Mathematics questions
18011 published questions with worked solutions.
- The tangent to the circle C_1 : x^2 + y^2 - 2x - 1 = 0 at the point (2, 1) cuts off a chord of length 4 from a circle C_2 whose...
- Suppose A is any 3 × 3 non-singular matrix and (A – 3I) (A – 5I) = O, where I = I_3 and O = O_3. If A + A^ -1 = 4I, then + is...
- The value of integral _ /4 ^ 3 /4 x 1 + x ,dx is -
- A tower T_1 of height 60 m is located exactly opposite to a tower T_2 of height 80 m on a straight road. From the top of T_1, if...Not in JEE syllabus
- If I_1 = _0^1 e^ -x ^2 x ,dx; I_2 = _0^1 e^ -x^2 ^2 x ,dx and I_3 = _0^1 e^ -x^3 ,dx; then -
- The sides of a rhombus ABCD are parallel to the lines, x - y + 2 = 0 and 7x - y + 3 = 0. If the diagonals of the rhombus...
- _ x 0 x 2x - 2x x (1 - 2x)^2 equals -
- Let f(x) = cases (x - 1)^ 1 2 - x , & x > 1, x 2 k, & x = 2 cases The value of k for which f is continuous at x = 2 is -
- If a, b, c are in A.P. and a^2, b^2, c^2 are in G.P. such that a < b < c and a + b + c = 3 4 , then the value of a is -
- Tangents drawn from the point (–8, 0) to the parabola y^2 = 8x touch the parabola at P and Q. If F is the focus of the parabola,...
- If the system of equations 2x + 3y - z = 0, x + ky - 2z = 0 and 2x - y + z = 0 has a non-trivial solution (x, y, z), then x y + y...
- The common tangent to the circles x^2 + y^2 = 4 and x^2 + y^2 + 6x + 8y - 24 = 0 also passes through the point:
- If e^ x ( x x ,f(x) + ( x x + ^2x) )dx = e^ x f(x) + C, then a possible choice of f(x) is:
- If the tangent to the parabola y^2 = x at a point (α, β), (β > 0) is also a tangent to the ellipse, x^2 + 2y^2 = 1, then α is...
- The total number of matrices A = pmatrix 0 & 2y & 1 2x & y & -1 2x & -y & 1 pmatrix , (x, y ∈ R, x ≠ y) for which A^TA = 3I_3 is:
- If f: R R is a differentiable function and f(2) = 6, then _ x 2 _6^ f(x) 2t ,dt (x-2) is:
- If a unit vector a makes angles π/3 with i, π/4 with j and θ ∈ (0, π) with k, then a value of θ is:
- The area (in sq. units) of the smaller of the two circles that touch the parabola, y^2 = 4x at the point (1, 2) and the x-axis is:
- Two newspapers A and B are published in a city. It is known that 25% of the city population reads A and 20% reads B while 8%...
- The sum of the series 1 + 2 × 3 + 3 × 5 + 4 × 7 + .... up to 11th term is: