒ x =, 9, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-4 - BITSAT-MOCK TEST 11-MATHS, , (z + 1)(z̄ + 1), , ¯, ¯, ¯ +, (A) zZ, , (B) ∣∣z, (C) |z, , 2, , 1, , ∣ + 1, ∣, , + 1|, , (D) |z|, , can be expressed as, , 2, , 2, , + 2, , Correct Option : C, , SOLUTION, ¯, ¯, ¯, ¯, ¯, ¯, ¯, ¯ = |z + 1|, (z + 1)(z̄ + 1) = (z + 1)(¯, z, +, 1), , 2, , ATTEMPT FREE TEST ON DOUBTNUT
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Let a,b,c be real number such that 4a + 2b + c, the quadratic equation ax, , 2, , + bx + c = 0, , = 0, , and ab, , > 0, , , than, , has, , (A) real roots, (B) non-real roots, (C) purely imaginary roots, (D) only one real roots, Correct Option : A, , SOLUTION, Since the coefficients of the equation one real, therefore, either both, the roots are real or both are non real , But, 4a + 2b + c = 0, , ⇒ a(2), , 2, , + b(2) + c = 0, , Hence 2 is a root of ax, , 2, , + bx + c = 0
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One root of the equation, ax, Both the roots of ax, , ∴, , 2, , 2, , + bx + c = 0, , + bx + c = 0, , is real., , are real., , ATTEMPT FREE TEST ON DOUBTNUT, , Q-7 - BITSAT-MOCK TEST 11-MATHS, , If x, , 1, = 2 +, 2+, , (A) √2, , − 1, , (B) √2, , + 1, , 1, 2 + ... ... ., , (C) 3, (D) none of these, Correct Option : B, , SOLUTION, Given x, , , then the value of x is, , 1, , 2 +, , 1, = 2 +, x
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⇒ x, , 2, , − 2x − 1 = 0, , ⇒ x = √2 + 1, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-8 - BITSAT-MOCK TEST 11-MATHS, , Sum of the series, , 3, , 5, +, , 4, , (A) 1, , upto n terms is, , +, 144, , 2, , n(n + 2), (n + 1), , (C), , 36, , 1, −, n, , (B), , 7, +, , n, , 2, , 2, , + 2n + 2, , (n + 1), , 2, , (D) none of these, Correct Option : B, , SOLUTION, Given series is ,, , 3, (1 × 2), , 5, 2, , +, (2 × 3), , 7, 2, , +, (3 × 4), , 2, , +
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Its nth term, , =, {n(n + 1)}, , 1, =, n, , (n + 1), , 3 + (n − 1) × 2, , 2, , − n, , =, , 2, , 2, , n (n + 1), , 2, , 2, , 1, −, , 2, , (n + 1), , 2, , Sum of series, 1, = (, 1, , 2, , 1, −, 2, , 2, , 1, ) + (, 2, , 2, , 1, −, 3, , 2, , 1, ) + .... . + (, n, , 2, , 1, −, (n + 1), , ATTEMPT FREE TEST ON DOUBTNUT, , Q-9 - BITSAT-MOCK TEST 11-MATHS, , Next term of the sequence4, , (A), , 863, 48, , (B), , 869, 48, , (C), , 865, 48, , (D) none of these, Correct Option : C, , 35, , 7, ,, 3, , 121, ,, , 6, , 335, ,, , 12, , 24, , .. is, , 2, , )
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SOLUTION, Given sequence is, 2 +, , 1, , 1, , 6 −, , 3, , 1, −, , 6, , 6, , 1, , Hence, the next term, , = 18 +, , 1, , 10 +, , 1, , 14 −, , 12, , 865, =, , 18, , 48, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-10 - BITSAT-MOCK TEST 11-MATHS, , (666. .6), , 2, , (8888), +, , n digits, , (A), , n digit, , 4, (10, , 2n, , − 1), , 9, , (B), , 4, (10, , n, , − 1), , 2, , 9, , (C), , 4, (10, , n, , − 1), , 9, , (D) none of these, Correct Option : A, , is equal to, , 24, , ,
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SOLUTION, (666.6), , 2, , + (888. .8), , = (6 + 60 + 600upto n terms), 6(10, , n, , 2, , − 1), , = {, , }, , 8(10, , 10, , n, , − 1), , [, 10 − 1, , − 1), , 10 − 1, , 36(10, , − 1, , =, , + (8 + 80 + 800. . upto n terms), , +, , 10 − 1, n, , n, , 2, , 4, + 8] =, , 10 − 1, , (10, , 2n, , − 1), , 9, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-11 - BITSAT-MOCK TEST 11-MATHS, , If n is an integer between 0 and, ⌊n ⌊21 − n, –, – ––––––––, , is, , (A) ⌊9⌊12, , – –––, , (B) ⌊10 ⌊11, , ––– –––, , (C) ⌊20, , –––, , (D) ⌊21, , –––, , > 1, , , then the minimum value of
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Correct Option : B, , SOLUTION, ., , n, , Cr, , is maximum for r, n − 1, , r =, 2, , Now, ., , 21, , or, , Cn =, , i.e. when n, , n + 1, 2, , n, =, 2, , if n is even and for, , where n is odd., , ⌊21, –––, ⌊21 − n ⌊n, –, –––––––– –, , is maximum, iff, , 21 − 1, 2, , ., , = 10, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-12 - BITSAT-MOCK TEST 11-MATHS, , If n is an even positive integer, then ., , (A) n, (B) 0, (C), , n, 2, , (D) none of these, , n, , Cr, , is maximum when r =
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Correct Option : C, , SOLUTION, We know,, ∴ ., , n, , ., ., , n, , Cr ≥ ., , n, , Cr, , n − r + 1, =, , Cr − 1, n, , r, , Cr − 1, , only if (, , n − r + 1, ) ≥ 1, r, , n, ∴ r =, 2, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-13 - BITSAT-MOCK TEST 11-MATHS, , A parallelogram is cur by two sets of n parallel lines parallel to the, sides of the parallelogram. The number of parallelogram thus formed, is, , (A) ., , n, , (B) ., , n−1, , (C) .n, , C2 × ., , n, , C2, , C2 × ., , C2 × ., , n−1, , n−1, , C2, , C2
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(D) none of these, Correct Option : B, , SOLUTION, we have to sets of parallel lines (inclusive of the parallelogram) each, containing (n + 2) lines. A parallelogram is formed when a pair of, parallel lines is selected from each set., ∴, , Required number, , = ., , n+2, , Cr × ., , n+2, , Cr, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-14 - BITSAT-MOCK TEST 11-MATHS, , If (3√3 + 5), , 2n + 1, , = p + f, , , when p is an interger and f is a proper, , fraction, then f (p + 1) is equal to, , (A) 5n − 1, (B) 3, , 2n − 1
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(C) 2, , 2n + 1, , (D) none of these, Correct Option : C, , SOLUTION, Let (3√3 − 5), (3√3 + 5), , 2n + 1, , 2n + 1, , = f', , a proper fraction, then, , − (3√3 − 5), , 2n + 1, , = p + f − f', , must be na integer, , ⇒ f = f', , ∴ (p + f )f = (p + f )f ', , = (3√3 + 5), , 2n + 1, , (3√3 − 5), , 2n + 1, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-15 - BITSAT-MOCK TEST 11-MATHS, , n, , The integral part of (8 + 3√7) is, , (A) an odd integer
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(B) an even integer, (C) zero, (D) nothing can be said, Correct Option : A, , SOLUTION, Let (8 + 3√7), let (8 − 3√7), , n, , = p + f, , n, , = f', , , where p, , and f is a proper fraction, and, , , a proper fraction, as, , 0 < (8 − 3√7) < (8 + 3√7), , since (8 − 3√7), , ∈ I, , ,, , n, , n, , + (8 − 3√7), , = p + f + f', , is an even integer., , Therefore, (p + 1) is even, ATTEMPT FREE TEST ON DOUBTNUT, , Q-16 - BITSAT-MOCK TEST 11-MATHS, , A square matrix A, for, , = [an ], , n×n, , is called a diagonal matrix if a, , n, , = 0
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(A) i, , = j, , (B) i, , < j, , (C) i, , > j, , (D) i, , ≠ j, , Correct Option : D, , SOLUTION, A = [aij], , n×n, , is a diagonal matrix iff all non-diagonal entries are 0,, , ie. Iff aij = 0 for i, , ≠ j, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-17 - BITSAT-MOCK TEST 11-MATHS, , The system of equations Ax, unique solution if, , = B, , of n equations in n unknowns has a
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(A) det A, , ≠ 0, , (B) det A, , ≠ 0, , , (Adj A) B = 0, , (C) det A = 0, (Adj A) B = 0, (D) det A = 0, (Adj A) B, , ≠ 0, , Correct Option : A, , SOLUTION, For AX, , = B, , has a unique solution only if det A, , ≠ 0, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-18 - BITSAT-MOCK TEST 11-MATHS, , If for a matrix A, A, equals, , (A) [, , 1, , 0, , 0, , 1, , ], , 2, , + l = 0, , , where is the identity matrix, then A
