Practice questions
88551 published questions with worked solutions.
- Let α, α + 2, α ∈ ℤ, be the roots of the quadratic equation x(x + 2) + (x + 1)(x + 3) + (x + 2)(x + 4) + … + (x + n − 1)(x + n +...
- Let x and y be real numbers such that 50 ( 2x 1 + 3i - y 1 - 2i ) = 31 + 17i, i = √−1. Then the value of 10(x − 3y) is:
- Let α, β ∈ ℝ be such that the system of linear equations x + 2y + z = 5, 2x + y + αz = 5, 8x + 4y + βz = 18 has no solution. Then...
- Let A = bmatrix 1 & 2 1 & bmatrix and B = bmatrix 3 & 3 & 2 bmatrix . If A² − 4A + I = O and B² − 5B − 6I = O, then among the two...
- Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of...
- The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least...
- If the mean of the data | Class | 5 − 10 | 10 − 15 | 15 − 20 | 20 − 25 | 25 − 30 | 30 − 35 | |---|---|---|---|---|---|---| |...
- Let the mid points of the sides of a triangle ABC be ( 52, 7 ), ( 52, 3 ) and (4, 5). If its incentre is (h, k), then 3h + k is...
- Let an ellipse x^2 a^2 + y^2 b^2 = 1, a < b, pass through the point (4, 3) and have eccentricity 5 3 . Then the length of its...
- If ( 18 ) ( 5 18 ) ( 7 18 ) = K, then the value of ( 10K 3 ) is:
- Let S = x ∈ [−π, π] : sin x(sin x + cos x) = a, a ∈ ℤ . Then n(S) is equal to:Not in JEE Main syllabus
- If the point of intersection of the lines x + 1 3 = y + a 5 = z + b + 1 7 and x - 2 1 = y - b 4 = z - 2a 7 lies on xy-plane, then...
- If a and b are two vectors such that | a| = 2 and | b| = 3, then the maximum value of 3|3 a + 2 b| + 4|3 a − 2 b| is:
- Let a line L passing through the point (1, 1, 1) be perpendicular to both the vectors 2î + 2ĵ + k̂ and î + 2ĵ + 2k̂. If P(a, b,...
- If _ x 2 (x^3 - 5x^2 + ax + b) ( x - 1 - 1) _e(x - 1) = m, then a + b + m is equal to:
- The number of critical points of the function f(x) = cases | x x |, & x 0 1, & x = 0 cases in the interval (−2π, 2π) is equal to:
- Let [·] denote the greatest integer function. Then the value of _0^3 ( e^x + e^ -x [x]! )dx is:
- Let y = y(x) be the solution curve of the differential equation (1 + sin x) dy dx + (y + 1)cos x = 0, y(0) = 0. If the curve y =...
- If the domain of the function f(x) = _ (0.6) ( | 2x - 5 x^2 - 4 | ) is (−∞, a] ∪ b ∪ [c, d) ∪ (e, ∞), then the value of a + b + c...
- If _ k=1 ^ n a_k = 6n^3, then _ k=1 ^ 6 ( a_ k+1 - a_k 36 )^2 is equal to _______.