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Modish Public School (Sondh), Class: XI, Name………, Time:1hour10mint., , Subject- Maths, Roll no. …………., , P.A-2(2021-22), Date:20/01/2022, M .M- 40, , General Instructions:1. All questions are compulsory., , Section – A., Multiple choice questions:-, , (1×20=20), , 1. Find the value of 2 cos 45° sin 15°, √3+1, 2, 4, , (A), , 1, , (B) 2, , √3−1, 2, , (C), , (D), , √3, 2, , 2. If cot x= 3 and lies in third quadrant then find value of sec x., 1, , 7, , (A) 4, , (B) 4, , 2, , (C), , (D), , 4, , −5, 4, , 3. If tan A= y2, tan B= y3 then tan (2A+B) is equal to, (A) 1, , (B) 2, , (C) 3, , (D), , 4, , 4. Express 50°3730 in radian, 1π, , 5π, , (A) 32, , (B) 32, , 9π, , (C), , 32, , π, , (D), , 32, , 5. The probability of obtaining sum 8 in a single throw of two dice is, 1, , (A) 36, , (B), , 5, 36, , 4, , 6, , (C) 36, , (D) 36, , 6. In a non leap year the probability of getting 53 Sunday or 53 Tuesday’s or, 53 Thursday’s is., 1, , (A) 7, , (B), , 4, 7, , 2, , (C) 7, , (D), , 3, 7, 1, , 13, , 7. If A and B are Mutually exclusive events and P(B)= 3, P(AUB)=21 then P(A), is equal to, (A), , 1, 7, , (B), , 4, 7, , (C), , 2, 7, , (D), , 5, 7

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8. If P(A) = 0.59, P(B)=0.30, P(A∩B)= 0.21 then P (A’∩B’) is, (A) 0.11, , (B) 0.38, , (C), , 0.32, , (D) None of these, , 9. Find the distance b/w points P(1,-3,4) and Q(-4,1,2), (A) √5, , (B) 5√3, , (C), , (D) 2 √2, , 3√5, , 10. Find the points on Y –axis which is at a distance of √10 units from the, point (1,2,3), (A) (0,4,0), , (B) (0,3,0) (C) (0,2,0) (D) (0,-1,0), , 11. The points (1,2,3) (-1,-1,-1) and (3,5,7) are the vertices of, (A) An equilateral triangle, (B) An Isosceles triangle, (C) A right triangle, (D) Name of these, 12. Mid- Point of the line joining the points (-1,2,3) and (2,-1,3) is, 1 1, , (A) (1,1,6), , 1 1, , (B) ( 2, 2,3) (C) (3,-3,0) (D) ( 3, 3 , 2), , 13. The 4th term in the expansion of (x-2y)12 is, (A) 1760 x3y9 (B) -1760 x9y3, x, , (C) 1760 x9y3 (D) None of these, 3, , 14. The co-efficient of x4 in ( 2 – X²)10 is equal to, (A), , 405, 256, , (B), , 504, 259, , (C), , 450, 263, , (D), , 420, 241, , 15. If nC12= nC8 then n is equal to, (A) 20 (B) 12 (C) 6 (D) 30, 16.If nC9 =nC8 find nC17 is, (A) 1, 1, , (B) 2, 1, , (C) 0 (D) 3, , x, , 17. If 8! + 9! + 10! Find x, (A) 90 (B) 100 (C) 80 (D) 95, 18. Find the value of ∩ such that nPy =, n-1py, (A) 11 (B) 10 (C) 13 (D) 12, , 5, 3, , , n>4

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19. The value of 1+ tan215° is, 1- tan215°, (A) 1, , 1, , (B), , √3, , (C), , 2, √3, , (D), , 2, , 20. one of the principal solution of √3 sec(x) = -2 is equal to, π, , (A) 2 3 (B), , π, 6, , (C), , 5π, 6, , π, , (D) 3, , SECTION – B, , (1×6=6), , 1. If tan θ=3, and θ lies in III quadrant, then find the value of Sin θ, 2. Convert 240 into radian’s, 3. Find r if 5 4pr = 65pr -1, 4. Find the number of permutations of the letters of the word ALLAHABAD, OR, Total number of four digit odd number that can be formed using 0,1,2,3,4,5,7, -----------3, , 1, , 5, , 5, , 5. Given P(A) = and P(B)= , find P( A or B) is A and B are mutually exclusive, event’s., 6. A coin is tossed twice what is the probability that at least one tail occurs?, OR, Evaluate sin 75°, SECTION –C, (2×3=6), 1. Evaluate (102)5, 2. Prove that Cos22x- Cos26x= Sin 4x sin 8x, 3. In how many ways can be team of 3 boys and 3 girls be selected from 5 boys, and 4 girls., OR, Find the equation of the set of points P which are equidistant from (1,2,3) and, (3,2,-1)

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SECTION –D, , (2×4=8), , 1. Prove that, Sinx+ sin 3x+ sin 5 x+ sin 7 x= 4 cosx co2x Sin 4x., 2. Prove that co-efficient of x^ in (1+x)2n is twice the co- efficient of x^ in (1+x)2n-1., , OR, Using section formula show that the points A(2,-3,4) B(-1,2,1) and C(0,13.2) are, Collinear.