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(B) [, (C) [, (D) [, , i, , 0, , 0, , −i, , ], , 1, , 2, , −1, , 1, , −1, , 0, , 0, , −1, , ], , ], , Correct Option : B, , SOLUTION, A, , 2, , + l = 0, , ⇒ A, , 2, , =, , − 1, , and for A [, , i, , 0, ], A, , 0, , 2, , i, , 0, , = [, , −1, , i, , 0, , ][, 0, , −1, , −1, , 0, , 0, , −1, , ] = [, 0, , −e, , ], , ATTEMPT FREE TEST ON DOUBTNUT, , Q-19 - BITSAT-MOCK TEST 11-MATHS, , The vlaue of, , 3 + cot 76cot 16, cot 76 + cot 16, , (A) cot 46 ∘, , is
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(B) tan 46, , ∘, , (C) tan 44, , ∘, , (D) none of these, Correct Option : B, , SOLUTION, 3 + cos 76cot 16, cot 76 + cot 16, 3sin 76sin 16 + cos 76cos 16, =, cos 76sin 16 + sin 76cos 16, 2sin 76sin 16 + cos(76 − 16), =, sin(76 + 16), cos 60 − cos 92 + cos 60, =, sin 92, 1 − cos 90, =, , = tan 46, sin 92, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-20 - BITSAT-MOCK TEST 11-MATHS, , If cos x = tan y. cos y = tan z and cos z = tan x, then a values of sin x is, equal to
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(A) 2cos 18, , ∘, , (B) cos 18 ∘, (C) sin 18 ∘, (D) 2sin 18 ∘, Correct Option : D, , SOLUTION, cos, , 2, , x = tan, , ⇒ (1 + cos, , 2, , 2, , y = sec, , 2, , y − 1 cot, , tan, , 2, , 1 − tan, ⇒ 1 + 1 − sin, , 2, , 2, , x, , sin, , 2, , x, , x =, cos, , ⇒ (2 − sin, , z − 1, , x, , x) =, , 2, , 2, , 2, , x)(1 − 2 sin, , x − sin, , 2, , 2, , x, , x) = sin, , 2, , x, 2, , ⇒ sin, , 2, , 4(√5 − 1), , 6 − 2√5, x =, , =, 4, , ⇒ sin x =, , = 4 sin, , 2, , 18, , 4, , ± 2sin 18, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-21 - BITSAT-MOCK TEST 11-MATHS
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If (tan, , −1, , 2, , x), , −1, , + (cot, , 5π, , 2, , x), , 2, , =, 8, , , then =, , (A) − 1, (B) 1, (C) 0, (D) none of these, Correct Option : A, , SOLUTION, Given (tan, ⇒ (tan, , −1, , −1, , 2, , x), , + (cot, , −1, , 5π, , 2, , x), , 2, , =, 8, , −1, , x + cot, , 2, , x), , − 2 tan, , 5π, , −1, , x cot x =, 8, , π, , 2, , ⇒, , − 2 tan, , −1, , π, x(, , 2, ⇒ 2t, , 2, , − tan, , −1, , 5π, x) =, 8, , 2, 3π, − πt −, , 2, , 2, , −, , = 0, , , where t, , = tan, , −1, , 8, 3π, ⇒ t =, , π, , −, , 4, , ⇒ tan, , 3π, x =, , 4, , tan(3π), ⇒ x =, , π, , − 1, , ), 4, , π, , −, , 4, , , tan( −, 4, , ⇒ x =, , −1, , 4, , x, , 2
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Q-23 - BITSAT-MOCK TEST 11-MATHS, , If tan α, , 1, =, 5, , , tan β, , 1, =, 239, , , then the value of tan (4α − β) is, , (A) 0, (B) − 1, (C) 1, (D) none of these, Correct Option : C, , SOLUTION, First find tan 2α, then tan 4α and then the (4α − β), 120, tan 4α =, 119, 120, , tan(4α − β) =, , 119, , 1 +, , −, 120, 199, , 1, 230, , ., , 1, , = 1, , 239, , ATTEMPT FREE TEST ON DOUBTNUT
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Q-24 - BITSAT-MOCK TEST 11-MATHS, , If {x} and [x̄] denote respectively that fraction and integral parts of a, real number x, then the solution set of the equation is, , (A) {0,, , 5, }, 3, , (B) {, , 5, }, 3, , (C) {0}, (D) none of these, Correct Option : A, , SOLUTION, 4{x} = x + [x], , ⇒ 4(x − [x]) = x + [x], , ⇒ 3x = 5[x]
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3x, ⇒ [x] =, 5, , ,, , which is satisfied only by x, , 5, =, , , 0, 3, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-25 - BITSAT-MOCK TEST 11-MATHS, , If f (x), , π, = tan x, −, , π, < 0 <, , 2, , 2, , and g(x), , = √3 − x, , of the function g of is, , (A) (, , π, −, , π, ,, , 2, , (B) (, , π, −, , π, ,, , 3, , (C) (, , ), 2, , π, −, , ), 3, π, , ,, 3, , ), 3, , (D) none of these, Correct Option : B, , SOLUTION, Here, D, , g, , = [ − √3, √3], , and D, , π, f, , = ( −, , π, ,, , 2, , ), 2, , 2, , , then domain
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Also R, , f, , = R, , ⇒ Rf Rg = ψ, , and D of, g, , , therefore, gof is defined, , = {xeDf : f (x) ∈ Dg ), π, , = x ∈ ( −, , π, ,, , 2, , ), 2, π, , tan x ∈ ( − √3, √3) = ( −, , π, ,, , 3, , ), 3, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-26 - BITSAT-MOCK TEST 11-MATHS, , 3 tan, , −1, , x = tan, , −1, , 3x − x, (, 1 − 3x, , (A) |x|, , ≤ 1, , (B) |x|, , ≥ 1, , (C) |x|, , <, , 1, 3, , (D) none of these, Correct Option : C, , 3, , 2, , ), , holds only if
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SOLUTION, Since , R.H.S. lies in ( −, , π, , π, ,, , ), , 2, , 2, , , therefore given statements is valid, , only, if, π, −, , < 3 tan, , −1, , π, x <, , 2, , 2, π, , i.e., if −, , < tan, , −1, , π, x <, , 6, , 6, , i.e.,if tan( −, , π, , π, ) < x < tan(, , 6, , 1, , i.e.,if −, , ), 6, , 1, < x <, , √3, , √3, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-27 - BITSAT-MOCK TEST 11-MATHS, , Solution set of the equation, tan, , −1, , x − 1, (, , ) + tan, , −1, , x − 2, , (A) {, , 1, ,, , 2, , (B) {, , }, 2, , 1, −, , 1, ,, , √2, , }, √2, , π, ) =, , x + 2, , 1, −, , x + 1, (, , 4, , is
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(C) {0}, (D) none of these, Correct Option : B, , SOLUTION, Given equation is., tan, , −1, , x − 1, (, , ) + tan, , −1, , x + 1, (, , x − 2, , x + 2, , x − 1, ⇒, , π, = tan{, , x − 2, 1 − (, , − tan, , x+2, , ), , =, , −1, , 4, , x + 1, (, , )}, x + 2, , 4, , x+1, , π, ) =, , 1, =, , 1 + (, , ⇒ 2x, , 2, , x+1, x+2, , ), , 2x + 3, , = 1, 1, , x =, , ±, √2, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-28 - BITSAT-MOCK TEST 11-MATHS, , If y, , = tan √, , π, , 2, , − x, 9, , 2, , , then
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(A) − √3, , ≤ y ≤ √3, , (B) 0, , ≤ y ≤ √3, , (C) 0, , ≤ y ≤ 3, , (D) none of these, Correct Option : B, , SOLUTION, First, we note that y is definef only when, i.e., when |x|, i.e., when −, , π, , ], 9, π, , [0,, , ], 3, , 9, , ≥ 0, , 9, , 3, , π, , π, ≤ x, , 3, , 3, π, , π, , 2, , ,, 3, , − x, , and hence, , 2, , takes values in, , 9, , 2, , [0,, , − x, , π, , ≤ x ≤, 3, , 2, , ≤, , π, , For −, , π, , √, , π, , 2, , − x, , 2, , takes values in, , 9, , so, y takes values in [0,, , 1, ], √3, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-29 - BITSAT-MOCK TEST 11-MATHS
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Lim, , 2, , −2(, , 1, x−1, , ), , is equal to, , x→1, , (A) 0, (B) 1, (C) does not exist, (D) none of these, Correct Option : B, , SOLUTION, 1, , When x, , = 1(x − 1) → 0,, 1, , 2, −2, , →, , − ∞, , x − 1, , Hence, ⇒ 2, , ⇒, , x−1, , 1, x, , −1, , → 0, , ,, , → 2 = 1, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-30 - BITSAT-MOCK TEST 11-MATHS
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2√2 − (sin x + cos x), Lim, x→, , 1 − sin 2x, , π, 4, , (A), , 3, , is equal to, , 3√3, 2, , (B), , 3√ 2, 2, 3, , (C), , 2√ 2, , (D) none of these, Correct Option : B, , SOLUTION, 2√2 − (sin x + cos x), , 3, , Lt, x→, , 1 − sin 2x, , π, 4, , 2√2(1 − cos, =, , Lt, x→0, , 2 sin, , 2, , 2, , h), , h, , √2(1 − cos h), =, , Lt, h→0, , sin, , 2, , (1 + cos h + cos, , Lt, h→0, , h), , h, , √2, =, , 2, , [1 + cos h + cos, , 2, , h], , 1 + cos h, , ATTEMPT FREE TEST ON DOUBTNUT
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⇒ sin, , −1, , x, , n, , − sin, , −1, , y, , n, , = 2 cot, , −1, , a, , Differentiate with respect to x we get, 1, nx, , n−1, , √1 − x2n, , 1, −, , ny, √1 − y, , n−1, , 2n, , dy, = 0, dx, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-32 - BITSAT-MOCK TEST 11-MATHS, , If √1 − x, , (A), , 2, , + √1 − y, , = a(x − y), , √1 − x 2, √1 − y, , (B) √1, (C), , 2, , 2, , 2, , − x √1 − y, , √1 − y, 1 − x, , 2, , 2, , (D) none of these, Correct Option : C, , 2, , , then, , dy, dx, , is equal to
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SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-33 - BITSAT-MOCK TEST 11-MATHS, , f (x + h) − f (x − h), Lt, , h, , h→0, , (A) f ' (x), (B), , 1, f ' (x), 2, , (C) 2f ' (x), (D) none of these, Correct Option : C, , SOLUTION, f (x + h) − f (x − h), Lt, h→0, , h, , , if it exists, is equal to
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{f (x + h) − f (x)} − {f (x − h) − f (x)}, =, , Lt, , h, , h→0, , f (x + h) − f (x), =, , Lt, , f (x − h) − f (x), +, , h, , h→0, , Lt, h→0, , −h, , = f (x) + f ' (x) = 2f ' (x), , ATTEMPT FREE TEST ON DOUBTNUT, , Q-34 - BITSAT-MOCK TEST 11-MATHS, , 1, ∫, , dx =, 1 + sin x + cos x, , ∣, , x ∣, , (A) log∣1, , + tan, , (B) log|1, , + sin x + cos x|, , ∣, , 2, , (C) 2 log∣1, (D), , + tan, , ∣, , x ∣, 2, , 1, , ∣, , x, ∣, ∣, log 1 + tan, ∣, 2, 2 ∣, , Correct Option : A, , SOLUTION, Let tan., , x, = t, 2, , , then
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2t, dx =, 1 + t, , 2, , 2t, sin x =, 1 + t, , 2, , , and cos x, , 1 − t, =, 1 + t, , 2, , 2, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-35 - BITSAT-MOCK TEST 11-MATHS, , 1, ∫, , dx =, 5 − 4 cos x, , (A), (B), , 2, tan, , −1, , x, (tan, , 3, , ), 2, , 2, tan, , −1, , x, (3tan, , 3, , (C), , 2, tan, , −1, , x, (3tan, , 9, , (D) none of these, Correct Option : B, , SOLUTION, N/A, , ), 2, , ), 2
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ATTEMPT FREE TEST ON DOUBTNUT, , Q-36 - BITSAT-MOCK TEST 11-MATHS, , sin x + cos x, ∫, , dx, , si equal to, , √9 + 16 sin 2x, , (A), , 1, , 1, log ∣ sin x − cos x +, , 4, , (B), , 1, sin, , −1, , (sin x − cos x), [4, , ], , 4, , (C), , √9 + 16 sin 2x, 4, , 5, , 1, sin, , −1, , (sin x − cos x), [4, , ], , 5, , 5, , (D) none of these, Correct Option : B, , SOLUTION, Put sin x − cos x, , = t, , , then, , (sin x + cos x)dx = dt, , and (sin x − cos x), , 2, , ⇒ 1 − 2 sin 2x = t, , = t, 2, , 2, , = 1
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ATTEMPT FREE TEST ON DOUBTNUT, , Q-37 - BITSAT-MOCK TEST 11-MATHS, , 4, , If ∫, , 4, , f (x)dx = 4, , , and ∫, , −1, , (3 − f (x))dx = 7, 2, , 2, , ∫, , f (x)dx, , is, , −1, , (A) − 2, (B) 3, (C) 5, (D) none of these, Correct Option : C, , SOLUTION, 4, , Since ∫, , 3 − f (x)dx = 7, , therefore,, , 2, 4, , ∫, , 4, , 3dx − ∫, 2, , f (x)dx = 7, 2, , 4, , ⇒ ∫, , 4, , f (x)dx = ∫, 2, , 3dx − 7, 2, , , then the value of
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4, , ⇒ ∫, , f (x)dx = 6 − 7 =, , − 1, , 2, 4, , Hence ∫, , f (x)dx = 4, −1, , 2, , 4, , ⇒ ∫, , f (x)dx + ∫, −1, , f (x)dx = 4, 2, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-38 - BITSAT-MOCK TEST 11-MATHS, , n, , If (a − x), , = f (x), , , then ∫, , xf (x)dx, 0, , (A), , a, , a, ∫, 2, , f (x)dx, 0, n, , (B) a∫, , f (x)dx, 0, , (C), , a, , a, , 2, , ∫, 2, , f (x)dx, 0, , (D) none of these, Correct Option : A, , is equal to
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SOLUTION, a, , l = ∫, , xf (x)dx, , , then, , 0, a, , l = ∫, , (a − x)f (a − x)dx, 0, a, , ⇒ l = ∫, , a, , a(f a − x)dx − ∫, 0, , xf (a − x)dx, 0, , a, , ⇒ l = ∫, , a, , af (x)dx − ∫, 0, , xf (x)dx, 0, , a, , ⇒ 2l = a∫, , f xdx, 0, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-39 - BITSAT-MOCK TEST 11-MATHS, , Area of the parallelogram whose diagonals are ā and ¯b is, , (A), , → →, a , b, , (B), , →∣, ∣→, ∣ a × b ∣, ∣, ∣, , (C), , →, →, a + b, , (D), , →∣, 1 ∣→, ∣ a × b ∣, ∣, 2 ∣
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Correct Option : D, , SOLUTION, Required Area, , =, , →∣, 1 ∣→, ∣ a × b ∣, ∣, 2 ∣, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-40 - BITSAT-MOCK TEST 11-MATHS, , If, , →∣, → →, ∣→∣∣, a . b =, a ∣ b ∣, ∣, ∣, ∣, ∣, , , then, , (A) perpendicular, (B) like parallel, (C) unlike parallel, (D) confident, Correct Option : B, , →, a, , and, , →, b, , are
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SOLUTION, → →, → ∣→∣, ∣, ∣, a . b =, a ∣ b ∣, ∣, ∣∣, ∣, ⇒, , →∣, →∣, ∣→∣∣, ∣→∣∣, a ∣ b ∣cos θ =, a ∣ b ∣, ∣, ∣, ∣, ∣, ∣, ∣, ∣, ∣, , ⇒ cos θ = 1, , ⇒ cos θ = 1, , ⇒ θ = 0, , ⇒, , →, a, , and, , →, b, , are like parallel., , ATTEMPT FREE TEST ON DOUBTNUT, , Q-41 - BITSAT-MOCK TEST 11-MATHS, , If, , → →, →, ∣→∣, ∣, ∣, a . b ×, a, × ∣ b ∣, ∣, ∣, ∣, ∣, , (A) perpendicular, (B) like parallel, (C) unlike parallel, , , then, , →, a, , and, , →, b, , are
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SOLUTION, ∣1, , 1, , Goven vectors are coplaner if ∣∣ 1, , 1, , m, , −1, , m, , ∣1, , m + 1∣, ∣, ∣, , = 0, , ∣, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-46 - BITSAT-MOCK TEST 11-PHYSICS, , In a transformed, the number of turns of primary coil and secondary, coil are 5 and 4 respectively. If 240 V is applied on the primary coil,, then the ratio of current in primary and secondary coil is, , (A) 5 : 9, (B) 5 : 4, (C) 4 : 5, (D) 9 : 5, Correct Option : C
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SOLUTION, P = P1 + P2 = 2D + ( − 4D) = 2D − 4D =, , − 2D, , ., , ATTEMPT FREE TEST ON DOUBTNUT, , Q-48 - BITSAT-MOCK TEST 11-PHYSICS, , Two vessels of different materials are similar is size in every respect., The same quantity of ice filled in them gets melted in 20 minutes and, 40 minutes respectively. The ratio of thermal conductivities of the, metal is, , (A) 3 : 1, (B) 6 : 5, (C) 5 : 6, (D) 2 : 1, Correct Option : D
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SOLUTION, KΔθt, Q =, , 1, ⇒ K ∝, , d, ⇒, , K1, , t, , =, , K2, , t2, , 40, =, , t1, , 2, =, , 20, , 1, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-49 - BITSAT-MOCK TEST 11-PHYSICS, , The part of a ttransistor, which is heavily doped to produce a large, number of majority carriers, is, , (A) collector, (B) emitter, (C) base, (D) none of these, Correct Option : B
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SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-50 - BITSAT-MOCK TEST 11-PHYSICS, , We have a galvanometer of resistance 25Ω wire. It is shunted by a 2.5, wire. The part of total current that flows through the galvanometer is, given as, , (A), (B), , l9, , 33, =, , l, l9, , 11, 33, =, , l, , (C), (D), , l9, , 11, 1, =, , l, l9, l, , 11, 4, =, 11, , Correct Option : C
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SOLUTION, lg, l, , S, =, , 2.5, =, , S + G, , 2.5, =, , 2.5 + 25, , 2.5, =, , 2.5 + 25, , 1, =, , 27.5, , 11, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-51 - BITSAT-MOCK TEST 11-PHYSICS, , The kinetic energy of a particle executing S.H.M., is 16 when it is in, its mean position. If the amplitude of oscillations is 29cm, and the, mass of the particle is 5.12kg, then time period of the oscillation is, , (A) 20π sec, (B) 2π sec, (C) π / 5 sec, (D) 5π sec, Correct Option : C
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SOLUTION, When the particle is in its mean position, the kinetic energy will be, maximum., 1, K max =, , 2, , mω a, , 2, , 2, , 1, , 4π, , 16 =, , × 5.12 ×, 2, , ⇒ T, , 2, , T, 2.56 × 4π, , 2, , 2, , 2, , × (0.25), , 2, , × 0.25, , =, , × 0.25, 4, 1.6 × 2π × 0.25, , ⇒ T =, , π, =, , 4, , sec, 5, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-52 - BITSAT-MOCK TEST 11-PHYSICS, , A body of mass 100gm is rotating in a circular path of radius r with, constant velocity. The work done in one complete revolution is, , (A), , 100, J, r, , (B), , r, J, 100, , (C) 100rJ
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(D) Zero, Correct Option : D, , SOLUTION, Displacement for complete revolution, Since, workdone, ∴, , Work done, , = 0, , = force × displacement, , = 0, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-53 - BITSAT-MOCK TEST 11-PHYSICS, , If the surface tension of water is 0.06N m, a tube of a diameter 1mm is (θ, , (A) 3.12cm, (B) 2.44cm, (C) 1.68cm, , = 0), , −1, , , then the capillary rise in
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(D) 3.86cm, Correct Option : B, , SOLUTION, Surface tension of water, diameter of tube, Capillary rise, h, , = 1, , = 0.06N m, , −1, , ,, , mm, , 2p cos θ, =, rρg, , 2 × 0.06 × cos 0, =, 0.5 × 10, , −3, , × 10, , 3, , × 10, , = 0.244m = 2.44cm, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-54 - BITSAT-MOCK TEST 11-PHYSICS, , Swimming is possible by the, , (A) Third law of motion, (B) Second law of motion, (C) First law of motion
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(D) Newton\'s law of gravitation, Correct Option : A, , SOLUTION, When swimmer push the water backward, then according to third law,, water push the swimmer in forward direction., ATTEMPT FREE TEST ON DOUBTNUT, , Q-55 - BITSAT-MOCK TEST 11-PHYSICS, , In an A.C. circuit the potential difference across an inductance and, resistance joined in series are respectively 16V and 20V . The total, potential difference across the circuit is, , (A) 31.9V, (B) 25.6V, (C) 20.0V
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(D) 53.5V, Correct Option : B, , SOLUTION, E = √V, , 2, , + V, , R, , 2, L, , = √16, , 2, , + 20, , 2, , = √656 = 25.6V, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-56 - BITSAT-MOCK TEST 11-PHYSICS, , Force of attraction between the plates of a parallel plate capacitor is, , (A), (B), (C), (D), , q, , 3, , 2ε0 A, q, ε0 AK, q, , 2, , 2ε0 AK, q, , 2, , 2, , 2ε0 A K, , Correct Option : C
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SOLUTION, Energy stored between the plates of the capacitor, U, 1, =, , (, , Kε0 A, , )V, , 2, , x, , 2, , where x is the separation between the plates, Let plates are pulled apart through a small distance dx. Then,, 1, U' =, , CV, , 2, , 1 Kε0 AV, , =, , 2, , 2, , 2 (x + dx), , Change in potential energy,, ΔU ' = U ' − U =, , −, , 1 Kε0 Adx, x, , 2, , 2, , V, , 2, , Therefore, force between the plates of the capacitor,, dU, F =, , −, , 1, =, , dx, 1, , 2, , 1, , =, , C, 2 ε0 AK, , (, , Kε0 AV, , 2, , V, , x, 2, , 2, , 2, , q, , ), , 2, , =, 2ε0 AK, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-57 - BITSAT-MOCK TEST 11-PHYSICS, , The velocity of sound is greatest in
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(A) vacuum, (B) air, (C) water, (D) metal, Correct Option : D, , SOLUTION, l = F × t,, , = 50 × 10, , −5, , × 3 = 1.5 × 10, , −3, , N − s, , ., , ATTEMPT FREE TEST ON DOUBTNUT, , Q-58 - BITSAT-MOCK TEST 11-PHYSICS, , A force of 50 dynes is acted on a body of mass 5gm which is at rest, for an interval of 3 sec, then impulse is, , (A) 1.5, , × 10, , −3, , N − s
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(B) 0.98, , × 10, , (C) 0.16, , × 10, , (D) 2.5, , × 10, , −3, , −3, , −3, , N − s, , N − s, , N − s, , Correct Option : A, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-59 - BITSAT-MOCK TEST 11-PHYSICS, , Which of the following does not change when light goes from one, medium to another ?, , (A) Speed, (B) Wavelength, (C) Frequency
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(D) Intensity, Correct Option : C, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-60 - BITSAT-MOCK TEST 11-PHYSICS, , The Doppler\'s effect is applicable for, , (A) Space waves, (B) Sound waves, (C) Light waves, (D) Both (b) and (c ), Correct Option : D
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SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-61 - BITSAT-MOCK TEST 11-PHYSICS, , S.I unit of magnetic flux is, , (A) weber per m, (B) weber, (C) weber-m − 3, (D) weber per m4, Correct Option : B, , SOLUTION, N/A
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ATTEMPT FREE TEST ON DOUBTNUT, , Q-62 - BITSAT-MOCK TEST 11-PHYSICS, , If the displacement of a particle executing S.H.M. is given bt, y = 0.30 sin(220t + 0.64), , in meter, then the frequency and maximum, , velocity of the particle is, , (A) 58H z, 113m / s, (B) 45H z, 93m / s, (C) 35H z, 66m / s, (D) 36H z, 133m / s, Correct Option : C, , SOLUTION, Given, Y, , = 0.30 sin(220t + 0.64), , Comparing this equation with the standard equation of simple
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SOLUTION, Kinetic energy, , p, , 2, , =, , (2), , 2, , =, 2m, , = 1J, 2 × 2, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-64 - BITSAT-MOCK TEST 11-PHYSICS, , A ray of light is incident on the surface of separation of a medium, with the velocity of light at an angle 45 and is refracted in the medium, at an angle 30. What will be the velocity of light in the medium ?, , (A) 3.18, , × 10 m / s, , (B) 2.12, , × 10 m / s, , (C) 1.96, , × 10 m / s, , (D) 3.33, , × 10 m / s, , 8, , 8, , 8, , 8, , Correct Option : B
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SOLUTION, Here,, , sin 45, , sin i, =, sin r, , 3 × 10, ∴, , = √2 = 1.414, , =, sin 30, , 8, , = 1.414, vm, 8, , ⇒ vm = 2.12 × 10 m / s, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-65 - BITSAT-MOCK TEST 11-PHYSICS, , If two balls, each of mass of 0.06kg, moving in opposite directions, with speed of 4m / s, collide and rebound with the same speed, then, the impulse imparted to each ball due to other is, , (A) 0.81kgm / s, (B) 0.53kgm / s, (C) 0.48kgm / s, (D) 0.92kgm / s, Correct Option : C
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SOLUTION, Impulse imparted to each ball,, I= change in momentum, = mu − ( − mu), = 2mu = 2 × 0.06 × 4 = 0.48kgm / s, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-66 - BITSAT-MOCK TEST 11-PHYSICS, , If a body of mass 3kg is dropped from the top of a tower of height 25, meters, then its kinetic energy after 3 seconds will be, , (A) 746J, (B) 1048J, (C) 1296J, (D) 557J
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Correct Option : C, , SOLUTION, Velocity of body after 3 sec,, v = u + gt = 0 + 9.8 × 3 = 29.4m / s, 1, ∴ K. E., , =, , mv, 2, , 2, , 1, =, , × 3 × (29.4), , 2, , 2, , = 1296J, , ., , ATTEMPT FREE TEST ON DOUBTNUT, , Q-67 - BITSAT-MOCK TEST 11-PHYSICS, , When the amount of work done is 333 cal and change in intermal, energy is 167 cal, then the heat supplied is, , (A) 500 cal, (B) 300 cal, (C) 100 cal, (D) 700 cal
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Correct Option : A, , SOLUTION, According to first law of the thermodynamics,, ΔQ = ΔU + ΔW, = 333cal + 167cal = 500cal, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-68 - BITSAT-MOCK TEST 11-PHYSICS, , If an iron ball and a wooden ball of the same radius are released from, a height \'h\' in vaccuum, then time taken by both of them to reach, ground will be, , (A) Roughly equal, (B) Exactly equal, (C) Unequal, (D) Zero
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Correct Option : B, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-69 - BITSAT-MOCK TEST 11-PHYSICS, , The E.M.F. of the Daniel cell is, , (A) 2.56V, (B) 1.12V, (C) 0.56V, (D) 3.12V, Correct Option : B
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SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-70 - BITSAT-MOCK TEST 11-PHYSICS, , The speed of a wave in a medium is 760m / s. IF 3600 waves are, passing through a point in the medium in 2 minutes, then its, wavelength is, , (A) 41.5m, (B) 25.3m, (C) 13.8m, (D) 57.2m, Correct Option : D
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SOLUTION, Frequency, , =, , Number of waves passing through a point per second., , 3600waves, ∴ V, , =, , = 30 sec, , −1, , 2min, v, ∴ λ =, , 760, =, , υ, , = 25.33m, 30, , ., , ATTEMPT FREE TEST ON DOUBTNUT, , Q-71 - BITSAT-MOCK TEST 11-PHYSICS, , If luminous-efficiency of a lamp is 2 lumen 1 watt and its luminousintensity is 42 candela then, power of the lamp is, , (A) 138W, (B) 76W, (C) 62W, (D) 264W, Correct Option : D
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SOLUTION, Luminous flux, φ, ∴, , Power, , = 4πl = 4 × 3.14 × 42, , lumen, , 4 × 3.14 × 42, =, , = 263.76 = 264W, 2, , ., , ATTEMPT FREE TEST ON DOUBTNUT, , Q-72 - BITSAT-MOCK TEST 11-PHYSICS, , The specific heat of a gas in an isothermal process is, , (A) negative, (B) Zero, (C) Infinite, (D) Remains constant, Correct Option : C
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SOLUTION, In isothermal process,, T =, , constant, Δθ, , ∴ ΔT = 0C =, , = ∞, mΔT, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-73 - BITSAT-MOCK TEST 11-PHYSICS, , A big drop is formed by 1000 small droplets of water, then the radius, of small drop is, , (A), , R, 6, , (B), (C), , R, 5, R, 2, , (D), , R, 10, , Correct Option : D
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SOLUTION, The volume of big drop should be equal to the volume of 1000 small, drops., 4, ∴ 1000 ×, , πr, , 3, , 4, =, , 3, , πR, , 3, , 3, , R, ⇒ r =, 10, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-74 - BITSAT-MOCK TEST 11-PHYSICS, , The kinetic energy of one g-molecule of a gas at normal temperature, and pressure is (R, , = 8.31J / mole − K), , (A) 2.7, , × 10 J, , (B) 1.3, , × 10 J, , 2, , 2, , (C) 0.56, , × 10 J, , (D) 3.74, , × 10 J, , 4, , 3
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Correct Option : D, , SOLUTION, K.E. per gm molecules, 3, =, , 3, RT =, , 2, , × 8.31(300), 2, 3, , = 3739.5J = 3.74 × 10 J, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-75 - BITSAT-MOCK TEST 11-PHYSICS, , The temperature-coefficient of resistacne of conductors is, , (A) Neutral, (B) Negative, (C) Positive, (D) First (c ) then (a), Correct Option : C
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SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-76 - BITSAT-MOCK TEST 11-PHYSICS, , A black body radiates heat energy at the rate of, 5, , 2 × 10 Joule / sec / m, , 2, , at a temperature of 127C . The temeprature of, , the black body, at which the rate of heat radiation is, 5, , 32 × 10 J / sec / m, , 2, , is, , (A) 873 ∘ C, (B) 527 ∘ C, (C) 273 ∘ C, (D) 927 ∘ C, Correct Option : B
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Correct Option : D, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-78 - BITSAT-MOCK TEST 11-PHYSICS, , When an electron is emitted from a nucleus, then effect on its neutronproton\'\'-ratio is, , (A) Remains same, (B) Decreased, (C) Increased, (D) First (a) then (b), Correct Option : B
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SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-79 - BITSAT-MOCK TEST 11-PHYSICS, , The half-life of a radioactive is 3.6 days. How much of 20 miligram of, that radioactive will remain after 40 days ?, , (A) 6.20, , × 10, , (B) 4.31, , × 10, , (C) 2.68, , × 10 mg, , (D) 9.76, , × 10, , −3, , −2, , mg, , mg, , 3, , −3, , mg, , Correct Option : D
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SOLUTION, 40, , Number of half lives, , =, , = 11.1, 3.6, , Aroms left after 11 half lives., n, , 1, N = N0 (, , 20, , ), 2, , 2, , 11, , = 9.76 × 10, , −3, , mg, , ., , ATTEMPT FREE TEST ON DOUBTNUT, , Q-80 - BITSAT-MOCK TEST 11-PHYSICS, , When a slow neutron goes sufficiently close to a U, process takes place is, , (A) Fusion of U 235, (B) Fusions of neutron, (C) Fission of U 235, (D) First (a), then (b), Correct Option : C, , 235, , nucleus then the
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SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-81 - BITSAT-MOCK TEST 11-PHYSICS, , The first operation involved in a carnot cycle is, , (A) Isothermal compression, (B) Adiabatic expansion, (C) Isothermal expansion, (D) Adiabatic compression, Correct Option : C, , SOLUTION, N/A
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ATTEMPT FREE TEST ON DOUBTNUT, , Q-82 - BITSAT-MOCK TEST 11-PHYSICS, , A parallel plate capacitor is charged to 60C . Due to a radioactive, source, the plate loses charge at the rate of 1.8 × 10, magnitude of displacement current is, , (A) 4.1, , × 10, , (B) 3.6, , × 10 C / s, , (C) 1.8, , × 10 C / s, , (D) 5.7, , × 10, , 11, , C /s, , 8, , 8, , 12, , C /s, , Correct Option : C, , SOLUTION, We know, q, ∴, , q, = it ⇒ i =, , Displacement current, , t, dq, =, , 8, , = 1.8 × 10 A, dt, , 8, , C /s, , . The
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ATTEMPT FREE TEST ON DOUBTNUT, , Q-83 - BITSAT-MOCK TEST 11-PHYSICS, , A body is executing simple harmonic motion with an angular, frequency 2rad / sec. The velocity of the body at 20mm displacement,, when the amplitude of motion is 60mm, is, , (A) 118mm / s, (B) 113mm / s, (C) 90mm / s, (D) 131mm / s, Correct Option : B, , SOLUTION, Velocity of body in SHM, v = ω√a, , 2, , − x, , 2
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= 2√(60 × 10, = 2 × 10, , −3, , −3, , 2, , ), , − (20 × 10, , −3, , 2, , ), , √3200 = 113mm / s, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-84 - BITSAT-MOCK TEST 11-PHYSICS, , The mass of moon is 7.34 × 10, , 22, , kg, , . If the acceleration due to the, , gravity on the moon is 1.4m / s , the radius of the moon is, 2, , (G = 6.667 × 10, , 11, , N − m, , (A) 1.92, , × 10 m, , (B) 1.86, , × 106 m, , (C) 0.56, , × 10 m, , (D) 1.01, , × 10 m, , 2, , 2, , / kg ), , 6, , 6, , 4, , 4, , Correct Option : B, , SOLUTION, GM, g =, R, , 2, , 6.667 × 10, , − 11, , =, R, , × 7.34 × 10, 2, , 22
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∴ R = √, , 6.67 × 10, , − 11, , × 7.34 × 10, , 22, 6, , = 1.86 × 10 m, 1.4, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-85 - BITSAT-MOCK TEST 11-PHYSICS, , A tunning fork makes 250 vibrations per seconds in air. When the, velocity of sound is 330m / s, then wave length of the tone emitted is, , (A) 1.11m, (B) 0.98m, (C) 0.56m, (D) 1.29m, Correct Option : A, , SOLUTION, 330, , v, λ =, , =, υ, , = 1.29m, 250
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ATTEMPT FREE TEST ON DOUBTNUT, , Q-86 - BITSAT-MOCK TEST 11-CHEMISTRY, , Heat exchanged in a chemical reaction at the constant temperature and, pressure is known as, , (A) internal energy, (B) entropy, (C) enthalpy, (D) free energy, Correct Option : C, , SOLUTION, The heat exchanged in a reaction at constant temeprature and pressure, is known as enthalpy., ATTEMPT FREE TEST ON DOUBTNUT
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Q-87 - BITSAT-MOCK TEST 11-CHEMISTRY, , The correct order of dipole moments of H F , H, , (A) H F, , < H2 S < H2 O, , (B) H F, , < H2 S > H2 O, , (C) H F, , > H2 S > H2 S, , (D) H F, , > H2 O < H2 S, , 2S, , and H, , 2O, , is., , Correct Option : A, , SOLUTION, The correct order of dipole moment of H F , H, , 2S, , and H, , H F < H2 S < H2 O, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-88 - BITSAT-MOCK TEST 11-CHEMISTRY, , 2O, , is
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A mole of any substance is related to, , (A) number of particles, (B) volume of gaseous substances, (C) mass of a substance, (D) all of above, Correct Option : D, , SOLUTION, A mole of any substance is related to number of particles, volume of, gaseous substanceand mass of a substance., ATTEMPT FREE TEST ON DOUBTNUT, , Q-90 - BITSAT-MOCK TEST 11-CHEMISTRY, , The alkane is not obtained from
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(A) accept proton, (B) donate electron, (C) lose a pair of electron, (D) gain a pair of electron, Correct Option : A, , SOLUTION, According to Bronsted theory an acid is a substance that donates, proton and a base is a substance that accept protons. Hence, base is, proton acceptor., ATTEMPT FREE TEST ON DOUBTNUT, , Q-92 - BITSAT-MOCK TEST 11-CHEMISTRY, , A mixture of sodium benzoate and sodalime on heating produce, , (A) CH4
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(B) 6.6, , × 10, , (C) 6.6, , × 10, , (D) 6.6, , × 10, , − 35, , − 36, , − 37, , m, , m, , m, , Correct Option : A, , SOLUTION, Wavelength, 6.6 × 10, =, 10, , −3, , h, =, mv, − 34, , = 6.6 × 10, , − 33, , m, , × 100, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-94 - BITSAT-MOCK TEST 11-CHEMISTRY, , Baeyer\'s reagent is used, , (A) in Benidict solution, (B) for oxidation, (C) for detection of unsaturation
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(D) for reduction, Correct Option : C, , SOLUTION, The Baeyer\'s reagent is alkaline KM nO solutions which is used for, 4, , detection of unsaturation., , ATTEMPT FREE TEST ON DOUBTNUT, , Q-95 - BITSAT-MOCK TEST 11-CHEMISTRY, , The number of electrons in [., , (A) 18, (B) 19, (C) 20, , 19, , K, , 40, , −1, , ]
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(D) 21, Correct Option : C, , SOLUTION, [.19 K, , 40, , −1, , ], , has 20 electrons because the atomic number of K is 19, , and it has 1 more electron., ∴, , Number of electrons, , = 19 + 1 = 20, , ., , ATTEMPT FREE TEST ON DOUBTNUT, , Q-96 - BITSAT-MOCK TEST 11-CHEMISTRY, , The molecular weight of a compound is 180. If its empirical formula is, CH2 O, , then the molecular formula of compound is, , (A) C2 H4 O2, (B) C3 H6 O3, (C) C6 H12 O6
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(D) C12 H24 O12, Correct Option : C, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-97 - BITSAT-MOCK TEST 11-CHEMISTRY, , In a reaction A + B, , ⇔ C + b, , , if the concentration of A and B is, , doubled, then the equilibrium constant is, , (A) remains same, (B) halved, (C) doubled, (D) increased four times
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Correct Option : A, , SOLUTION, The empirical formula of coumpound is CH, , 2O, , ., , Hence empirical formula mass, = 12 + 2 + 16 = 30, , Molecular weight, We know, n, , ., , = 180, , molecular weight, =, empirical weight, , 180, =, , = 6, 30, , Molecular formula, = (CH2 O), , 6, , = (empirical formula), , n, , = C6 H12 O6, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-98 - BITSAT-MOCK TEST 11-CHEMISTRY, , The weight of lime obtained by heating 200kg of 95 % pure lime, stone is
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Q-99 - BITSAT-MOCK TEST 11-CHEMISTRY, , The Oxidation state of chromium in potassium dichromate is, , (A) + 4, (B) − 4, (C) + 6, (D) − 6, Correct Option : C, , SOLUTION, Let the oxidation state of Cr in K, , 2 Cr2 O7, , ∴ (2 × 1) + (2 × x) + 7( − 2) = 0, , or 2 + 2x + ( − 14), or 2x, or x, , = 0, , = 14 − 2 = 12, , =, , + 6, , = x
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ATTEMPT FREE TEST ON DOUBTNUT, , Q-100 - BITSAT-MOCK TEST 11-CHEMISTRY, , The percentage of carbon in anthracite is, , (A) 60 %, (B) 70 %, (C) 80 %, (D) 90 %, Correct Option : D, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-101 - BITSAT-MOCK TEST 11-CHEMISTRY
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The reactivity of metals with water is in the order of, , (A) N a, , > M g > Zn > F e > Cu, , (B) Cu, , > F e > Zn > M g > N a, , (C) M g, , > Zn > N a > F e > Cu, , (D) M g, , > Zn > N a > F e > Cu, , Correct Option : A, , SOLUTION, Sodium reacts rapidly with water but copper is least reactive with, water. Therefore the reactivity of metals with water is, N a > M g > Zn > F e > Cu, , Most reactive, , −, −, −, −, −, −, −, −, −, −, −, →, , least reactive., , decreasing reactivity, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-102 - BITSAT-MOCK TEST 11-CHEMISTRY
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Magnalium cantains, , (A) Al, , + Mg, , (B) M g, , + Cu, , (C) M g, , + Fe, , (D) M g, , + Ag, , Correct Option : A, , SOLUTION, Magnalium is an alloy containing 95% aluminium and 5% magnesium, it is used to make light instruments., ATTEMPT FREE TEST ON DOUBTNUT, , Q-103 - BITSAT-MOCK TEST 11-CHEMISTRY, , Graphite is a good condutor of heat and electricity because it contains
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(A) layers of carbon atoms, (B) sheet like structure, (C) sheet like structure, (D) no free electrons, Correct Option : B, , SOLUTION, Graphite is good conductor of heat and electricity due to the presence, of free electrons in graphite crystals. The fourth valence electron of, each carbon atom is free to move., ATTEMPT FREE TEST ON DOUBTNUT, , Q-104 - BITSAT-MOCK TEST 11-CHEMISTRY, , The boiling point fo three saturated hydro carbon A, B and C− 102C, j − 43.4C, , and − 0.6C respectively. The hydrocarbon having
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the maximum number of carbon atoms in its molucule is, , (A) A, (B) B, (C) C, (D) None of these, Correct Option : C, , SOLUTION, The hydrocarbons having the highest boiling point will have the, maximum number of carbon atoms in its molecules here hydrocarbon, C has the highest boiling point of − 0.6C therefore it have the, maximum number of carbon atoms in its molecule., ATTEMPT FREE TEST ON DOUBTNUT, , Q-105 - BITSAT-MOCK TEST 11-CHEMISTRY
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1 × 10, ∴, , 1 × 5, =, , 300, , or T, , T2, 1 × 5 × 300, , 2, , =, , = 150K, 10, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-106 - BITSAT-MOCK TEST 11-CHEMISTRY, , The coordinate bond is found in, , (A) SO3, (B) H2 SO4, (C) O3, (D) all the above, Correct Option : D, , SOLUTION, The bond formed by one sided sharing of electrons are known are
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known as cordinat bond. All the above SO , H, 3, , 2 SO4, , and O have, 3, , coordinate bonds., ATTEMPT FREE TEST ON DOUBTNUT, , Q-107 - BITSAT-MOCK TEST 11-CHEMISTRY, , Which of the following isomerism is exhibited by CH, and C, , 2 H5 OC2 H5, , 3, , − O − C3 H7, , ?, , (A) optical isomersm, (B) chain isomerism, (C) metamerism, (D) position isomersm, Correct Option : C, , SOLUTION, The isomerism exhibited is metamerism this is exhibited by the
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members of same homologous series due to different alkyl groups,, attached to functional group., ATTEMPT FREE TEST ON DOUBTNUT, , Q-108 - BITSAT-MOCK TEST 11-CHEMISTRY, , Chlorine oxidises ethyl alcohol to, , (A) CH3 CH O, (B) CCl3 CH O, (C) H CH O, (D) CH3 COOH, Correct Option : B, , SOLUTION, The oxidation takes place as below:
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Cl2, , 3Cl2, , CH3 CH2 Oh −, −, −, −, → CH3 CH O −, −, −, −, → CCl3 CH O, − 2H Cl, , ., , − 3H Cl, , Thus the oxidation product is CCl, , 3 CH O, , ., , ATTEMPT FREE TEST ON DOUBTNUT, , Q-109 - BITSAT-MOCK TEST 11-CHEMISTRY, , Tyndall effect can be observed in, , (A) colloidal solution, (B) solvent, (C) solute, (D) precipitate., Correct Option : A, , SOLUTION, N/A
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Q-111 - BITSAT-MOCK TEST 11-CHEMISTRY, , Mg does not decompose, , (A) cold water, (B) hot water, (C) steam, (D) boiled water, Correct Option : A, , SOLUTION, Mg does not decomposed cold water due to the formation of, M g(OH ), , 2, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-112 - BITSAT-MOCK TEST 11-CHEMISTRY
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(A) methyl orange, (B) phenolphthalein, (C) dil. H2 SO4, (D) none of the above, Correct Option : A, , SOLUTION, Methyl orange is the most suitable indicator used for titrating, N a2 CO3, , solution with HCl. It produces pink colour in strong acidic, , solution., ∴, , equivalent weight, , Molecular weight, =, 2, , 200, =, , = 100, 2, , Here volume of 100 ml =0.1 litre, we know strength, =normality, , ×, , volume, , ×, , = 0.1 × 0.1 × 100 = 1, , equivalent weight, , gm
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ATTEMPT FREE TEST ON DOUBTNUT, , Q-114 - BITSAT-MOCK TEST 11-CHEMISTRY, , The amount of dibasic acid present in 100 ml of the aq. Solution to, give strength is [mol wt=200, normality =0.1], , (A) 0.5 gm, (B) 1 gm, (C) 1.5 gm, (D) 2 gm, Correct Option : B, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT
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Q-115 - BITSAT-MOCK TEST 11-CHEMISTRY, , Calcium formate on dry heating produce, , (A) H CH O, (B) CH3 CH O, (C) CH3 COCH3, (D) CH3 COOH, Correct Option : A, , SOLUTION, Calcium fomated on heating produce, Heat, , (H COO) Ca −, −, → CaCO3 +, 2, , H CH O, formaldehyde, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-116 - BITSAT-MOCK TEST 11-CHEMISTRY
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(A) linear, (B) tetrahedral, (C) planar, (D) pyramidal, Correct Option : A, , SOLUTION, CO2, , has linear structure its dipole moment is zero. In CO the, 2, , hybridisation of carbon is sp. O, , = C = O, , ATTEMPT FREE TEST ON DOUBTNUT, , Q-119 - BITSAT-MOCK TEST 11-CHEMISTRY, , The gas evolved by heating potassium ferrocyanide crystals with conc., H2 SO4, , is, , (A) CO
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(B) negative, (C) positive, (D) depend on molecular weight., Correct Option : A, , SOLUTION, For an ideal gas joule-Thomson coefficient is zero because van der, waal\'s forces of attraction are negligible and there is no expenditure of, energ in overcoming these forces of attraction., ATTEMPT FREE TEST ON DOUBTNUT, , Q-121 - BITSAT-MOCK TEST 11-CHEMISTRY, , By which reaction a ketone can be converted into a hydrocarbon?, , (A) aldol condensation, (B) reimer-tiemann reaction
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(C) cannizzaro reaction, (D) wolf-kishner reaction, Correct Option : D, , SOLUTION, , A ketone can be converted into hydrocarbon by woff kishner reaction., ATTEMPT FREE TEST ON DOUBTNUT, , Q-122 - BITSAT-MOCK TEST 11-CHEMISTRY, , The photo-chemical laws are applicable to
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(A) primary reaction, (B) secondary reaction, (C) both of these, (D) none of these, Correct Option : A, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-123 - BITSAT-MOCK TEST 11-CHEMISTRY, , A compound having molecular mass =78 contains C, H = 7.69 %, , its molecular formula is, , (A) C5 H12, , = 92.31 %, , and
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Q-124 - BITSAT-MOCK TEST 11-CHEMISTRY, , In lake test of Al, , 3+, , ion there is formation of coloured floating lake. It, , is due to, , (A) adsorption of litmus by H2 O, (B) adsorption of litmus by Al(OH )3, −, , (C) Adsorption of litmus by Al(OH )4, (D) none of these, Correct Option : B, , SOLUTION, In lake test of Al, , 3+, , ion there is formation of coloured floating lake. It, , is due to the fact that Al(OH ) a solid surface absorbed litmus colour, 3, , hecen appears as coloured floating lake., ATTEMPT FREE TEST ON DOUBTNUT
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Q-125 - BITSAT-MOCK TEST 11-CHEMISTRY, , Half life of radius is 1580 years. Its average life will be, , (A) 1.832, (B) 2.5, , × 10, , × 10, , 3, , 3, , years, , yrs, , (C) 2.275, , × 10, , (D) 8.825, , × 10, , 3, , 2, , yrs, yrs, , Correct Option : C, , SOLUTION, Average life of radium, , = 1.44 ×, , half the, , = 1.44 × 1580, , 2.275 × 10, , 3, , years., , ATTEMPT FREE TEST ON DOUBTNUT
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Q-126 - BITSAT-MOCK TEST 11-ENGLISH & LR, , If ZUBIN is coded at ATCHO, then MEHTA will coded as, , (A) NDISB, (B) NDHSI, (C) NDGSB, (D) NDIUB, Correct Option : A, , SOLUTION, Letters at the odd places are coded one letter ahead. And letter at the, even places are coded one letter behind in the alphabetical order., ATTEMPT FREE TEST ON DOUBTNUT, , Q-127 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Engineer:Machine::Doctor, , (A) disease, (B) medicine, (C) hospital, (D) none of these, Correct Option : A, , SOLUTION, As the engineer is directly related to machines similarly doctor is, related to diseases., ATTEMPT FREE TEST ON DOUBTNUT, , Q-130 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Q\'s mother is the sister of R and daughter of S, N is the daugter of R, and sister of M. How M is related to S?, , (A) son, (B) brother, (C) daughter\'s son, (D) data inadequate, Correct Option : D, , SOLUTION, From the above question it is clear that S is the mother of R (not, confirmed R is either male or female). On thhe other hand N is the, daughter of R and sister of M (whose sex is also not known.) if R is, male and M will be grand daughter/son of S in case of R is female, than M will be maternal daughter/son of S. Hence as per the option, data is inadiquate.
