Mathematics questions
18011 published questions with worked solutions.
- Let f : R → R be a function given by f(x) = cases 1 - 2x x^2 , & x < 0 , & x = 0 1 - x x , & x > 0 cases , where α, β ∈ R. If f...
- Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected...
- If the solution y = y(x) of the differential equation (x^4 + 2x^3 + 3x^2 + 2x + 2)dy - (2x^2 + 2x + 3)dx = 0 satisfies y(-1) = -...
- Let the sum of the maximum and the minimum values of the function f(x) = 2x^2 - 3x + 8 2x^2 + 3x + 8 be mn where gcd(m, n) = 1....
- One of the points of intersection of the curves y = 1 + 3x − 2x² and y = 1x is ( 12, 2 ). Let the area of the region enclosed by...
- If the system of equations x + (√2 sin α)y + (√2 cos α)z = 0, x + (cos α)y + (sin α)z = 0, x + (sin α)y − (cos α)z = 0 has a...
- There are 5 points P_1, P_2, P_3, P_4, P_5 on the side AB, excluding A and B, of a triangle ABC. Similarly there are 6 points...
- Let f(x) = cases -2, & -2 x 0 x - 2, & 0 < x 2 cases and h(x) = f(|x|) + |f(x)|. Then _ -2 ^ 2 h(x) ,dx is equal to-
- The sum of all rational terms in the expansion of (2^ 15 + 5^ 13 )^ 15 is equal to-
- Let a unit vector which makes an angle of 60º with 2 i + 2 j - k and an angle of 45º with i - k be C. Then C + (- 12 i + 1 3 2 j...
- Let the first three terms 2, p and q, with q ≠ 2, of a G.P. be respectively the 7th, 8th and 13th terms of an A.P. If the 5th...
- Let a, b ∈ R. Let the mean and the variance of 6 observations −3, 4, 7, −6, a, b be 2 and 23, respectively. The mean deviation...
- If 2 and 6 are the roots of the equation ax² + bx + 1 = 0, then the quadratic equation, whose roots are 1 2a + b and 1 6a + b ,...
- Let α and β be the sum and the product of all the non-zero solutions of the equation ( z)^2 + |z| = 0, z ∈ C. Then 4(α² + β²) is...
- Let the point, on the line passing through the points P(1, −2, 3) and Q(5, −4, 7), farther from the origin and at a distance of 9...
- A square is inscribed in the circle x² + y² − 10x − 6y + 30 = 0. One side of this square is parallel to y = x + 3. If (x_i, y_i)...
- If the domain of the function ^ -1 ( 3x - 22 2x - 19 ) + _e ( 3x^2 - 8x + 5 x^2 - 3x - 10 ) is (α, β], then 3α + 10β is equal to-
- Let f(x) = x⁵ + 2e^ x/4 for all x ∈ R. Consider a function g(x) such that (gof)(x) = x for all x ∈ R. Then the value of 8g′(2) is:
- Let α ∈ (0, ∞) and A = bmatrix 1 & 2 & 1 & 0 & 1 0 & 1 & 2 bmatrix . If det(adj(2A − Aᵀ) · adj(A − 2Aᵀ)) = 2⁸, then (det(A))² is...
- In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied...