Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50.
Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A... View Article
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Let A be a 2×2 real matrix with enries from {0,1} and A ≠ 0. Consider the following two statements:
Let A be a 2×2 real matrix with enries from {0,1} and A ≠ 0. Consider the following two statements:... View Article
Let P(h,k) be a point on the curve y = x2+7x+2, nearest to the line, y = 3x-3. Then the equation of the normal to the curve at P is
a) x+3y-62 = 0 b) x-3y-11 = 0 c) x-3y+22 = 0 d) x+3y+26 = 0 Solution: C: y =... View Article
The value of (1+sin (2π/9)+i cos(2π/9)/(1+sin (2π/9)-i cos(2π/9))3 is
a) (-1/2)(1-i√3) b) (1/2)(1-i√3) c) (-1/2)(√3-i) d) (1/2)(√3-i) Solution: = (ei(5π/36)+i(5π/36))3 = (e2i(5π/36))3 = ei(30π/36) = ei(5π/6) = cos (5π/6)+... View Article
If R = {(x,y):x,y ∈ Z, x2+3y2 ≤ 8} is a relation on the set of integers Z, then the domain of R-1 is
a) {-1, 0, 1} b) {-2, -1, 1, 2} c) {0,1} d) {-2,-1,0,1,2} Solution: 3y2 ≤ 8-x2 R:{(0,1), (0,-1), (1,0),... View Article
The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in
a) (-∞, -9]∪[3, ∞) b) [-3, ∞) c) (-∞, -9] d) (-∞, -3]∪[9, ∞) Solution: (a/r).a.ar = 27 a =... View Article
If a function f(x) defined by
If a function f(x) defined by be continuous for some a, b, c ∈ R and f’(0)+f’(2) = e, then... View Article
The domain of the function f(x) = sin-1 [(|x|+5)/(x2+1)] is (-∞, -a]U[a,∞). Then a is equal to:
a) (√17-1)/2 b) √17/2 c) (1+√17)/2 d) (√17/2)+1 Solution: -1≤ (|x|+5)/x2+1 ≤1 -x2-1≤|x|+5≤ x2+1 Case 1 -x2-1≤ |x|+5 This inequality... View Article
A line parallel to the straight line 2x-y = 0 is tangent to the hyperbola (x2/4)-(y2/2) = 1 at the point (x1, y1).
A line parallel to the straight line 2x-y = 0 is tangent to the hyperbola (x2/4)-(y2/2) = 1 at the... View Article
If the line, 2x-y+3 = 0 is at a distance 1/√5 and 2/√5 from the lines 4x-2y+α = 0 and 6x-3y+β = 0, respectively, then the sum of all possible values of α and β is
Solution: L1 : 2x-y+3 = 0 L2 : 4x-2y+α = 0 L3 : 6x-3y+β = 0 |(α/2)-3|/√5 = 1/√5 ⇒... View Article
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ’SYLLABUS’ such that two letters are distinct and two letters are alike, is
Solution: SS, Y, LL, A, B, U ABCC type words Answer: 240
Let f(x) = x[x/2], for -10<x<10, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f is equal to
Solution: f(x) = x[x/2] x∈ (-10, 10) x/2 ∈(-5,5) → 9 integers Check continuity at x = 0 f(0) =... View Article
Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is
Solution: P(at 2, 3 or 4) = 4C2 (2/6)2(4/6)2+ 4C3 (2/6)3(4/6)1+ 4C4 (2/6)4 = 6×(1/9)×(4/9)+4×(1/27)×(2/3)+(1/81) = 33/81 = 11/27 ⇒... View Article
The natural number m, for which the coefficient of x in the binomial expansion of (xm+1/x2)22 is 1540 is
Solution: Tr+1 = 22Cr (xm)22-r(1/x2)r = 22Cr (x)22m-mr-2r Given 22Cr = 1540 = 22C19 ⇒ r = 19 Since 22m-rm-2r... View Article
If α is positive root of the equation, p(x) = x2-x-2 = 0,
If α is positive root of the equation, p(x) = x2-x-2 = 0, then \(\begin{array}{l}\lim_{x\to\alpha ^{+} }\frac{\sqrt{(1-\cos p(x))}}{x+\alpha -4}\end{array} \)... View Article
If the co-ordinates of two points A and B are (√7, 0) and (-√7, 0) respectively and P is any point on the conic, 9x2+16y2 = 144, then PA+PB is equal to
a) 6 b) 16 c) 9 d) 8 Solution: (x2/16)+(y2/9) = 1 e = √(1-9/16) = √7/4 F1(√7, 0), F2(-√7,... View Article
The negation of the Boolean expression x ↔ y is equivalent to
a) (x˄y) ˄(∼x˅∼y) b) (x˄y) ˅ (∼x˄∼y) c) (x˄∼y) ˅ (∼x˄∼y) d) (∼x˄y) ˅ (∼x˄∼y) Solution: As we know p... View Article
If [latex]int left ( e^{2x}+2e^{x}-e^{-x}-1 right )e^{(e^{x}+e^{-x})}dx=g(x)e^{(e^{x}+e^{-x})}+c[/latex] where c is a constant of integration, then g(0) is equal to
a) 2 b) e c) 1 d) e2 Solution: ⇒ g(0) = 2 Answer: a
If the four complex numbers z, [latex]bar{z}[/latex] , [latex]bar{z}-2Rebar{z}[/latex] and z-2Re(z) represent the vertices of a square of side 4 units in the Argand plane, then |z| is equal to
a) 2 b) 4 c) 4√2 d) 2√2 Solution: Let z = x+iy CA2 = AB2+BC2 22x2+22y2 = 32 x2+y2... View Article
If the function f(x) is twice differentiable
If the function is twice differentiable, then the ordered pair (k1, k2) is equal to: a) (1,1) b) (1,0) c)... View Article
