The area enclosed between the curves y² = x and y = |x| is

Test the continuity of the function at x = 2 

The value of 

If $3 sin x + 4 cos x = 5$, then $6tan\frac{x}{2}-9tan^2\frac{x}{2}$

If A is a subset of B and B is a subset of C, then cardinality of A ∪ B ∪ C is equal to

If , then the values of n and r are:

If $A = \{4^x- 3x - 1 : x ∈ N\}$ and $B = \{9(x - 1) : x ∈ N\}$, where N is the set of natural numbers, then

If A = { x, y, z }, then the number of subsets in powerset of A is

How many words can be formed starting with letter D taking all letters from the word DELHI so that the letters are not repeated:

Naresh has 10 friends, and he wants to invite 6 of them to a party. How many times will 3 particular friends never attend the party?

There is a young boy’s birthday party in which 3 friends have attended. The mother has arranged 10 games where a prize is awarded for a winning game. The prizes are identical. If each of the 4 children receives at least one prize, then how many distributions of prizes are possible?

A problem in Mathematics is given to 3 students A, B, and C. If the probability of A solving the problem is 1/2 and B not solving it is 1/4 . The whole probability of the problem being solved is 63/64 , then what is the probability of solving it by C?

A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both win a prize. The probability that they will not win a prize in a single trial is

A, B, C are three sets of values of x: 

Standard deviation for the following distribution is 

Roots of equation are $ax^2-2bx+c=0$ are n and m , then the value of $\frac{b}{an^2+c}+\frac{b}{am^2+c}$ is

The number of values of $k$ for which the linear equations

Let A = (a_ij) and B = (b_ij) be two square matricesof order n and det(A) denotes the determinant of A. Then, which of the following is not correct.

The tangent to an ellipse x² + 16y² = 16 and making angel 60° with X-axis is:

Find the number of point(s) of intersection of the ellipse $\dfrac{x^2}{4}+\dfrac{(y-1)^2}{9}=1$ and the circle  x² + y² = 4

An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Then what is the common difference?

If a + b + c = 0, then the value of $\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}$

Find

If $f(x)=\begin{cases}{{x}^2} & {,\leq0} \\ {2\sin x} & {,0}\end{cases}$, then x = 0 is

If  is a continuous function at x = 0, then the value of k is

Find the interval(s) on which the graph y=2x³e^x is increasing

Evaluate

If  where n is a positive integer, then the relation between I_n and I_n-1 is

The value of  depends on the

Find the area bounded by the line y = 3 - x, the parabola y = x² - 9 and

If  are three non-coplanar vectors, then 

Two forces F₁ and F₂ are used to pull a car, which met an accident. The angle between the two forces is θ . Find the values of θ for which the resultant force is equal to

If  are four vectors such that is collinear with  and is collinear with  then  =

Forces of magnitude 5, 3, 1 units act in the directions 6i + 2j + 3k, 3i - 2j + 6k, 2i - 3j - 6k respectively on a particle which is displaced from the point (2, −1, −3) to (5, −1, 1). The total work done by the force is

The position vectors of points A and B are  and  . Then the position vector of point p dividing AB in the ratio m : n is

If a, b, c are three non-zero vectors with no two of which are collinear, a + 2b  is collinear with c and b + 3c is collinear with a , then | a + 2b + 6c | will be equal to

Vertices of the vectors i - 2j + 2k , 2i + j - k and 3i - j + 2k form a triangle. This triangle is

If the volume of a parallelepiped whose adjacent edges are 

Solve the equation sin² x - sinx - 2 = 0 for for x on the interval 0 ≤ x < 2π

If $\frac{tanx}{2}=\frac{tanx}{3}=\frac{tanx}{5}$ and x + y + z = π, then the value of tan²x + tan²y + tan²z is

Find the value of sin 12°sin 48°sin 54°

If cos x = tan y , cot y = tan z and cot z = tan x, then sinx =

The value of  is

The value of sin 10°sin 50°sin 70° is