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MATHEMATICS +» FOR NDA AND N.A, , , , 18., , 19., , 21., , 25., , 27., , Ix? + y? = J, then, aw’ tOFs1=0 b. py" +27P +1 =0, cy” 2»? 11-0 d. yy" 1 (F150, The solution ofthe differential equation y (9? —x) = yis, a y-3y=C b.y'+ 3xy=C, cx -3xy=C d. ye -xwat, The order and de; ree of the differential, : dy (sy py, tion) 2—— + | — = 3 spective, equal on aa (= ~ are respectively, a2and2 b 2and! oc 3and2 d 3and3, , Laser chabbaalatalald point (x, y) other than the arigin,, , isye% Then the equation of the curve is, , a y= Cre! b y=ate' + +C), co. xy=Ce* d. y+xe"=C, , ‘The domain of the function f(x) = y= 3x + log, x is, , a O<x<u b. stse, , © Oexst d, -w<x<0, , IE f(1)= 1, fn) = f(a) and f(2n + 1) = (f(a)? - 2 for, , n= 1,2, 3 then the value of f((1) + /(2) +... (25) is equal, to, al b.-15 c.=17 del, , Let X and Y be two non-empty sets such that, XOA ~YOA > B and XNOA = FUA for some nonempty set 4. Then, , a Nisaproper subset of ¥ b. Yis a proper subset of X, c X=¥ d. Xand ¥ are disjoint sets, , The set (A\B) U (BVA) is equal to, a [AMAR O[B\(ANB), b. (AU B)\(ANB), , c. A\(ANB) d. ANB\AUB, , t, ‘The range of the function f(x) 2 cos tx is, , *, 220) bE23) e (3.2) a(}.), , =], , 2” }, Inaclass of 8) students numbered 1 to 80, all odd numbered, students opt for Cricket, students whose numbers are, divisible by 5 opt for Football and those whose numbers, are divisible by 7 opt for Hockey. The number of students, who do not opt any of the three games, is, a 13 b. 24 c. 28 d. 52, , If Re(1 = iy)? = -26, wherey is a real number, then the, value of |p| is, , a2 b3 «4 d6, , 29., , 32., , . It f(z)=, , ifs =x} fy is a complex number such that =| = Re(iz) 11,, then the locus of zis, , axty?-1 b x -2y 1, cy =2x-1 dy =1-2x, Let? =-1, then, \ fo f, ("-3 1 fn lee fe feb 2) L, u PB BU, Lal b. -1-i e. 1+i asi, , 3, , , , , i , Where = = x + dy with= = 1 then, , Re} f(=)} reduces to, a vey +at+1=0, ex -y—-xt+1=0, , 2_\2, bo x-yit+x-1=0, d x -yo tat t=O, , If: = 1+ 4, then the argument of -*e*~!, & r= x a, 3 6 “4, , tilt, , 33. If the difference betweenthe roats of x’ +Ipx+q=0 is, , 34., , 35., , 36,, , x., , 38,, , 39., , two times the difference between the roots of, x +qr+B=0 where p # gq, then, , ap-qil=0 b p-q-1=0, , c ptq-1=0 d p+qt 1=0, , Sum of the roots of the equation |x - 37 + x - 3|-2=0is, equal to, , a2 b4 c 6 d. 16, , ‘The quadratic equation whose roots are three tumes the roots, st igepetio i +3r¢ 5 =0, is, , +9x+45=0 b 2x? + 9x45 =0, © Sx°+9x+45=0 d 2v7-9x=45=0, , [fx is real number, then —5 Z, ~5x+, , lend ec. -lland] d -land Il, , ; musiliebetween, , 1, a We! b., , If the roots of the equation (x — ajix— 5) + (x- b\ix-c), +(x-e)(x—a)=0 are equal, then +h+, , aathte b la+bt+e, ©. Jabe d ab>be+ca, Tf one root of a quadratic equation is —= i : 5° . then the, quadratic equation is +, a ix’+x-1=0 b. 2x7 -2x-1=0, ¢ 2? +2x+1=0 d txt 1=0, , The 5 and 8" terms ofa GP are 1458 and $4 respectively, The common ratio of the GP. ss, , “as b 3 «9 d., , 7, 3 9

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Practice Paper - 4, , , , 41., , 42., , 45., , 47., , 49., , Let Sim) denote the sum of the digits of a positive integer, a, For example, S(178) = 1+7+8 = 16. Then the value of, SUL) + S(2)+ SIB) + + S199) is equal to, a. 476 b. 998 c. 782 d. 900, , An AP. consists of 23 terms. If the sum of the 3 terms in, the middle is 141 and the sumof the last 3 terms is 261,, then the first term is, , a6 b 5 ce 4 d 3, , 14" term ofaG P. is 32 whose common ratio is half of the, first grr, then the 158 term is, a2? b. 2/8 «. 2! a. 2i6, , Let S; be a square of side 5 cm. Another square S> is drawn, by joining the midpoints of the sides of S; . Square 5; is drawn, by joining the midpoints of the sides of S, and soon. Then, (area of S; + arca of S, + area of S; +...+ area of Sp) =, , 1 |, a as(1-3| b. s0(1-—), (1 1, c. 21-5] d. SW, , Ifa, 6, care in A P and ifthe squares taken in the same, order form a GP. then (a+c)* =, dae, , alae? b © Bare?, The value of x satisfying the relation 11("C3)=24("*%C;), 8, , a’ bo eH d. 10, , The power of x in the term with the greatest coefficient in, the expansion of (1+) is, , a2 b 3 c4 ds, , The number of S-digit numbers (no digit is repeated) that, , can be formed by using the digits 0, 1,2... , 7 ts, , a. 1340 b. 1860 c. 240 d. 2160, If mr and my satisfy the relation, , wea = Lm)" then my + mz is equal to, a. lO bo ¢.13 d.l7, , Sum of cocfficients of the last 6 terms in the expansion of, (+x)! "I when the expansion is in ascending powers of x,, , is 2048 b. 32 e. 512, d 64, Ie Cy C. re As are ee coefficients in, 15 2 Gs, ! > then Gi 9G yyy ysis, rea ten CTE Gt ISG, a 60 b 120 c 64 d 124, , Si., , 52., , SS., , 36., , 59,, , 12 3 4 8 1S, WA=|2 3 SlandA'=|3 6 12, then, 3 6 12 23 5, , as'=24 b.A'=-2A, , cA=A d Vv=-A, +x 3 5, , The roots of the equation] 2. 21x §, , 2 3 x+4, b1,1,-9, d.-2,-1,-8, , =Oare, , a2l-9, e-1,1,9, , 0 3 2b, 1f}2 0 1 is singular, then the value of 6 is equal to, ls -1 6, , c-6 46, , x x-1], 1 | and ifdet 4 = 9 then values of x are, . b 23, z, , a33, 2, , , meren, ry, , {he value of determinant, in? 36° cos? 36° coll 35°, * 53° cotl35* sin” 37° ts equitl lo, leat 135° cos* 25° cos” 65, , a2 b.-! c0 al, , HEA ond B anc square unntrices of the same ocder end if, A=A". B= B" (ABA) =, , a BAB b.ABA cABAB 4B”, If x ~ 3] < 2x | 9, then x lies in the interval, a (-»,-2) bh (-2,0) ¢ (-2,«) d (2,2), , The area and perimeter of a rectangle are 4 and P, , respectively. Then 7 and 4 satisfy the inequality, a P+A>PA bPecs, c A-P<2 dP s4A, , A person goes tu office by car of scooter or bus or train,, probability of which are 1/7, 3'7, 2/7 and L/7 respectively., Probability that he reaches office late, if he takes car,, scooter, bus or train is 2/9, 1/9, 4/9 and 1/9 respectively., Given that he reached office in time, the probability that, he travelled by a car is, , a 7 b, 27 ¢, , cle) 4.47

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MATHEMATICS +» FOR NDA AND N.A, , , , él., , 67,, , 7m., , If the mean and variance of a binomual distribution are 4, and 2 respectively, then the probability af 2 successes of, , that binomial variate X, is, at » 29 3 ai, “4 256 * 256 of, , The mean and variance of a random variable X having a, binomial distribution are 4 and 2 respectively, find the, value of P(X = 1), , 1 J 7 f., “4 > 16 © ig 4 33, 0.1, if tan = ythen the value of sin@ is, a < ° b, 7 €. Lt dl, 3 5 2 , Ifx=5 + 2sec@ and y= 5 + 2tan®, then (x - 5}°-(y-5)°, , is equal to, , a3 bl c.0 a4, , ‘The value of tan 15° | tan 75° ts equal to, , a 243 b.2 c2-v3 d 43, , ‘The period of the function f(x) = cos 4x + tun 3x is, « i= x d, , * 1 6 “3 *, , tan@, If sin(@ + 4) = wsin(@ — 4), m #1 then the vatue of 4 is, equal to, , a batt . asa!, =I l= asl, 1 1, 2tan@'| —}+2tan-!| — |=, =o, 6 1, tia, aan fa oie Ey, on 4.0, 4, Ifcos” ‘y+ cos"ly= % then the value of sin”! x+ sin”! yp, is equal to, re my &, a4 7 “7 9, , If cos”! x > sin”! x, then x lies in the interval, b 0,1] ¢ |-u5] ape, , If 0S x¥ 2m, then the number of solutions of the equation, sin’ x + cos® x= 1 is, , a2 b.3, , «(ha, , c4 d.5, , Let A(0, 0) and A(8, 0) be two vertices of a right angled, triangle whose hypotenuse is BC. If the circumcenire is, (4,2), then the point Cis, a (2.4) b. (0, 8), , «. (0,4) d. (0,6), , 72,, , 73,, , 74,, , 78,, , 76., , 77., , 78., , 79,, , Ifeoordinates of the circumcentre and the orthocentre of a, triangle are respectively (5, 5) and (2, 2), then the, coordinates of the centroid are, a(l,l) b. (3,1) c.{3.3) d. (2,2), , If the points A(3, 4), lx, ¥) and Ax, pykare such that, both 3, x,,x, and 4, y,, y, wre m AP, then, , a A, B, C are vertices of an isosceles triangle, , b. A, 8, C are collinear pomts, , cA, B, C are vertices ofa right angled triangle, , dA, B, C are vertices of a scalene triangle, , If p, and p, are respectively length of perpendiculars from, the origin to the straight lines xsec® + y ose = aand, acos@ — y sin8 = a cos28, then 4p +p =, ba ©. +, , a, , al da, The distance between the point (1, 2) and the point of, intersection of the lines 2x + y= Zam x + 2y = 2s, wo, vis wz, vio, , ay 3 e's 3, , Ifa straight line ts perpendicular to 2x + 8y = LO and meets, the x-axis at (5, 0), then it meets the y-axis at, a (0,-2) b (0,-8) ¢(0,-10) = 4 (0,-16), If the straight line 5x + y = & forms a triangle with the, coordinate axes of area 10 sq_ units, then the values of k, are, , a il§ b 10 ce $5 d +20, , A circle passes through the point (6, 2). If segments of the, straight lines x + y = 6 and x + 2y = 4 are two diameters, of the circle, then tts radius is, , ad bs co. V5 4. 25, , The parametric form of equation of the circle, x? + y? 6x +2y-28=05s, , a x=-34V 38 cos, y=-1+V38 sin, , b x=¥28 cos6, y= V28sin8, , « xe =3~V38cos0, y= 14 y38sind, , d. x=34V38cus0, y = -1+V38sin0, , The point on the cirle (x — 1)? +o-1P = 1 whichis, , nearest to the circle (x - 5)" + (y- 5)" =4 is, 33, a (2,2) b. (3.3), V2+1 J2+1, 7 d, c ( oe) (2, 42)

