Practice questions
88551 published questions with worked solutions.
- Given that the slope of the tangent to a curve y = y(x) at any point (x, y) is 2y x^2 . If the curve passes through the centre of...
- Let f: [-1, 3] R be defined as f(x) = cases |x| + [x], & -1 x < 1 x + |x|, & 1 x < 2 x + [x], & 2 x 3 cases where [t] denotes the...
- The vector equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is...
- The sum _ k=1 ^ 20 k , 1 2^k is equal to:
- The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is:
- If the fourth term in the binomial expansion of ( x^ 1 1+ _ 10 x + x^ 1 12 )^6 is equal to 200, and x > 1, then the value of x is:
- In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci...
- Let a = 3 i + 2 j + x k and b = i - j + k, for some real x. Then | a b| = r is possible if:
- Let S( ) = (x, y) : y^2 x, 0 x and A(α) is area of the region S(α). If for a λ, 0 < λ < 4, A(λ) : A(4) = 2 : 5, then λ equals:
- If f(1) = 1, f′(1) = 3, then the derivative of f(f(f(x))) + (f(x))^2 at x = 1 is:
- The tangent and the normal lines at the point ( 3, 1) to the circle x^2 + y^2 = 4 and the x-axis form a triangle. The area of...
- The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is:
- Suppose that the points (h, k), (1, 2) and (−3, 4) lie on the line L_1. If a line L_2 passing through the points (h, k) and (4,...
- If the system of linear equations x - 2y + kz = 1, 2x + y + z = 2, 3x - y - kz = 3 has a solution (x, y, z), z ≠ 0, then (x, y)...
- The tangent to the parabola y^2 = 4x at the point where it intersects the circle x^2 + y^2 = 5 in the first quadrant, passes...
- The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3, 4, 5 (repetition of...
- The number of integral values of m for which the equation (1 + m^2)x^2 - 2(1 + 3m)x + (1 + 8m) = 0 has no real root is:
- Let f(x) = _0^x g(t) ,dt, where g is a non-zero even function. If f(x + 5) = g(x), then _0^x f(t) ,dt equals:
- If z = 3 2 + i 2 (i = -1 ), then (1 + iz + z^5 + iz^8)^9 is equal to:
- If the eccentricity of the standard hyperbola passing through the point (4, 6) is 2, then the equation of the tangent to the...