Practice questions
88551 published questions with worked solutions.
- Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, x^2 4 + y^2 2...
- The area (in sq. units) of the region A (x, y) : |x| + |y| < 1, 2y^2>|x| is :
- The position of a moving car at time t is given by f(t)=at^2+bt+c, t > 0, where a, b and c are real numbers greater than 1. Then...
- The general solution of the differential equation 1+x^2+y^2+x^2y^2 +xy dy dx =0 is (where C is a constant of integration) :
- Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that...
- If and be two roots of the equation x^2-64x+256=0. Then the value of ( ^3 ^5 )^ 1/8 + ( ^3 ^5 )^ 1/8 is -
- If f(x + y) = f(x) f(y) and _ x=1 ^ f(x)=2, x, y ∈ N, where N is the set of all natural numbers, then the value of f(4) f(2) is -
- If I_1= _0^1(1-x^ 50 )^ 100 dx and I_2= _0^1(1-x^ 50 )^ 101 dx such that I_2= I_1 then equals to -
- The shortest distance between the lines x-1 0 = y+1 -1 = z 1 and x + y + z + 1 = 0, 2x – y + z + 3 = 0 is -
- Let L_1 be a tangent to the parabola y^2=4(x+1) and L_2 be a tangent to the parabola y^2=8(x+2) such that L_1 and L_2 intersect...
- let a, b, c, d and p be any non zero distinct real numbers such that (a^2+b^2+c^2)p^2-2(ab+bc+cd)p+(b^2+c^2+d^2)=0. Then -
- The negation of the Boolean expression p ( p q) is equivalent to :Not in JEE syllabus
- The values of and for which the system of linear equations x + y + z = 2 x + 2y + 3z = 5 x + 3y + = has infinitely many solutions...
- A ray of light coming from the point (2,2 3 ) is incident at an angle 30º on the line x = 1 at the point A. The ray gets...
- Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets...
- The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to...Not in JEE syllabus
- Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8 m, BC = 11 m and AB = 10m; then the...
- Let f : R → R be defined as f(x)= cases x^5 ( 1 x )+5x^2, & x<0 0, & x=0 ^5 ( 1 x )+ x^2, & x>0 cases . The value of for which f...
- If a and b are unit vectors, then the greatest value of 3 | a + b |+| a - b | is ________.
- Two planets have masses M and 16 M and their radii are a and 2a, respectively. The separation between the centres of the planets...