2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time is
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1 . If P(A) = x, P = 2x, P(A B) = 2, P ( A B) = 2 3, then the value of x is (A) A die is rolled 3 times, the probability of getting a number larger than the previous number each time is (A) If Ramu and Raju can solve 80% and 60% respectively of the problems in a book, what is the probability that at least one of them will solve the problem selected at random from the book. (A) MATHS 3 SET-4
2 4. The dual of the statement p (q r) (p q) r is (A) p (q r) (p q) r p (q r) (p q) r p (q r) (p q) r None of these 5. A function is defined as f(x) = (A) 3 2 kx x +, x, then for what value of k is f(f(x)) = x 6. The maximum value of + 8 sin 2 θ 2 cos 2 θ 2 is (A) SET-4 4 MATHS
3 7. The coefficient of x 4 in the expansion of (A) x + + 3x2 e x is A set S has 5 distinct elements. Then the number of distinct one-one functions that can be defined from S to S is (A) The digit in the units place of! + 2! + 3! + 4! +. + n!, where n > 4 is (A) MATHS 5 SET-4
4 0. For n N, 6 n 5n is always divisible by (A) The quadratic equation whose roots are p and q where 3 sin x 4 sin 3 x p = lim x 0 x 2 tan x and q = lim x 0 tan 2 x is (A) x 2 + 5x + 6 = 0 x 2 + 3x + 2 = 0 x 2 5x + 6 = 0 x 2 3x + 2 = 0 2. If ( + i) 00 = 2 49 (x + iy), then x 2 + y 2 is equal to (A) SET-4 6 MATHS
5 3. For the complex number i, i 4n + i 4n + + i 4n i 4n i 4n i 4n + 6 is (A) In the expansion of (A) (2 x) (2 + x) ( x) ( + x), x <, the term that is independent of x is 5. For three real numbers a, b, c with a 6; if (A) a + b + c a 2b 2c 3 b c 4 a b = 0, then abc = ab + b c 0 b 3 MATHS 7 SET-4
6 6. The number of solutions of the system of equations 2x + y z = 7; x 3y + 2z = ; x + 4y 3z = 5 is (A) For non-zero numbers p, q, r, a, b, c, if (A) pqr = p + q + r = p + q + r = 0 pqr = 0 pa qb rc qc ra pb rb pc qa = pqr a b c c a b b c a then 8. Let is (A) x 2 x x 2 x 6 x x 6 = Ax 4 + Bx 3 + Cx 2 + Dx + E, then the value of 9A 4B + 3C + 5D + 6E SET-4 8 MATHS
7 9. If A = 0 0, then the matrix A204 is same as (A) A A I I 20. If A = (A) , then adj(adja) is 2. The value of sec 2 (tan 2) + cosec 2 (cot 3) is (A) MATHS 9 SET-4
8 22. Given that sin α + sin β = p and cos α cos β = q, then the value of cos(α β) is (A) p 2 q 2 p 2 + q 2 2pq p 2 + q 2 2pq p 2 q 2 p 2 + q 2 p 2 q The value of 3 cosec 20 sec 20 is (A) If x = sin 2 θ + cos 4 θ, then for all values of θ, the interval x belongs to is (A) 0 x x x 4 x 2 SET-4 0 MATHS
9 25. The equality cot α = tan α holds good only when (A) α = 0 α α < 0 α > The approximate value of tan (.00) is (A) π π π π The roots of x 2 2 3x + 2 = 0 represent the lengths of two sides of a triangle and if the angle between these sides is 60, then the perimeter of the triangle is (A) MATHS SET-4
10 28. The area bounded by the ellipse x y2 343 = is (A) 50 7π 5π 200π 245π 29. If x 2y a = 0 is a chord of the parabola y 2 = 4ax, then its length is given by (A) 0a 20a 30a 40a 30. A pair of straight lines is given by x 2 (sin 2 α ) + y 2 cos 2 α yx cos 2 α = 0, the angle between them is given by (A) π π 4 π 2 2π 3 SET-4 2 MATHS
11 3. If the projection of a line segment on x, y and z axes are 4, 2, 2 respectively, then length of the line segment is (A) The equations of common tangents to the circle x 2 + y 2 = 8 and parabola y 2 = 6x are (A) x = ± (y + 2) x = ± (y + 4) y = ± (x + 2) y = ± (x + 4) 33. If p, q, r are in Arithmetic Progression, then px + qy + r = 0 represents a (A) point single line family of concurrent lines family of circles MATHS 3 SET-4
12 34. The tangents drawn at any point on these two curves 3x 2 y y 3 2 = 0 and x 3 3xy = 0 cut at (A) The smaller of the two areas enclosed between the ellipse x2 4 + y2 6 = and the line x 2 + y 4 = is (A) 2π 4 2 π 2 2π 2 π For some natural number n, if n = 55, then n 2 is (A) SET-4 4 MATHS
13 37. If the sum of two of the roots of x 3 + ax 2 + bx + c = 0 is zero, then the value of ab is (A) 2c 3c c c 38. The value of the sum 8 C C C C 8 is (A) The sum of the series + x 2 + x(x ) x(x ) (x 2) to is (A) 3 x 4 4 x 3 3 x 2 3 x 2 MATHS 5 SET-4
14 The value of to is (A) The product of all n th roots of unity (n > ) is (A) (n) n 0 ( ) n 42. If α, β, γ are the direction cosines of a line then for some real number c, the value of c[cos 2α + cos 2β + cos 2γ] is (A) c 0 2c c SET-4 6 MATHS
15 43. If a = 3^i 5^j; b = 6^i + 3^j and c = a b, then a : c : b = (A) 34 : 39 : : 35 : : 39 : : 39 : If a, b are non-collinear vectors and x, y are scalars such that (2 a b)x + (2 b a)y + ( a + 2 b) = 0, then (A) x = 4 3, y = 5 3 x = 4 3, y = 5 3 x = 0, y = 4 x = 5 3, y = If ABCD is a square, then AB + 2 BC + 3 CD + 4 DA is (A) 5 CA 2 CA 3 CA 8 CA MATHS 7 SET-4
16 46. The direction cosines of two lines that are at right angles are l, m, n and l 2, m 2, n 2, then the direction cosines of a line which is perpendicular to both these lines are (A) l + kl 2, m km 2, n + kn 2 m n 2 m 2 n, n l 2 n 2 l, l m 2 l 2 m l l 2, m m 2, n n 2 l + l 2, m + m 2, n + n If a = 4; b = 2 and the angle between a and b is π 6, then a b is (A) If the vectors a = 3 i + 6 j + 2 k and b are collinear and b = 28, then b = (A) ± 3 (2 i + 6 j + k) ± 4 (3 i + 6 j + 2 k) ± 28 (3 i + 6 j + 2 k) ± 2 (3 i + 6 j + 2 k) SET-4 8 MATHS
17 49. For three vectors, a = b = c, angle between each pair of these vectors is π 3 and a + b + c = 6, then a is (A) 3 2 log( + ax) log ( bx) 50. The value of the limit lim x is x 0 (A) a b a + b ab a b 5. If the function x = x(y) is defined as x = e y+ey+ey+ then dy dx is given by (A) + x x x x + x MATHS 9 SET-4
18 52. The value of the integral.. e2x + sin 2x + cos 2x dx is (A) 2 e2x tan 2x + c 2 e2x tan x + c 2 e2x sin 2x + c 2 e2x cos 2x +c 53. If m + m.. f(x)dx = m2, where m, then 3.. f(x)dx is (A) SET-4 20 MATHS
19 54. If f(θ) = sec θ cos θ cos 2 θ cos 2 θ, then the value of the definite integral 0 π/2.. f(θ)dθ is (A) The solution of dy dx = y 2 + sin y, y 0, with an arbitrary constant c is (A) x = y 3 cos 2 y + c x = y cos y + c x = y3 3 cos y + c x = y 2 cos y 3 + c MATHS 2 SET-4
20 56. The differential equation governing the solution ax 2 by 2 = 6 is y d2 2 y dx 2 + dy dx = (A) y dy dx dy x dx y dy x dx x dy y dx 57. If dy dx = u2, where u = 4x + y + then, (A) 2 tan u 2 = x + c tan u 2 = 2 (x + c) y = 2 tan x + c u 2 2 = tan xy + c SET-4 22 MATHS
21 58. The order and degree of the differential equation (A) 2, 3 3, 6 3, 2 3, 3 dy dx d 3 y dx 3 = 4 is 59. If y = (234)e x + (5678)e x then d2 y dx2 is equal to (A) 234y 5678y 2y 33y 60. The differential equation that represents the family of lines ax + by + c = 0 is (A) dy dx = 0 x + y dy dx + d2 y dx 2 = 0 d 2 y dx 2 = 0 y = x dy dx + c MATHS 23 SET-4
22 Space For Rough Work SET-4 24 MATHS
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