Mathematics questions
18011 published questions with worked solutions.
- If e^x ( x ^ -1 x 1-x^2 + ^ -1 x (1-x^2)^ 3/2 + x 1-x^2 )dx = g(x)+C, Where C is the constant of integration, then g ( 1 2 )...
- Let _ and _ be the distinct roots of 2x^2 + ( )x - 1 = 0, (0, 2 ). If m and M are the minimum and the maximum values of _ ^4+ _...
- If the system of linear equations : x + y + 2z = 6, 2x + 3y + az = a + 1, –x – 3y + bz = 2b, Where a, b R has infinitely many...
- Let a and b be two unit vectors such that the angle between them is 3 . If a +2 b and 3 a - b are perpendicular to each other,...
- Let E: x^2 a^2 + y^2 b^2 =1, a > b and H: x^2 A^2 - y^2 B^2 =1. Let the distance between the foci of E and the foci of H be 2 3....
- If A and B are two events such that P(A B) = 0.1, and P(A|B) and P(B|A) are the roots of the equation 12x^2-7x+1=0, then the...
- The sum of all values of [0, 2 ] satisfying 2 ^2 = 2 and 2 ^2 = 3 isNot in JEE Main syllabus
- Let y = f(x) be the solution of the differential equation dy dx + xy x^2-1 = x^6+4x 1-x^2 , -1 < x < 1 such that f(0) = 0. If 6 _...
- Let A(6, 8), B(10 , -10 ) and C(-10 , 10 ), be the vertices of a triangle. If L(a, 9) and G(h, k) be its orthocenter and centroid...
- If _ r=1 ^ 30 r^2 ( ^ 30 C_r )^2 ^ 30 C_ r-1 = 2^ 29 , then is equal to _______.
- Let A = 1, 2, 3 . The number of relations on A, containing (1, 2) and (2, 3), which are reflexive and transitive but not...
- If in the expansion of (1 + x)^p (1 – x)^q, the coefficients of x and x^2 are 1 and –2, respectively, then p^2 + q^2 is equal to :
- Let A = (x, y) R × R : |x + y| 3 and B = (x, y) R × R : |x| + |y| 3 . If C = (x, y) A B : x = 0 or y = 0 , then _ (x,y) C |x+y| is
- The system of equations x + y + z = 6, x + 2y + 5z = 9, x + 5y + = , has no solution if
- Let x^3 x ,dx = g(x) + C, where C is the constant of integration. If 8 (g ( 2 ) + g' ( 2 ) ) = ^3 + ^2 + , , , Z. Then + - equals...
- A rod of length eight units moves such that its ends A and B always lie on the lines x – y + 2 = 0 and y + 2 = 0, respectively....
- The distance of the line x-2 2 = y-6 3 = z-3 4 from the point (1, 4, 0) along the line x 1 = y-2 2 = z+3 3 is :
- Let the point A divide the line segment joining the points P(–1, –1, 2) and Q(5, 5,10) internally in the ratio r : 1 (r > 0). If...
- If the area of the region (x, y) : –1 x 1, 0 y a + e^ |x| –e^ –x , a > 0 is e^2 + 8e + 1 e , then the value of a is :
- Let x = x(y) be the solution of the differential equation y = (x - y dx dy ) ( x y ), y > 0 and x(1) = 2 . Then (x(2)) is equal...