JEE Main Practice Test- 25 - JEE MCQ

The area contained between the curve x y = a² , the vertical line x = a, x = 4a (a > 0) and x -axis is

The interval in which y=x²e^-x is increasing with respect to x, is

The equation of the ellipse whose focus is (1,-1), directrix is the line x - y - 3 = 0 and eccentricity is 1/2 is

If f(x) = is continuous at   , then a =

Let f(x) be a function satisfying f ′ x = f x with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x², then value of integral
dx is equal to

If f^'(2) = 4 and f^' (1) = 2 then

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion (A): The vector equation of the plane passing through the points (1, -2, 5), (0, -5, -1), (-3, 5, 0) is 
Reason (R): The vector equation of the plane passing through the points

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): The equation x² + 2ax - b² = 0 can have repeated roots, where a,b are real numbers.
Reason(R): The equation Ax² + Bx + C = 0 will have repeated roots when the determinant becomes zero.

In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): The expression is a zero vector .
Reason(R): If   be three vectors   is known as vector triple product, given

The number of values of x where f (x)   = cosx + cos√2 x attains its maximum value is

Mean deviation is minimum when deviations are taken from:

The equation of the tangent to the parabola y²=16x which is ⊥ to the line y=3x+7 is

Box A contains 2 black and 3 red balls, while box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random, and the probability of choosing box A is double that of box B. If a red ball is drawn from the selected box then the probability that it has come from box B is

The mcan and standard deviation of a binomial variate X are 4 and √3 respectively. Then P (X ≥ 1)   =

A tetrahedron has vertices at O (0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C (-1, 1, 2). Then the angle between the faces OAB and ABC will be

Given that θ is a acute and that sin θ =3/5. Let x,y be positive real numbers such that 3(x-y) =1, then one set of solutions for x and y expressed in terms of θ is given by

If the vectors  and   
are coplanar, then the value of