Mathematics questions
18011 published questions with worked solutions.
- If _0^xf(t) ,dt = x^2 + _x^1t^2f(t) ,dt, then f' ( 12 ) is:
- Let A = bmatrix 2 & b & 1 b & b^2 + 1 & b 1 & b & 2 bmatrix where b > 0. Then the minimum value of (A) b is:
- The value of λ such that sum of the squares of the roots of the quadratic equation, x^2 + (3 - )x + 2 = has the least value is:
- On which of the following lines lies the point of intersection of the line, x-4 2 = y-5 2 = z-3 1 and the plane, x + y + z = 2?
- The positive value of λ for which the co-efficient of x^2 in the expression x^2 ( x + x^2 )^ 10 is 720, is:
- Let z = ( 3 2 + i2 )^5 + ( 3 2 - i2 )^5. If R(z) and I(z) respectively denote the real and imaginary parts of z, then:
- The number of values of θ ∈ (0, π) for which the system of linear equations x + 3y + 7z = 0, −x + 4y + 7z = 0, (sin 3θ)x + (cos...
- The curve amongst the family of curves represented by the differential equation, (x^2 - y^2)dx + 2xy ,dy = 0 which passes through...
- Let f: (−1, 1) → R be a function defined by f(x) = -|x|, - 1 - x^2 . If K be the set of all points at which f is not...
- If = ( - 2) a + b and = (4 - 2) a + 3 b be two given vectors where vectors a and b are non-collinear. The value of λ for which...
- The plane which bisects the line segment joining the points (−3, −3, 4) and (3, 7, 6) at right angles, passes through which one...
- If the area of an equilateral triangle inscribed in the circle x^2 + y^2 + 10x + 12y + c = 0 is 27 3 sq units then c is equal to:
- If x^5e^ -4x^3 dx = 1 48 e^ -4x^3 f(x) + C, where C is a constant of integration, then f(x) is equal to:
- A helicopter is flying along the curve given by y - x^ 3/2 = 7, (x ≥ 0). A soldier positioned at the point ( 12, 7 ) wants to...
- In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is...
- Let a = 2 i + _1 j + 3 k, b = 4 i + (3 - _2) j + 6 k, and c = 3 i + 6 j + ( _3 - 1) k be three vectors such that b = 2 a and a is...
- Consider the statement: "P(n): n^2 - n + 41 is prime". Then which one of the following is true?Not in JEE syllabus
- If a circle C passing through the point (4, 0) touches the circle x^2 + y^2 + 4x - 6y = 12 externally at the point (1, −1), then...
- If the parabolas y^2 = 4b(x - c) and y^2 = 8ax have a common normal, then which one of the following is a valid choice for the...
- The plane passing through the point (4, −1, 2) and parallel to the lines x+2 3 = y-2 -1 = z+1 2 and x-2 1 = y-3 2 = z-4 3 also...