Mathematics questions
18011 published questions with worked solutions.
- Choose the incorrect statement about the two circles whose equations are given below : x^2+y^2-10x-10y+41=0 and...
- Which of the following is true for y (x) that satisfies the differential equation dy dx =xy-1+x-y ; y(0) = 0 :
- The value of _ x 0^+ ^ -1 (x-[x]^2) ^ -1 (x-[x]^2) x-x^3 [x] denotes the greatest integer x is :
- If the function f(x) = ( x)- x x^4 is continuous at each point in its domain and f(0) = 1 k , then k is ——
- If f(x) = ( ^ -1 ( 1-2^ 2x 1+2^ 2x ) ) and its first derivative with respect to x is - b a _e2 when x = 1, where a and b are...
- Let there be three independent events E_1, E_2 and E_3. The probability that only E_1 occurs is , only E_2 occurs is and only E_3...
- If a = i + j +3 k , b =- i - j - k and c = i -2 j - k such that a . b =1 and b . c =-3, then 1 3 (( a b ). c ) is equal to ——
- If A= bmatrix 2&3 0&-1 bmatrix , then the value of det(A^4) + det(A^ 10 – (Adj(2A))^ 10 ) is equal to ——
- The minimum distance between any two points P_1 and P_2 while considering point P_1 on one circle and point P_2 on the other...
- If the equation of the plane passing through the line of intersection of the planes 2x – 7y + 4z – 3 = 0, 3x – 5y + 4z + 11 = 0...
- If (2021)^ 3762 is divided by 17, then the remainder is ——
- Let y = y(x) be the solution of the differential equation dy dx =(y+1)((y+1)e^ x^2/2 -x), 0 < x < 2.1, with y(2) = 0. Then the...
- Let c , a , b be a triangle with | a |=8, | b |=7, | c |=10. Projection of vector c on b is equal to :
- Let the system of linear equations 4x + + 2z = 0 2x – y + z = 0 + 2y + 3z = 0, , R. has a non-trivial solution. Then which of the...
- Let f(x) = x-2 x-3 . Let g : R R be given as g(x) = 2x – 3. Then, f^ -1 (x)+g^ -1 (x) is equal to :
- Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be along the...
- Consider a hyperbola H : x^2-2y^2=4. Let the tangent at a point P(4, 6) meet the x-axis at Q and latus rectum at R(x_1,y_1),...
- Let g(x) = _0^xf(t)dt, where f is continuous function in [0, 3] such that 1 3 f(t) 1 for all t [0, 1] and 0 f(t) 1 2 for all t...
- Let S_1 be the sum of first 2n terms of an arithmetic progression. Let S_2 be the sum of first 4n terms of the same arithmetic...
- Let a complex number be w = 1- 3i. Let another complex number z be such that |zw| = 1 and arg(z) – arg(w) = 2 . Then the area of...