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Practice Paper - 4, , , , 87., , The line segment joining (5,0) and (10 cos 6 10 sin 8) is, divided internally in the ratio 2° 3 at P. 11 varies, then the, locus of # is, , a. a pair of straight lines, c. a straight line, , b.acirele, d.a parabola, , ABCD is a square with side a, If AB and AD are along the, , coordinate axes, then the equation of the circle passing, through the vertices A, B and D is, , axayavlaxey) br 4y7= a, , r- yr =9is, , Sie = d 32, v2 3 2, , a.2,-2 bo4 ¢. 0,-2 d.0,2, , cx +y?=alx+y) a2+yP=a x>y), , The distance between the directrices of the hyperbola, 2 b> «2, , If the line y= kx touches the parabola y= (x 1)", then the, , values of & are, , Ifthe semi-major axis of an ellipse ts 3 and the latus rectum, , is “g, Hem the standard eqqeation of the elltpye is, , 2 2 2, aX 42% 21 b. x 4% 21, _ & & 9, 2 ae, Pa a Bey, 9 8 8 9, x 8), Ifa point P(x, y) moves along the ellipse ata land, if C ts the centre of the ellipse, then, 4max{CP} +, Smin{CP} =, a.25 6.40 ©. 45 d. 54, , The one end of the latus rectum of the parahola, y- 4x-2y-3Uisat, a(0,-1) b ON), , ¢. (0,-3) 4d. (3,0), , The angle between the two vectors i+j+hand, 2) +2 is equal to, , ceri} bow), com) a ows), , dit j+h.b w 4i +3j-+4k and, @=i+ay+pé are coplanar and | ¢ |= 3, then, , aaev2,pel b. a@=1,fp=41, c.a=thpe-l dat) p=-1, , Let PCL, 2 3) and Of-1, -2, -3) be the two points and let 0, be the origin. Then | PO + OP| =, a. 13 b Via c. V24 d. viz, , 92., , 93., , 9S., , 6., , 97,, , oR., , Let ABCD be a parallelogram. if AB =i +3) 47k,, Ab=2i+ 3j- 5k and Pisaunit vector parallel to a,, then is equal to, a 302i + j+2%) b yai-2)+8), c pla +6) +2h) & Loi +2]+38), , Let Ob-742j+2k and O4=47+2)+2k. The, distance of the point 8 from the straight line passing through, , Aand allel to the vector 2i + 3/-+ 6K is a NS b — a c v5 d 5, O° 7 7, , i Sik and B=2)+2j+Ak are at right, a ., , angle, then the value of |@ +8 |-|a-8| is equal to, , a2 bl c0 d-l, , Let the position vectors of the paints 4, 8 and C be a, and ¢ respectively. Let Q be the point of intersection of, the medians of the triangle AABC. Then G4 + OB + OC, , > >, a +B brasBee, , > 3 > G+Bee, Ca+beec ono, The angle between the lines 2x = 3y =-cand 6x = —y=-42, is, , x T n x, as b. : eg d 3, , The projection of the line segment joining (2, 0, -3} and, (5, -1, 2) on a straight line whose direction ratios are 2, 4,, , 4 1s equal to, ci 10 13 13, as b. 3, , The angle between the straight line, P=() 4274+) 450 — 7 +6) and the plane, 7 (@-j+h w4is, b. aa 2), \, , (2, cof) aw), , Ifa straight line makes angles a, fi, y with the coordinate, -tan*a, , axes then, , , , miet =2sin? y =, +tan?@ sec2B :, bo s. -2, , a-l d.2