JEE Main questions
34495 published questions with worked solutions.
- If ^4 + 4 ^4 + 2 = 4 2 ; α, β ∈ [0, π], then cos(α + β) − cos(α − β) is equal to:
- If a circle of radius R passes through the origin O and intersects the coordinate axes at A and B, then the locus of the foot of...
- The integral 3x^ 13 + 2x^ 11 (2x^4 + 3x^2 + 1)^4 dx is equal to: (where C is a constant of integration)
- Let S and S′ be the foci of an ellipse and B be any one of the extremities of its minor axis. If ΔS′BS is a right angled triangle...
- Let Z be the set of integers. If A = x Z : 2^ (x+2)(x^2-5x+6) = 1 and B = x Z : -3 < 2x - 1 < 9 , then the number of subsets of...
- Let S be the set of all real values of λ such that a plane passing through the points (- ^2, 1, 1), (1, - ^2, 1) and (1, 1, - ^2)...
- If the function f given by f(x) = x^3 - 3(a - 2)x^2 + 3ax + 7, for some a ∈ R is increasing in (0, 1] and decreasing in [1, 5),...
- _ n ( n n^2 + 1^2 + n n^2 + 2^2 + n n^2 + 3^2 + + 1 5n ) is equal to:
- In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is...
- If A = bmatrix 1 & & 1 - & 1 & -1 & - & 1 bmatrix ; then for all ( 3 4 , 5 4 ), det(A) lies in the interval:
- Let z_1 and z_2 be two complex numbers satisfying |z_1| = 9 and |z_2 - 3 - 4i| = 4. Then the minimum value of |z_1 - z_2| is:
- If ^nC_4, ^nC_5 and ^nC_6 are in A.P., then n can be:
- If the angle of elevation of a cloud from a point P which is 25 m above a lake be 30° and the angle of depression of reflection...Not in JEE syllabus
- Let f be a differentiable function such that f(1) = 2 and f′(x) = f(x) for all x ∈ R. If h(x) = f(f(x)), then h′(1) is equal to:
- If an angle between the line, x+1 2 = y-2 1 = z-3 -2 and the plane, x − 2y − kz = 3 is ^ -1 ( 2 2 3 ), then a value of k is:
- If a straight line passing through the point P(−3, 4) is such that its intercepted portion between the coordinate axes is...
- Let a, b and c be three unit vectors, out of which vectors b and c are non-parallel. If α and β are the angles which vector a...
- The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then...
- The tangent to the curve y = x^2 - 5x + 5, parallel to the line 2y = 4x + 1, also passes through the point:
- The set of all values of λ for which the system of linear equations x − 2y − 2z = λx, x + 2y + z = λy, −x − y = λz has a...