Mathematics questions
18011 published questions with worked solutions.
- Let Ajay will not appear in JEE exam with probability p = 27, while both Ajay and Vijay will appear in the exam with probability...
- If the domain of the function f(x) = x^2 - 25 (4 - x^2) + _ 10 (x^2 + 2x - 15) is (−∞, α) ∪ [β, ∞), then α² + β³ is equal to:
- Consider a ΔABC where A(1, 3, 2), B(−2, 8, 0) and C(3, 6, 7). If the angle bisector ∠BAC meets the line BC at D, then the length...
- Let S_n denote the sum of the first n terms of an arithmetic progression. If S_ 10 = 390 and the ratio of the tenth the fifth...
- Let α and β be the roots the equation px² + qx − r = 0, where p ≠ 0. If p, q and r be the consecutive terms of a non-constant...
- Let the locus of the midpoints of the chords of the circle x² + (y − 1)² = 1 drawn from the origin intersect the line x + y = 1...
- If the mirror image of the point P(3, 4, 9) in the line x - 1 3 = y + 1 2 = z - 2 1 is (α, β, γ), then 14(α + β + γ) is:
- Let m and n be the coefficients of seventh and thirteenth terms respectively in the expansion of ( 13x^ 13 + 1 2x^ 23 )^ 18 ....
- Let the system of equations x + 2y + 3z = 5, 2x + 3y + z = 9, 4x + 3y + λz = μ have infinite number of solutions. Then λ + 2μ is...
- Let P be a point on the ellipse x^2 9 + y^2 4 = 1. Let the line passing through P and parallel to y-axis meet the circle x² + y²...
- Consider the relations R_1 and R_2 defined as aR_1b ⇔ a² + b² = 1 for all a, b ∈ R and (a, b) R_2 (c, d) ⇔ a + d = b + c for all...
- Let P and Q be the points on the line x + 3 8 = y - 4 2 = z + 1 2 which are at a distance of 6 units from the point R(1, 2, 3)....
- Let f(x) = |2x² + 5|x| − 3|, x ∈ R. If m and n denote the number of points where f is not continuous and not differentiable...
- Consider 10 observations x_1, x_2, , x_ 10 such that _ i=1 ^ 10 (x_i - ) = 2 and _ i=1 ^ 10 (x_i - )^2 = 40, where α, β are...
- The number of solutions of the equation 4 sin²x − 4 cos³x + 9 − 4 cos x = 0; x ∈ [−2π, 2π] is:Not in JEE Main syllabus
- The value of _0^1(2x^3 - 3x^2 - x + 1)^3dx is equal to:
- Let A = I_2 − 2MM^T, where M is a real matrix of order 2 × 1 such that the relation M^TM = I_1 holds. If λ is a real number such...
- If three successive terms of a G.P. with common ratio r (r > 1) are the lengths of the sides of a triangle and [r] denotes the...
- The sum of squares of all possible values of k, for which area of the region bounded by the parabolas 2y² = kx and ky² = 2(y − x)...
- If y = ( x + 1)(x^2 - x) x x + x + x + 1 15 (3 ^2x - 5) ^3x, then 96 ,y' ( 6 ) is equal to ______.