Mathematics questions
18011 published questions with worked solutions.
- Let f(x) = e^x - x and g(x) = x^2 - x, ∀ x ∈ R. Then the set of all x ∈ R, where the function h(x) = (f∘g)(x) is increasing, is:
- If the line x − 2y = 12 is tangent to the ellipse x^2 a^2 + y^2 b^2 = 1 at the point (3, - 92 ), then the length of the latus...
- Let z_0 be a root of the quadratic equation, x^2 + x + 1 = 0. If z = 3 + 6iz_0^ 81 - 3iz_0^ 93 , then arg z is equal to:
- Let f: [0, 1] → R be such that f(xy) = f(x)·f(y), for all x, y ∈ [0, 1], and f(0) ≠ 0. If y = y(x) satisfies the differential...
- The coefficient of t^4 in the expansion of ( 1 - t^6 1 - t )^3 is:
- Let a = i + j + 2 k, b = b_1 i + b_2 j + 2 k and c = 5 i + j + 2 k be three vectors such that the projection vector of b on a is...
- If f(x) = 5x^8 + 7x^6 (x^2 + 1 + 2x^7)^2 dx, (x ≥ 0), and f(0) = 0, then the value of f(1) is:
- If x = 3 tan t and y = 3 sec t, then the value of d^2y dx^2 at t = 4, is:
- The sum of the following series 1 + 6 + 9(1^2 + 2^2 + 3^2) 7 + 12(1^2 + 2^2 + 3^2 + 4^2) 9 + 15(1^2 + 2^2 + + 5^2) 11 + up to 15...
- Let a, b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P. If these are also the three consecutive terms...
- A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x-axis....
- Let the equations of two sides of a triangle be 3x − 2y + 6 = 0 and 4x + 5y − 20 = 0. If the orthocentre of this triangle is at...
- A data consists of n observations: x_1, x_2, , x_n. If _ i=1 ^n(x_i + 1)^2 = 9n and _ i=1 ^n(x_i - 1)^2 = 5n, then the standard...
- If 0 x < 2, then the number of values of x for which sin x − sin 2x + sin 3x = 0, is:Not in JEE Main syllabus
- If the lines x = ay + b, z = cy + d and x = a′z + b′, y = c′z + d′ are perpendicular then:
- The equation of the plane containing the straight line x2 = y3 = z4 and perpendicular to the plane containing the straight lines...
- Let f be a differentiable function from R to R such that |f(x) - f(y)| 2|x - y|^ 3/2 , for all x, y ∈ R. If f(0) = 1 then _0^1...
- Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on...
- The area of the region A = (x, y) : 0 y x|x| + 1 and -1 x 1 in sq. units, is:
- If the circles x^2 + y^2 - 16x - 20y + 164 = r^2 and (x - 4)^2 + (y - 7)^2 = 36 intersect at two distinct points, then: