Let an be the nth term of a G.P. of positive terms. If sum from n=1 to 100 for 2n+1 terms and sum for 2n terms = 100
a. 300 b. 175 c. 225 d. 150 Solution: an is a positive term of GP. Let GP be a,... View Article
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If one end of focal chord AB of the parabola y2 = 8x is at A(1/2,-2) , then the equation of tangent to it at B is
a. x+2y+8 = 0 b. 2x-y-24 = 0 c. x-2y+8 = 0 d. 2x+y-24 = 0 Solution: Let PQ be... View Article
If [latex]\frac{dy}{dx}= \frac{xy}{x^{2}+y^{2}}[/latex] , y(1) = 1, then a value of x satisfying y(x)= e is
a. √3e b. (1/2)√3e c. √2e d. e/√2 Solution: Let y = vx dy/dx = v+x(dv/dx) v+x(dv/dx) = vx2/(x2(1+v2) =... View Article
If [latex]x = \sum_{n=0}^{\infty }(-1)^{n}\tan ^{2n}\theta[/latex] and [latex]y = \sum_{n=0}^{\infty }\cos ^{2n}\theta[/latex] where 0 < θ < π/4, then:
a. y(1+x) = 1 b. x(1-y) = 1 c. y(1-x) = 1 d. x(1+y) = 1 Solution: y = 1+cos2... View Article
The length of minor axis (along y-axis) of an ellipse of the standard form is 4/√3. If this ellipse touches the line x + 6y = 8, then its eccentricity is
a. (1/2)(√5/3) b. (1/2)√(11/3) c. √(5/6) d. (1/3)√(11/3) Solution: If 2b = 4/√3 b = 2/√3 Comparing y = (-x/6)+(8/6)... View Article
If p -> (p ∧~ q) is false. Then the truth values of p and q are respectively
a. F, T b. T, F c. F, F d. T, T Solution: Given p ->(p ∧~ q) Truth table:... View Article
The following system of linear equations:7x+6y-2z = 0, 3x+4y+2z = 0 and x-2y-6z = 0, has
a. infinitely many solutions, (x,y,z) satisfying y = 2z b. infinitely many solutions (x,y,z) satisfying x = 2z c. no... View Article
Find the area (in sq. units) of the region bounded by the curves y = f(x) and y = g(x) between the lines 2x = 1 to 2x = √3 is
Given: and g(x)= (x− 1/2)2, x ∈ R. Then the area (in sq. units) of the region bounded by the... View Article
Let a-2b+c = 1. If f(x) is a matrix having entries x+a x+2 x+1 x+b x+3 x+2 x+c x+4 x+3, then
a. f(-50) = 501 b. f(-50) = -1 c. f(50) = 1 d. f(-50) = -501 Solution: Given f(x) =... View Article
Let [t] denotes the greatest integer
Let [t] denotes the greatest integer ≤ t and \(\begin{array}{l}\lim_{x\to0} x\left [ \frac{4}{x} \right ]= A\end{array} \) . Then the... View Article
Let a function f:[0,5] R, be continuous, f(1) = 3 and F be defined as:
Let a function f:[0,5] R, be continuous, f(1) = 3 and F be defined as: F(x) = \(\begin{array}{l}\int_{1}^{x}t^{2}g(t)dt\end{array} \) ,where... View Article
Let a,b ∈R, a ≠ 0, such that the equation, ax2-2bx+5 = 0 has a repeated root
Let a,b ∈R, a ≠ 0, such that the equation, ax2-2bx+5 = 0 has a repeated root α, which is... View Article
In the expansion of….
In the expansion of \(\begin{array}{l}\left ( \frac{x}{\cos \theta }+\frac{1}{x\sin \theta } \right )^{16}\end{array} \) , if l1 is the least... View Article
Let f and g be differentiable functions on R, such that fog is the identity function. If for some a, b ∈ R, g’(a) = 5 and g(a) = b, then f'(b) is equal to
a. 2/5 b. 5 c. 1 d. 1/5 Solution: f(g(x) = x f’(g(x))g’(x) = 1 put x = a f’(g(a))g’(a)... View Article
If x = 2 sin θ – sin 2 θ and y = 2 cos θ – cos 2 θ, θ ∈ [0, 2π], then d2y/dx2 at θ =π is:
a. -3/8 b. 3/4 c. 3/2 d. -3/4 Solution: dx/d θ = 2 cos θ -2 cos2 θ dy/d θ... View Article
If 10 different balls has to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is
a. 965/210 b. 945/210 c. 945/211 d. 965/211 Solution: Total ways to distribute 10 balls in 4 boxes is =... View Article
If A = {x∈ R∶ |x| <2} and B = {x∈ R∶ |x-2| ≥3} then
a. A – B = [-1,2] b. B – A = R-(-2,5) c. A⋃B = R-(2,5) d. A∩B = (-2,-1)... View Article
The coefficient of x4 in the expansion of (1+x+x)10 is
Solution: General term of the given expression is given by \(\begin{array}{l}\frac{10!}{p!q!r!}x^{q+2r}\end{array} \) Here, q+2r =4 For p = 6, q... View Article
If for x ≥ 0,y = y(x) is the solution of the differential equation (1+x)dy = [(1+x)2+y-3]dx, y(2) = 0, then y(3) is equal to:
Solution: (1+x) dy/dx = [(1+x)2 + (y-3)] (1+x) (dy/dx) -y = (1+x)2 -3 (dy/dx)-(1/1+x)y = 1+x – 3/(1+x) I.F =... View Article
The number of distinct solutions of the equation
Solution: sin 2x = ±1/2 Therefore, we have 8 solutions for x ∈ [0,2] Answer: (8)
