Mathematics questions
18011 published questions with worked solutions.
- Let y = y(x) be the solution of the differential equation cosec^2xdy+2dx=(1+y 2x)cosec^2xdx, with y ( 4 )=0 Then, the value of...
- Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 × 2 matrices. The probability that such...
- Let a vector a be coplanar with vectors b =2 i + j + k and c = i - j + k . If a is perpendicular to d =3 i +2 j +6 k , and | a |=...
- If _0^ 100 ^2x e^ ( x - [ x ] ) dx= ^3 1+4 ^2 , R where [x] is the greatest integer less than or equal to x, then the value of is...
- Let three vectors a , b and c be such that a b = c , b c = a and | a |=2. Then which one of the following is not true ?
- The values of and such that the system of equations x + y + z = 6, 3x + 5y + 5z = 26, x + 2y + = has no solution, are :
- If the shortest distance between the straight lines 3(x – 1) = 6(y – 2) = 2 (z – 1) and 4(x – 2) = 2(y – ) = (z – 3), R is 1 38 ,...
- Let A = [a_ ij ] be a real matrix of order 3 × 3, such that a_ i1 +a_ i2 +a_ i3 = 1, for i = 1, 2, 3. Then, the sum of all the...
- Let the circle S : 36x^2+36y^2-108x+120y+C=0 be such that it neither intersects nor touches the co-ordinate axes. If the point of...
- Let n denote the number of solutions of the equation z^2+3 z=0, where z is a complex number. Then the value of _ k=0 ^ 1 n^k is...
- The number of solutions of ^7x+ ^7x=1, x [0, 4 ] is equal toNot in JEE Main syllabus
- If the domain of the function f(x)= ^ -1 x^2-x+1 ^ -1 ( 2x-1 2 ) is the interval ( , ], then + is equal to -
- Let f : R R be defined as f(x)= cases x^3 (1- 2x)^2 _e ( 1+2xe^ -2x (1-xe^ -x )^2 ), & x 0 , & x=0 cases If f is continuous at x...
- Let a line L : 2x + y = k, k > 0 be a tangent to the hyperbola x^2-y^2=3. If L is also a tangent to the parabola y^2= x, then is...
- Let E_1: x^2 a^2 + y^2 b^2 =1, a > b. Let E_2 be another ellipse such that it touches the end points of major axis of E_1 and the...
- Let A = 0, 1, 2, 3, 4, 5, 6, 7 . Then the number of bijective functions f : A A such that f(1) + f(2) = 3 – f(3) is equal to
- If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers...
- Let A= bmatrix 0&1&0 1&0&0 0&0&1 bmatrix . Then the number of 3×3 matrices B with entries from the set 1, 2, 3, 4, 5 and...
- Consider the following frequency distribution Class: 0-6, 6-12, 12-18, 18-24, 24-30; Frequency: a, b, 12, 9, 5 If mean = 309 22...
- The area (in sq. units) of the region bounded by the curves x^2+2y-1=0, y^2+4x-4=0 and y^2-4x-4=0, in the upper half plane is...