Practice questions
88551 published questions with worked solutions.
- Let the latus rectum of the parabola y^2=4x be the common chord to the circles C_1 and C_2 each of them having radius 2 5 . Then,...
- If the value of the integral _0^ 1/2 x^2 (1-x^2)^ 3/2 dx is k 6 , then k is equal to -
- Let x_i (1 i 10) be ten observations of a random variable X. If _ i=1 ^ 10 (x_i-p)=3 and _ i=1 ^ 10 (x_i-p)^2=9 where 0 p R, then...
- Let R_1 and R_2 be two relations defined as follows : R_1= (a,b) R^2; a^2+b^2 Q and R_2= (a,b) R^2: a^2+b^2 Q , where Q is the...
- The probability that a randomly chosen 5-digit number is made from exactly two digits is :
- Let p, q, r be three statements such that the truth value of (p q) ( q r) is F. Then the truth values of p, q, r are respectively.Not in JEE syllabus
- Let a, b, c R be such that a^2+b^2+c^2=1. If a =b ( + 2 3 )=c ( + 4 3 ), where = 9 , then the angle between the vectors a i +b j...
- If the sum of the series 20+19 3 5 +19 1 5 +18 4 5 + upto n^ th term is 488 and the n^ th term is negative, then-
- If z_1, z_2 are complex numbers such that Re (z_1)=|z_1-1|, Re (z_2)=|z_2-1| and (z_1-z_2)= 6 , then Im (z_1+z_2) is equal to -
- If ^ -1 ( x 1+x )dx=A(x) ^ -1 ( x )+B(x)+C, where C is a constant of integration, then the ordered pair (A(x), B(x)) can be -
- _ x a (a+2x)^ 1/3 -(3x)^ 1/3 (3a+x)^ 1/3 -(4x)^ 1/3 (a 0) is equal to -
- If the term independent of x in the expansion of ( 3 2 x^2- 1 3x )^9 is k, then 18 k is equal to -
- If x^3dy+xy ,dx=x^2dy+2y ,dx ; y(2) = e and x > 1, then y(4) is equal to -
- Let A be a 3 × 3 matrix such that adj A= bmatrix 2&-1&1 -1&0&2 1&-2&-1 bmatrix and B = adj (adj A). If |A| = and |(B^ -1 )^T|= ,...
- If the surface area of a cube is increasing at a rate of 3.6 cm ^2/sec, retaining its shape, then the rate of change of its...
- Suppose f(x) is a polynomial of degree four, having critical points at –1, 0, 1. If T= x R|f(x)=f(0) , then the sum of squares of...
- If a has vertices A(–1, 7), B(–7,1) and C(5, –5), then its orthocentre has coordinates -
- The plane which bisects the line joining the points (4, –2, 3) and (2, 4, –1) at right angles also passes through the point -
- The set of all real values of for which the quadratic equations, ( ^2+1)x^2-4 x+2=0 always have exactly one root in the interval...
- If the tangent to the curve, y=e^x at a point (c,e^c) and the normal to the parabola, y^2=4x at the point (1, 2) intersect at the...