Mathematics questions
18011 published questions with worked solutions.
- Let the range of the function f(x) = 6 + 16 x ( 3 -x ) ( 3 +x ) 3x 6x, x R be [ , ]. Then the distance of the point ( , ) from...
- Let the shortest distance from (a, 0), a > 0, to the parabola y^2 = 4x be 4. Then the equation of the circle passing through the...
- Let X = R × R. Define a relation R on X as: (a_1, b_1) R (a_2, b_2) b_1 = b_2. Statement-I: R is an equivalence relation....
- The length of the chord of the ellipse x^2 4 + y^2 2 = 1, whose mid-point is (1, 1 2 ), is :
- Let A = [a_ ij ] be a 3 × 3 matrix such that A bmatrix 0 1 0 bmatrix = bmatrix 0 0 1 bmatrix , A bmatrix 4 1 3 bmatrix = bmatrix...
- The number of complex numbers z, satisfying |z| = 1 and | z z + z z | = 1, is
- If the square of the shortest distance between the lines x-2 1 = y-1 2 = z+3 -3 and x+1 2 = y+3 4 = z+5 -5 is m n , where m, n...
- If I = _0^ /2 ^ 3/2 x ^ 3/2 x + ^ 3/2 x dx, then _0^ 2I x x x ^4 x + ^4 x dx, equals :
- _ x (2x^2 - 3x + 5)(3x-1)^ x/2 (3x^2+5x+4) (3x+2)^x is equal to:
- The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is...
- The variance of the numbers 8, 21, 34, 47, …, 320, is _____.
- The roots of the quadratic equation 3x^2 – px + q = 0 are 10th and 11th terms of an arithmetic progression with common difference...
- The value of _ e^2 ^ e^4 1 x ( e^ (( _e x)^2+1)^ -1 e^ (( _e x)^2+1)^ -1 +e^ ((6- _e x)^2+1)^ -1 )dx is-
- Let I(x) = dx (x-11)^ 11/13 (x+15)^ 15/13 . If I(37) - I(24) = 1 4 ( 1 b^ 1/13 - 1 c^ 1/13 ), b, c N, then 3(b+c) is equal to-
- If the function f(x) = cases 2 x (k_1+1)x + (k_2-1)x , & x < 0 4, & x=0 2 x _e ( 2+k_1x 2+k_2x ), & x>0 cases is continuous at x...
- If the line 3x – 2y + 12 = 0 intersects the parabola 4y = 3x^2 at the points A and B, then at the vertex of the parabola, the...
- Let a curve y = f(x) pass through the points (0, 5) and ( _e2, k). If the curve satisfies the differential equation 2(3+y)e^ 2x...
- Let f(x) = _ex and g(x) = x^4-2x^3+3x^2-2x+2 2x^2-2x+1 . Then the domain of fog is-
- If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms,...
- Let | z -i 2 z +i | = 1 3 , Z ∈ C, be the equation of a circle with center at C. If the area of the triangle, whose vertices are...