Mathematics questions
18011 published questions with worked solutions.
- In R ^3, let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from...
- Let P and Q be distinct points on the parabola y^2=2x such that a circle with PQ as diameter passes through the vertex O of the...
- Let y(x) be a solution of the differential equation (1+e^x)y'+ye^x=1. If y(0)=2, then which of the following statements is (are)...
- Consider the family of all circles whose centers lie on the straight line y=x. If this family of circles is represented by the...
- Let g: R R be a differentiable function with g(0)=0, g'(0)=0 and g'(1) 0. Let f(x)= cases x |x| g(x), & x 0 0, & x=0 cases and...
- Let f(x)= ( 6 ( 2 x ) ) for all x R and g(x)= 2 x for all x R . Let (f g)(x) denote f(g(x)) and (g f)(x) denote g(f(x)). Then...
- Let PQR be a triangle. Let a = QR , b = RP and c = PQ . If | a |=12, | b |=4 3 and b c =24, then which of the following is (are)...
- For any integer k, let _k= ( k 7 )+i ( k 7 ), where i= -1 . The value of the expression _ k=1 ^ 12 | _ k+1 - _k| _ k=1 ^ 3 | _...
- Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum of the first seven...
- Suppose that the foci of the ellipse x^2 9 + y^2 5 =1 are (f_1,0) and (f_2,0) where f_1>0 and f_2<0. Let P_1 and P_2 be two...
- Let m and n be two positive integers greater than 1. If _ 0 ( e^ ( ^n) -e ^m )=- ( e 2 ) then the value of m n is
- Let f: R R be a continuous odd function, which vanishes exactly at one point and f(1)= 1 2 . Suppose that F(x)= _ -1 ^ x f(t) ,dt...
- Suppose that p , q and r are three non-coplanar vectors in R ^3. Let the components of a vector s along p , q and r be 4, 3 and...
- Let S be the set of all non-zero real numbers such that the quadratic equation x^2-x+ =0 has two distinct real roots x_1 and x_2...
- If =3 ^ -1 ( 6 11 ) and =3 ^ -1 ( 4 9 ), where the inverse trigonometric functions take only the principal values, then the...
- Let E_1 and E_2 be two ellipses whose centers are at the origin. The major axes of E_1 and E_2 lie along the x-axis and the...
- Consider the hyperbola H:x^2-y^2=1 and a circle S with center N(x_2,0). Suppose that H and S touch each other at a point...
- The option(s) with the values of a and L that satisfy the following equation is(are) _0^ 4 e^t( ^6at+ ^4at) ,dt _0^ e^t( ^6at+...
- Let f,g:[-1,2] R be continuous functions which are twice differentiable on the interval (-1,2). Let the values of f and g at the...
- Let - 6 < <- 12 . Suppose _1 and _1 are the roots of the equation x^2-2x +1=0 and _2 and _2 are the roots of the equation x^2+2x...