Archives

In the expansion of….

In the expansion of l2/l1 = 16:1Answer: (a)... 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. 2/5b. 5c. 1d. 1/5Solution:f(g(x) = xf’(g(x))g’(x) = 1put x = af’(g(a))g’(a) = 1f’(b) ×5 = 1f’(b) = 1/5Answer: (d)... 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. -3/8b. 3/4c. 3/2d. -3/4Solution:dx/d θ = 2 cos θ -2 cos2 θ dy/d θ = -2 sin θ + 2 sin2 θdy/dx = cot (3... 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. 965/210b. 945/210c. 945/211d. 965/211Solution:Total ways to distribute 10 balls in 4 boxes is = 410 Total ways of placing exactly 2 and 3... 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)Solution:A = {x: x ∈ (-2,2)}B = {x: x ∈ (∞,-1] ⋃ [5, ∞)}A∩B = {x: x ∈ (-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 Here, q+2r =4For p = 6, q = 4, r = 0, coefficient = 10!/(6!×4!) = 210For p = 7, 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 = y = x(1+x) + 3+c(1+x)At x = 2, y = 0... 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)... View Article

The projection of the line segment joining the points (1,-1,3) and (2,-4,11) on the line joining the points (-1,2,3) and (3,-2,10) is

Solution: Answer: (8)... View Article

M	T	W	T	F	S	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28	29	30	31

Archives

In the expansion of….

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

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:

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

If A = {x∈ R∶ |x| <2} and B = {x∈ R∶ |x-2| ≥3} then

The coefficient of x⁴ in the expansion of (1+x+x)¹⁰ is

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:

The number of distinct solutions of the equation

The projection of the line segment joining the points (1,-1,3) and (2,-4,11) on the line joining the points (-1,2,3) and (3,-2,10) is

If vectors p, q and r are coplanar

In a box, there are 20 cards out of which 10 are labelled as A and remaining 10 are labelled as B

The integral is equal to:

Let the observations x_i(1 ≤ i ≤ 10) satisfy the equations

If the number of five digit numbers with distinct digits and 2 at the 10th place is 336k, then k is equal to:

A pack of cards has one card missing.

Let a complex number z, |z| ≠ 1, satisfy log_1/√2 [(|z| + 11) / (|z| – 1)²] ≤ 2.

Let the functions f: R→R and g: R →R be defined as:

The range of a ∈ R for which the function f (x) = (4a – 3) (x + log_e5) + 2 (a – 7) cot (x / 2) sin² (x / 2),

If for a>0, the feet of perpendiculars from the points A

Let a vector [latex]alpha hat{i}+beta hat{j}[/latex] be obtained by rotating

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