Mathematics questions
18011 published questions with worked solutions.
- Match List I with List II and select the correct answer using the code given below the lists : List I P. ( 1 y^2 ( ( ^ -1 y) + y...
- Consider the lines L_1 : x - 1 2 = y -1 = z + 3 1 , L_2 : x - 4 1 = y + 3 1 = z + 3 2 and the planes P_1 : 7x + y + 2z = 3, P_2 :...
- Match List – I with List – II and select the correct answer using the code given below the lists : List – I P. Volume of...
- Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M N^2 and M^2 = N^4, then
- For every pair of continuous functions f, g : [0, 1] → ℝ such that f(x) : x [0, 1] = g(x) : x [0, 1] , the correct statement(s)...
- Let f : (0, ∞) → ℝ be given by f(x) = _ 1 x ^ x e^ - (t + 1 t ) dt t . Then
- Let a ∈ ℝ and let f : ℝ → ℝ be given by f(x) = x^5 - 5x + a. Then
- Let f : [a, b] → [1, ∞) be a continuous function and let g : ℝ → ℝ be defined as g(x) = cases 0 & if x < a, _a^x f(t) ,dt & if a...
- From a point P(λ, λ, λ), perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = −x, z = −1. If P is...
- Let x, y and z be three vectors each of magnitude 2 and the angle between each pair of them is 3 . If a is a nonzero vector...
- A circle S passes through the point (0, 1) and is orthogonal to the circles (x - 1)^2 + y^2 = 16 and x^2 + y^2 = 1. Then
- Let M be a 2 × 2 symmetric matrix with integer entries. Then M is invertible if
- Let a, b, c be positive integers such that b a is an integer. If a, b, c are in geometric progression and the arithmetic mean of...
- Let f : ℝ → ℝ and g : ℝ → ℝ be respectively given by f(x) = |x| + 1 and g(x) = x^2 + 1. Define h : ℝ → ℝ by h(x) = cases f(x),...
- The value of _0^1 4x^3 d^2 dx^2 (1 - x^2)^5 dx is
- The slope of the tangent to the curve (y - x^5)^2 = x(1 + x^2)^2 at the point (1, 3) is
- The largest value of the nonnegative integer a for which _ x 1 -ax + (x - 1) + a x + (x - 1) - 1 ^ 1-x 1- x = 1 4 is
- Let f : [0, 4π] → [0, π] be defined by f(x) = ^ -1 ( x). The number of points x ∈ [0, 4π] satisfying the equation f(x) = 10 - x...
- Let a, b, and c be three non-coplanar unit vectors such that the angle between every pair of them is 3 . If a b + b c = p a + q b...
- The following integral _ 4 ^ 2 (2 , cosec ,x)^ 17 ,dx is equal to