JEE Main questions
34495 published questions with worked solutions.
- Let f : [−1, 2] → R be given by f(x) = 2x² + x + [x²] − [x], where [t] denotes the greatest integer less than or equal to t. The...
- The differential equation of the family of circles passing the origin and having center at the line y = x is:
- Let S_1 = z ∈ C : |z| ≤ 5 , S_2 = z C : Im ( z + 1 - 3i 1 - 3i ) 0 and S_3 = z ∈ C : Re(z) ≥ 0 . Then the area of region S_1 ∩...
- The area enclosed between the curves y = x|x| and y = x − |x| is:
- Let a = 2 i + 5 j - k, b = 2 i - 2 j + 2 k and c be three vectors such that ( c + i) ( a + b + i) = a ( c + i), a c = -29, then c...
- Consider three vectors a, b, c. Let | a| = 2, | b| = 3 and a = b c. If α ∈ [0, 3 ] is the angle between the vectors b and c, then...
- Let A(−1, 1) and B(2, 3) be two points and P be a variable point above the line AB such that the area of ΔPAB is 10. If the locus...
- Let (α, β, γ) be the image of the point (8, 5, 7) in the line x - 1 2 = y + 1 3 = z - 2 5 . Then α + β + γ is equal to
- If the constant term in the expansion of ( [5] 3 x + 2x [3] 5 )^ 12 , x ≠ 0, is α × 2⁸ × [5] 3 , then 25α is equal to:
- Let f, g : R → R be defined as: f(x) = |x − 1| and g(x) = cases e^x, & x 0 x + 1, & x 0 cases . Then the function f(g(x)) is
- Let the circle C_1: x² + y² − 2(x + y) + 1 = 0 and C_2 be a circle having centre at (−1, 0) and radius 2. If the line of the...
- Let the set S = 2, 4, 8, 16, ....., 512 be partitioned into 3 sets A, B, C with equal number of elements such that A ∪ B ∪ C = S...
- The values of m, n, for which the system of equations x + y + z = 4, 2x + 5y + 5z = 17, x + 2y + mz = n has infinitely many...
- The coefficients a, b, c in the quadratic equation ax² + bx + c = 0 are from the set 1, 2, 3, 4, 5, 6 . If the probability of...
- Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the...
- Let β(m, n) = _0^1x^ m-1 (1 - x)^ n-1 dx, m, n > 0. If _0^1(1 - x^ 10 )^ 20 dx = a (b, c), then 100(a + b + c) equals _______.
- Let αβ ≠ 0 and A = bmatrix & & 3 & & - & & 2 bmatrix . If B = bmatrix 3 & -9 & 3 - & 7 & -2 -2 & 5 & -2 bmatrix is the matrix of...
- If y( ) = 2 + 2 3 + 4 2 + 5 + 2 , then at θ = 2, y″ + y′ + y is equal to:
- For x ≥ 0, the least value of K, for which 4^ 1+x + 4^ 1-x , K2, 16^x + 16^ -x are three consecutive terms of an A.P. is equal to:
- Let the mean and the standard deviation of the probability distribution | X | α | 1 | 0 | −3 | |---|---|---|---|---| | P(X) | 1/3...