Mathematics questions
18011 published questions with worked solutions.
- If a > 0 and z = (1 + i)^2 a - i , has magnitude 25 , then z is equal to:
- If the length of the perpendicular from the point (β, 0, β) (β ≠ 0) to the line, x 1 = y-1 0 = z+1 -1 is 32 , then β is equal to:
- If _1 = vmatrix x & & - & -x & 1 & 1 & x vmatrix and _2 = vmatrix x & 2 & 2 - 2 & -x & 1 2 & 1 & x vmatrix , x ≠ 0; then for all...
- Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional...
- If _ x 1 x^4 - 1 x - 1 = _ x k x^3 - k^3 x^2 - k^2 , then k is:
- If a directrix of a hyperbola centred at the origin and passing through the point (4, -2 3) is 5x = 4 5 and its eccentricity is...
- If f(x) = cases (p+1)x + x x , & x < 0 q, & x = 0 x + x^2 - x x^ 3/2 , & x > 0 cases is continuous at x = 0, then the ordered...
- If the coefficients of x^2 and x^3 are both zero, in the expansion of the expression (1 + ax + bx^2)(1 - 3x)^ 15 in powers of x,...
- If the circles x^2 + y^2 + 5Kx + 2y + K = 0 and 2(x^2 + y^2) + 2Kx + 3y - 1 = 0, (K ∈ R), intersect at the points P and Q, then...
- The sum 3 1^3 1^2 + 5 (1^3 + 2^3) 1^2 + 2^2 + 7 (1^3 + 2^3 + 3^3) 1^2 + 2^2 + 3^2 + up to 10th term is:
- Let f: R R be differentiable at c ∈ R and f(c) = 0. If g(x) = |f(x)|, then at x = c, g is:
- If Q(0, −1, −3) is the image of the point P in the plane 3x − y + 4z = 2 and R is the point (3, −1, −2), then the area (in sq....
- If dx (x^2 - 2x + 10)^2 = A ( ^ -1 ( x-1 3 ) + f(x) x^2 - 2x + 10 ) + C where C is a constant of integration then:
- The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, −3), then its radius is:
- The value of _0^ 2 [ 2x(1 + 3x)] ,dx, where [t] denotes the greatest integer function is:
- Let A(3, 0, −1), B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the midpoint of AC. If G divides BM in the...
- If the system of linear equations x + y + z = 5, x + 2y + 2z = 6, x + 3y + λz = μ, (λ, μ ∈ R), has infinitely many solutions,...
- The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is...
- If for some x ∈ R, the frequency distribution of the marks obtained by 20 students in a test is: | Marks | 2 | 3 | 5 | 7 |...
- If a_1, a_2, a_3, , a_n are in A.P. and a_1 + a_4 + a_7 + + a_ 16 = 114, then a_1 + a_6 + a_ 11 + a_ 16 is equal to: