Mathematics questions
18011 published questions with worked solutions.
- Let a = 2 i - 3 j + 4 k, b = 3 i + 4 j - 5 k and a vector c be such that a ( b + c) + b c = i + 8 j + 13 k. If a c = 13, then (24...
- If Re ( z-1 2z+i )=1, where z = x + iy, then the point (x, y) lies on a :
- If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus...
- Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is
- The greatest positive integer k, for which 49^k+1 is a factor of the sum 49^ 125 +49^ 124 + +49^2+49+1, is :
- Let and be two real roots of the equation (k+1) ^2x- 2 x=(1-k), where k ( -1) and are real numbers. If ^2( + )=50, then a value...
- The logical statement (p q) (q p) is equivalent to :Not in JEE syllabus
- If y = mx + 4 is a tangent to both the parabolas, y^2=4x and x^2=2by, then b is equal to
- If y = y(x) is the solution of the differential equation, e^y ( dy dx -1 )=e^x such that y(0) = 0, then y(1) is equal to :
- If f(a + b + 1 – x) = f(x), for all x, where a and b are fixed positive real numbers, then 1 a+b _a^b x(f(x)+f(x+1)) ,dx is equal...
- Let the function, f : [–7, 0] → R be continuous on [–7, 0] and differentiable on (–7, 0). If f(–7) = – 3 and f'(x) 2, for all x...
- Let P be a plane passing through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R be any point (2, 1, 6). Then the image of R...
- If g(x)=x^2+x-1 and (g f)(x)=4x^2-10x+5, then f ( 5 4 ) is equal to:
- Let be a root of the equation x^2+x+1=0 and the matrix A= 1 3 bmatrix 1&1&1 1& & ^2 1& ^2& ^4 bmatrix , then the matrix A^ 31 is...
- Five number are in A.P. , whose sum is 25 and product is 2520. If one of these five numbers is - 1 2 , then the greatest number...
- The area of the region, enclosed by the circle x^2+y^2=2 which is not common to the region bounded by the parabola y^2=x and the...
- If the system of linear equations 2x+2ay+az=0, 2x+3by+bz=0, 2x+4cy+cz=0 Where a, b, c R are non-zero and distinct; has a non-zero...
- A vector a = i +2 j + k ( , R) lies in the plane of the vectors, b = i + j and c = i - j +4 k . If a bisects the angle between b...
- _ x 2 3^x+3^ 3-x -12 3^ -x/2 -3^ 1-x is equal to
- Let A(1, 0), B(6, 2) and C ( 3 2 ,6 ) be the vertices of a triangle ABC. If P is a point inside the triangle ABC such that the...