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ATTEMPT FREE TEST ON DOUBTNUT, , Q-131 - BITSAT-MOCK TEST 11-ENGLISH & LR, , Introducing a man, a woman said, "he is the only son of my mother\', mother". How is the woman related to man?, , (A) mother, (B) cousin, (C) niece, (D) none of these, Correct Option : C, , SOLUTION, Son of woman\'s mother\'s mother means the brother of mother and, brother of mother is maternal uncle. Hence woman is related as niece, to the man.
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ATTEMPT FREE TEST ON DOUBTNUT, , Q-132 - BITSAT-MOCK TEST 11-ENGLISH & LR, , Direction- Find the missing number in the series 1,2,3,5,7, , (A) 9, (B) 8, (C) 10, (D) 13, Correct Option : C, , SOLUTION, Series moves with a difference of 1,1,2,2,3,3 and so on hence the, missing number is 10., ATTEMPT FREE TEST ON DOUBTNUT
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Q-133 - BITSAT-MOCK TEST 11-ENGLISH & LR, , Direction- Find the missing number in the series, 4,7,11,18,29,47..123,199, , (A) 76, (B) 70, (C) 84, (D) 102, Correct Option : A, , SOLUTION, Third number if the sum of first and second fourth number is the sum, of second and third fifth number is the sum of third ad fourth and so, on. Hence missing number will be 29 + 47, , = 76, , ATTEMPT FREE TEST ON DOUBTNUT
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Q-134 - BITSAT-MOCK TEST 11-ENGLISH & LR, , Direction- Find out the wrong number in each case., 49,56,64,71,81,90,100,110, , (A) 56, (B) 64, (C) 71, (D) 81, Correct Option : C, , SOLUTION
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2, , 2, , 2, , (7) (8) (9) (10), , 2, , Term at odd places are 7, , 2, , 2, , 2, , , 8 , 9 , 10, , 2, , and terms at even places are 56,, , 72, 90, 110, i.e., with difference of 16, 18 and 20 ., ATTEMPT FREE TEST ON DOUBTNUT, , Q-135 - BITSAT-MOCK TEST 11-ENGLISH & LR, , Direction- Find out the wrong number in each case., 5,8,10,12,15,18,20,23, , (A) 8, (B) 12, (C) 15, (D) 18, Correct Option : B
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SOLUTION, , therefore number 12 is wrong., ATTEMPT FREE TEST ON DOUBTNUT, , Q-136 - BITSAT-MOCK TEST 11-ENGLISH & LR, , Direction- read the passage and answer the following questions., If I ahs been asked in my early youth wheter I preferred to have, dealings only with men or only with books, my answer would, certainly have been in favour of boods. In later years. This has become, less and less the case. not that i have had so much bitter experiences, with men that with books, on the contrary, purely delightful books
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even now come my way more often that purely delightful men. but the, many bad experiences with men have nourished the meadow of my, life as the noblest block could not do., Q. In his early yout the author, , (A) liked to have more dealings with men than with books, (B) likes to have more dealings with books than with men, (C) liked to have dealings more with men than with books, (D) preferred to have dealings only books., Correct Option : B, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-137 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Direction- read the passage and answer the following questions., If I ahs been asked in my early youth wheter I preferred to have, dealings only with men or only with books, my answer would, certainly have been in favour of boods. In later years. This has become, less and less the case. not that i have had so much bitter experiences, with men that with books, on the contrary, purely delightful books, even now come my way more often that purely delightful men. but the, many bad experiences with men have nourished the meadow of my, life as the noblest block could not do., Q. Which one of the following statements best reflects the main, argument of the passage?, , (A) it is the experience with other human beings that, nourishes one\' life and not necessarly books, (B) books are always better than men, (C) neither man nor books give any worthwhile
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(D) there are more purely delightful men than purely, delightful books., Correct Option : A, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-138 - BITSAT-MOCK TEST 11-ENGLISH & LR, , Direction- read the passage and answer the following questions., If I ahs been asked in my early youth wheter I preferred to have, dealings only with men or only with books, my answer would, certainly have been in favour of boods. In later years. This has become, less and less the case. not that i have had so much bitter experiences, with men that with books, on the contrary, purely delightful books, even now come my way more often that purely delightful men. but the
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many bad experiences with men have nourished the meadow of my, life as the noblest block could not do., Q. The author says that in later years his love of books dimished, because., , (A) he had given up the habit of reading books, (B) he did not get many delightful books to read, (C) even the bad experiences he has with men were more, valuable than what the noblest book gave, (D) he had better experience with men than with books., Correct Option : C, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-139 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Choose the incorrect work in the given sentence., Q. Our college has good furniture\'s, , (A) good, (B) our, (C) furnitures, (D) has, Correct Option : C, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-140 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Choose the incorrect work in the given sentence., Q. Can your child recongnise english alphabets., , (A) your, (B) can, (C) alphabets, (D) recognise., Correct Option : C, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-141 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Choose the incorrect work in the given sentence., Q. The magistrate issued orders for the releases of, , (A) orders, (B) the, (C) release, (D) issued., Correct Option : A, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-142 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Choose antonym for the given words from each set., Q. AMNESTY, , (A) remission, (B) pardon, (C) punishment, (D) mercy, Correct Option : C, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-143 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Choose antonym for the given words from each set., Q. SEQUENCE, , (A) progression, (B) succession, (C) break, (D) chain, Correct Option : C, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-144 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Choose antonym for the given words from each set., Q. AGNOSTIC, , (A) believer, (B) atheist, (C) enmity, (D) unbeliever, Correct Option : A, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-145 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Choose synonym from the given words from each set., Q. GROUSE, , (A) brave, (B) complain, (C) lazy, (D) tired, Correct Option : A, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-146 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Choose synonym from the given words from each set., Q. ABSOLUTION, , (A) sensual, (B) convicton, (C) amnesty, (D) charge., Correct Option : C, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-147 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Pick up from answers-choices which will complete the sentence, correctly., Q. So quickly____he reacted on time, , (A) did he run that, (B) he ran time., (C) would be run that, (D) he ran as., Correct Option : A, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-148 - BITSAT-MOCK TEST 11-ENGLISH & LR
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Pick up from answers-choices which will complete the sentence, correctly., Q. These days, my house is unser, , (A) the repairs, (B) repairs, (C) the repair, (D) repair., Correct Option : B, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-149 - BITSAT-MOCK TEST 11-ENGLISH & LR
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select the pair of words. Which are related in the same way as the, capitalised words ar related to each other, Q. WIND: AIR::?, , (A) request:command, (B) ocean:sea, (C) government,legisiator, (D) master,sevent., Correct Option : B, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT, , Q-150 - BITSAT-MOCK TEST 11-ENGLISH & LR
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select the pair of words. Which are related in the same way as the, capitalised words ar related to each other, Q.MEANS: METHOD?, , (A) elegance:style, (B) air:kite, (C) teacher:pupil, (D) smoke:cigarette, Correct Option : A, , SOLUTION, N/A, ATTEMPT FREE TEST ON DOUBTNUT