Mathematics questions
18011 published questions with worked solutions.
- 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...
- Let f: R R be a differentiable function satisfying f'(3) + f'(2) = 0. Then _ x 0 ( 1 + f(3+x) - f(3) 1 + f(2-x) - f(2) )^ 1/x is...
- Let the numbers 2, b, c be in an A.P. and A = bmatrix 1 & 1 & 1 2 & b & c 4 & b^2 & c^2 bmatrix . If det(A) ∈ [2, 16], then c...
- Two vertical poles of heights, 20 m and 80 m stand apart on a horizontal plane. The height (in meters) of the point of...
- Let = 3 i + j and = 2 i - j + 3 k. If = _1 - _2, where _1 is parallel to and _2 is perpendicular to , then _1 _2 is equal to:
- Let S be the set of all values of x for which the tangent to the curve y = f(x) = x^3 - x^2 - 2x at (x, y) is parallel to the...
- Let S = [-2 , 2 ] : 2 ^2 + 3 = 0 . Then the sum of the elements of S is:Not in JEE Main syllabus
- For any two statements p and q, the negation of the expression p ( p q) is:Not in JEE syllabus
- The solution of the differential equation x dy dx + 2y = x^2 (x 0) with y(1) = 1, is: