Mathematics questions
18011 published questions with worked solutions.
- Let E_ 1 and E_ 2 be two events such that the conditional probabilities P(E_ 1 | E_ 2 ) = 1/2, P(E_ 2 | E_ 1 ) = 3/4 and P(E_ 1...
- Let A = bmatrix 0 & -2 2 & 0 bmatrix . If M and N are two matrices given by M = _ k=1 ^ 10 A^ 2k and N = _ k=1 ^ 10 A^ 2k-1 then...
- Let f : ℝ ℝ and g : ℝ ℝ be two functions defined by f(x) = _ e (x^ 2 + 1) - e^ -x + 1 and g(x) = (1 - 2e^ 2x )/e^ x . Then, for...
- Let a = a_ 1 i + a_ 2 j + a_ 3 k , a_ i > 0, i = 1, 2, 3 be vector which makes equal angles with the coordinate axes OX, OY and...
- Let y = y(x) be the solution of the differential equation (x + 1)y' - y = e^ 3x (x + 1)^ 2 , with y(0) = 1/3. Then, the point x =...
- If y = m_ 1 x + c_ 1 and y = m_ 2 x + c_ 2 , m_ 1 m_ 2 are two common tangents of circle x^ 2 + y^ 2 = 2 and parabola y^ 2 = x,...
- Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S : x + y + z = 5. If a line L passing through (1,...
- If the solution curve y = y(x) of the differential equation y^ 2 dx + (x^ 2 − xy + y^ 2 )dy = 0, which passes through the point...
- Let x = 2t, y = t^ 2 /3 be a conic. Let S be the focus and B be the point on the axis of the conic such that SA BA, where A is...
- Let a circle C in complex plane pass through the points z_ 1 = 3 + 4i, z_ 2 = 4 + 3i and z_ 3 = 5i. If z ( z_ 1 ) is a point on C...
- Let C_ r denote the binomial coefficient of x^ r in the expansion of (1 + x)^ 10 . If for , ℝ, C_ 1 + 3 2C_ 2 + 5 3C_ 3 + .......
- Let be the angle between the vectors a and b , where | a | = 4, | b | = 3 and ( /4, /3). Then |( a - b ) ( a + b )|^ 2 + 4( a b...
- Let the abscissae of the two points P and Q be the roots of 2x^ 2 − rx + p = 0 and the ordinates of P and Q be the roots of x^ 2...
- The number of values of x in the interval ( /4, 7 /4) for which 14 ^ 2 x - 2 ^ 2 x = 21 - 4 ^ 2 x holds, is _____.Not in JEE Main syllabus
- Let the lines L_ 1 : r = ( i + 2 j + 3 k ), ℝ and L_ 2 : r = ( i + 3 j + k ) + ( i + j + 5 k ), ℝ intersect at the point S. If a...
- The minimum value of the sum of the squares of the roots of x^ 2 + (3 - a)x + 1 = 2a is
- If z = x + iy satisfies |z| − 2 = 0 and |z − i| − |z + 5i| = 0, then
- Let A = bmatrix 1 1 1 bmatrix and B = bmatrix 9^ 2 & -10^ 2 & 11^ 2 12^ 2 & 13^ 2 & -14^ 2 -15^ 2 & 16^ 2 & 17^ 2 bmatrix , then...
- _ i,j=0, i j ^ n ^nC_i , ^nC_j is equal to
- Let P and Q be any points on the curves (x - 1)^ 2 + (y + 1)^ 2 = 1 and y = x^ 2 , respectively. The distance between P and Q is...