151.If 3 and 3 5but 2 2 − = − = ≠ then the equation having and as its roots is a) 0 3 19x 3x2 = + − b) 0 3 -19x 3x2 = + c) 0 3 -19x 3x2 = − d) 0 3 5x x2 = + − 152.If y = n 2 ) x 1 (x + + , then dx dy x dxy d ) x 1 2 2 2 + + is a) y n2 b) y n -2 c) -y d) y 2x2 153.If 1, 2), (3 log x 1 9 + − log3 1), (4.33x − are in A.P then x equals a) 4 log3 b) 4 log 1 3 + c) 3 log 1 4 − d) 3 log4 154.A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 41 and 31 , 21 . Probability that the problem is solved is a) 43 b) 21 c) 32 d) 31 155.The period of Sin 2 is a) 2 b) c) 2 d) /2 156.l, m, n are the th th th r and q , p term of a G. P all positive, then 1 r n log 1 q m log 1 p l log equals a) -1 b) 2 c) 1 d) 0 157. 2x 2x cos 1 lim0 x − → is a) 1 b) -1 c) zero d) does not exist 158.A triangle with vertices (4, 0), (-1, -1), (3, 5) is a) isosceles and right angled b) isosceles but not right angled c) right angled but not isosceles d) neither right angled nor isoceles 159.In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls? a) 73 b) 65 c) 68 d) 74 160. x, ) cos ( tan ) cos ( cot 1 1 = = − − then sin x = a) 2tan 2 b) 2cot2 c) tan d) 2cot 161.The order and degree of the differential equation 3 3 2/3 dxy d 4 dx dy 3 1 = + are a) 32 , 1 b) (3, 1) c) (3, 3) d) (1, 2) 162.A plane which passes through the point (3, 2, 0) and the line 4 4 z 5 7 y 1 4 x − = − = − is a) x -y + z = 1 b) x + y + z = 5 c) x + 2y -z = 1 d) 2x -y + z =5 163.The solution of the equation 2x 2 2 e dxy d − = a) 4 e 2x − b) d cx 4 e 2x + + − c) d cx e 41 2 2x + + − d) d cx e 41 4x + + − MATHEMATICS Questions -75 Paper -I I Time -90 Min -www.way2freshers.com164 x1 2 2 x 3 x x 3 5x x lim + + ∞ + + → a) 4 e b) 2 e c) 3 e d) 1 165.The domain of -1 sin is (x/3)] [log3 a) [1, 9] b) [-1, 9] c) [-9, 1] d) [-9, -1] 166. The value of 1/6 1/8 1/4 .8 .4 2 +... ∞ is a) 1 b) 2 c) 3/2 d) 4 167.Fifth term of an GP is 2, then the product of its 9 terms is a) 256 b) 512 c) 1024 d) none of these 168. ∫ 10 0 is dx | x sin | a) 20 b) 8 c) 10 d) 18 169. ∫ = 0 n n dx x tan I then ] I n[I lim 2 n n n − ∞ → + equals a) 21 b) 1 c) ∞ d) zero 170. ∫2 0 2 is dx ] [x a) 2-2 b) 2+ 2 c) 2 -1 d) 2 -2 171. ∫ + + −2 x cos 1 x) sin 2x(1 dx is a) 4 2 b) 2 c) zero d) 2π 172.Let f(x) = 4 and f’(x) = 4. Then 2 x (x) 2f (2) xf lim2 x −− → is given by a) 2 b) -2 c) -4 d) 3 173.z and w are two nonzero complex numbers such that | z | = | w | and Arg z + Arg w = then z equals a) w b) -w c) w d) -w 174.If | z -4 | < | z -2 |, its solution is given by a) Re(z)>0 b) Re(z)<0 c) Re(z)>3 d) Re(z)>2 175.The locus of the centre of a circle which touches the circle | b | z z | and a | z -z | 2 1 = − = externally (z, z1 & z2 are complex numbers) will be a) an ellipse b) a hyperbola c) a circle d) none of these 176.Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is a) 5 b) 3/5 c) 8/5 d) 1/5 177. = + + + − + − 3 3 3 3 3 9 .... 4 3 2 1 a) 425 b) -425 c) 475 d) -475 178.Difference between the corresponding roots of 0 b ax x2 = + + and 0 a bx x2 = + + is same and a ≠ b. then a) a + b + 4 = 0 b) a + b -4 = 0 c) a -b -4 = 0 d) a -b + 4 = 0 179.Product of real roots of the equation 0 9 | x | x t 2 2 = + + a) is always positive b) is always negative c) does not exist d) none of these -www.way2freshers.com180.If p and q are the roots of the equation 0 q px x2 = + + , then a) p=1, q= -2 b) p=0, q=1 c) p=-2, q=0 d) p=-2, q=1 181.If a, b, c, are distinct +ve real numbers and 1 c b a 2 2 2 = + + then ab + bc + ca is a) less than 1 b) equal to 1 c) greater that 1 d) any real no. 182.Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are a) 216 b) 375 c) 400 d) 720 183.Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4, (repetition allowed) is a) 125 b) 105 c) 375 d) 625 184.Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4, 6 and 7 without repetition. Total number of such numbers are a) 312 b) 3125 c) 120 d) 216 185.The sum of integers from 1 to 100 that are divisible by 2 or 5 is a) 3000 b) 3050 c) 3600 d) 3250 186.The coefficients of xp and xq in the expansion of (1+x)p+q are. a) equal b) equal with opposite signs c) reciprocals of each other d) none of these 187.If the sum of the coefficients in the expansion of (a +b)n is 4096, then the greatest coefficient in the expansion is a) 1594 b) 792 c) 924 d) 2924 188.The positive integer just greater than ( 1+0.0001)10000 is a) 4 b) 5 c) 2 d) 3 189.r and n are positive integers r > 1, r > 2 and coefficient of (r + 2)th term and 3rth term in the expansion of (1+x)2n are equal, then n equals a) 3r b) 3r + 1 c) 2r d) 2r + 1 190.If a > 0 discriminant of c 2bx ax2 + + is -ve, then 0 c bx b ax c bx c b b ax b a + + ++ is a) +ve b) (ac-b2) (ax2+2bx+c) c) -ve d) 0 191.If .... 7 7 7 an + + + = haing n radical signs then by methods of mathematical induction which is true a) 1 n 7 an ≥ ∀ > b) 1 n 7 an ≥ ∀ > c) 1 n 4 an ≥ ∀ < d) 1 n 3 an ≥ ∀ < 192.The sides of a triangle are 3x + 4y, 4x + 37 and 5x + 57 where x, y > 0 then the triangle is a) right angled b) obtuse angled c) equilateral d) none of these 193.Locus of mid point of the portion between the axes of x cos + y sin = p where p is constant is a) 2 2 2 p4 y x = + b) 2 2 2 4p y x = + c) 2 2 2 p2 y1 x1 = + d) 2 2 2 p4 y1 x1 = + 194.If the pair of lines 0 c 2fy 2gx by 2hxy ax 2 2 = + + + + + intersect on the y -axis then a) 2fgh = bg2+ch2 b) 2 2 ch bg ≠ c) abc = 2fgh d) none of these 195.The point of lines represented by 0 2)y (a 5xy 3ax 2 2 2 = − + + and perpendicular to each other for a) two values of a b) ∀ a c) for one value of a d) for no values of a 196.If the chord y = mx +1 of the circle x2 + y2 = 1 subtends an angle of measure 450 at the major segment of the circle then value of m is a) 2 2 ± b) 2 2 -± c) 2 1 -± d) none of these -www.way2freshers.com197.The centres of a set of circle, each of radius 3, lie on the circle 25. y x 2 2 = + The locus of any point in the set is a) 64 y x 4 2 2 ≤ + ≤ b) 25 y x 2 2 ≤ + c) 25 y x 2 2 ≥ + d) 9 y x 3 2 2 ≤ + ≤ 198.The centre of the circle passing through (0, 0) and (1, 0) and touching the circle x2 +y2 = 9 is a) 21 . 21 b) 2 -. 21 c) 21 . 23 d) 23 . 21 199.The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is a) 2 2 2 9a y x = + b) 2 2 2 16a y x = + c) 2 2 2 4a y x = + d) 2 2 2 a y x = + 200.Two common tangents to the circle 2 2 2 a 2 y x = + and parabola 8ax y2 = are a) 2a) (y x + ± = b) 2a) (x y + ± = c) a) (y x + ± = d) a) (x y + ± = 201.In a triangle with sides a, b, c, 3 2 1 r r r > > (which are the ex-radii) then a) a>b>c b) ab and b 0 is a) a-b b) a+b c) 2 2 b a + d) 2 2 b a − -www.way2freshers.com211.If 2a+3b+6c = 0, (a,b,c ∈R) then the quadratic equation ax2 + bx c = 0 has a) at least one root in [0, 1] b) at least one root in [2, 3] c) at least one root in [4, 5] d) none of these 212.If y = f(x) makes +ve intercept of 2 and 0 unit on x and y axes and encloses an area of 3/4 square unit with the axes then ∫ 2 0 (x)dx xf' is a) 3/2 b) 1 c) 5/4 d) -3/4 213.The area bounded by the curves y = In x, y = In |x|, y = |In x| and y = | In | |x| is a) 4sq. units b) 6sq. units c) 10sq. units d) none of these 214.If | b | 4 | a | = =2 and the angle between aand bis /6 then 2 ) b a ( × = 2 is equal to a) 48 b) 16 c) ad) none of these 215.If c , b , a are vectors such that ] c . b . a [ = 4 then = × × × ] a c c b b a [ a) 16 b) 64 c) 4 d) 8 216.If c , b , a are vectors show that c b a + + = 0 and 7, | a | = 5, | b | = 3 | c | = then angle between vector c and b is a) 0 60 b) 0 30 c) 0 45 d) 0 90 217.If |a| = 5, |b| = 4, |c| = 3, thus what will be the value of |a b + b.c +c.a|, given that c b a + + = 0 a) 25 b) 50 c) -25 d) -50 218. 0 ) b a ( 2c 3= × + then a) 0 23= + b) 23= c) = d) 0 = + 219. j ˆ 5 i ˆ3 a − = and j ˆ 3 i ˆ6 b − = are two vectors and cis a vector such that b a c × = then | c |:| b | |: a | a) 39 : 45 : 34 b) 39 : 45 : 34 c) 34 : 39 : 45 d) 39 : 35 : 34 220.If c b a then a c c b b a + + × = × = × = a) abc b) -1 c) 0 d) 2 221.A and B are events such that P(A ∪ B)=3/4, (A ∩ B) = 1/4, P( A ) = 2/3 then P( A ∩ B) is a) 5/12 b) 3/8 c) 5/8 d) 1/4 222.A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is a)8/3 b) 3/8 c) 4/5 d) 5/4 223.The d.r of normal to the plane through (1, 0, 0,), (0, 1, 0) which makes an angles /4 with plane x +y = 3 are a) 1, 2 ,1 b) 1,1, 2 c) 1, 1, 2 d) 2 , 1,1 224.The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N. The magnitude of the two forces are a) 13, 5 b) 12, 6 c) 14, 4 d) 11, 7 225.A bead of weight w can slide on smooth circular wire in a vertical plane. The bead is attached by a light thread to the highest point of the wire and in equilibrium, the thread is taut and make an angle with the vertical then tension of the thread and reaction of the wire on the bead are. a) T = w cos R = w tan b) T = 2w cos R = w c) T = w R = w sin d) T = w sin R = wcot -www.way2freshers.com