Mathematics questions
18011 published questions with worked solutions.
- 5 students of a class have an average height 150 cm and variance 18 cm^2. A new student, whose height is 156 cm, joined them. The...
- Let A = (- 2, ) : 3 + 2i 1 - 2i is purely imaginary . Then the sum of the elements in A is:
- Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from...
- For any ( 4, 2 ), the expression 3( - )^4 + 6( + )^2 + 4 ^6 equals:
- Equation of a common tangent to the circle x^2 + y^2 - 6x = 0 and the parabola, y^2 = 4x, is:
- Let a_1, a_2, , a_ 30 be an A.P., S = _ i=1 ^ 30 a_i and T = _ i=1 ^ 15 a_ (2i-1) . If a_5 = 27 and S − 2T = 75, then a_ 10 is...
- For x^2 n + 1, n ∈ N (the set of natural numbers), the integral x 2 (x^2-1) - 2(x^2-1) 2 (x^2-1) + 2(x^2-1) ,dx is equal to:...
- If ^ -1 ( 2 3x ) + ^ -1 ( 3 4x ) = 2 (x > 34 ), then x is equal to:
- Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0. Which one of the following statements is true?
- Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of...
- The equation of the line passing through (−4, 3, 1), parallel to the plane x + 2y − z − 5 = 0 and intersecting the line x+1 -3 =...
- The plane through the intersection of the planes x + y + z = 1 and 2x + 3y − z + 4 = 0 and parallel to y-axis also passes through...
- If θ denotes the acute angle between the curves, y = 10 - x^2 and y = 2 + x^2 at a point of their intersection, then |tan θ| is...
- The value of _0^ | x|^3 ,dx is:
- The area (in sq. units) bounded by the parabola y = x^2 - 1, the tangent at the point (2, 3) to it and the y-axis is:
- If y = y(x) is the solution of the differential equation, x dy dx + 2y = x^2 satisfying y(1) = 1, then y ( 12 ) is equal to:
- Let 0 < < 2. If the eccentricity of the hyperbola x^2 ^2 - y^2 ^2 = 1 is greater than 2, then the length of its latus rectum lies...
- The integral 2x^3 - 1 x^4 + x dx is equal to: (Here C is a constant of integration)
- For x ∈ (0, 3/2), let f(x) = x, g(x) = tan x and h(x) = 1 - x^2 1 + x^2 . If φ(x) = ((hof)og)(x), then ( 3 ) is equal to:
- If _0^ /2 x x + x dx = m( + n), then m · n is equal to: