Mathematics questions
18011 published questions with worked solutions.
- The sum of all rational terms in the expansion of (2+ 3)^8 is
- The sum 1 + 3 + 11 + 25 + 45 + 71 + ..... upto 20 terms, is equal to
- If the domain of the function f(x) = _e ( 2x-3 5+4x ) + ^ -1 ( 4+3x 2-x ) is [ , ), then ^2 + 4 is equal to
- Let f(x) = x^3 3-x^2 ,dx. If 5f( 2) = -4, then f(1) is equal to
- Let a_1, a_2, a_3, be a G.P of increasing positive numbers. If a_3a_5 = 729 and a_2+a_4 = 111 4 , then 24(a_1+a_2+a_3) is equal to
- Let α and β be the roots of x^2+ 3x-16=0, and γ and δ be the roots of x^2+3x-1=0. If P_n = ^n+ ^n and Q_n = ^n+ ^n, then P_ 25 +...
- If y(x) = vmatrix x & x & x+ x+1 27&28&27 1&1&1 vmatrix , x R, then d^2y dx^2 +y is equal to
- Let a = i+ j+ k, b = 3 i+2 j- k, c = j+ k and d be a unit vector such that a d = b d and c. d = 1. If c is perpendicular to a,...
- Let the product of the focal distances of the point (4, 2 3) on the hyperbola H : x^2 a^2 - y^2 b^2 =1 be 32. Let the length of...
- 1 + 3 + 5^2 + 7 + 9^2 + … upto 40 terms is equal to
- Considering the principal values of the inverse trigonometric functions, ^ -1 ( 3 2 x + 1 2 1-x^2 ), - 1 2 < x < 1 2 , is equal to
- Let A = 1, 6, 11, 16, … and B 9, 16, 23, 30, … be the sets consisting of the first 2025 terms of two arithmetic progressions....
- Consider two vectors u = 3 i - j and v = 2 i + j - k , λ > 0. The angle between them is given by ^ -1 ( 5 2 7 ). Let v = v_1 +...
- Let f, g : (1, ∞) → ℝ be defined as f(x) = 2x+3 5x+2 and g(x) = 2-3x 1-x . If the range of the function fog : [2, 4] → ℝ is [α,...
- In the expansion of ( [3] 2 + 1 [3] 3 )^n, n ∈ ℕ, if the ratio of 15th term from the beginning to the 15th term from the end is 1...
- The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers...
- If 10 ^4 + 15 ^4 = 6, then the value of 27 ^6 + 8 ^6 16 ^8 is
- Consider the equation x^2 + 4x – n = 0 where n ∈ [20, 100] is a natural number. Then the number of all distinct values of n, for...
- The value of _ -1 ^ 1 (1+ |x|-x )e^x + ( |x|-x )e^ -x e^x+e^ -x dx is equal to
- If _ x 1 (x-1)(6+ (x-1))+ (1-x) (x-1)^3 = -1, where λ, μ ∈ ℝ, then λ + μ is equal to