Mathematics questions
18011 published questions with worked solutions.
- Consider two sets A= x z:||(x-3)-3| 1 and B= x R- 1,2 : (x-2)(x-4) x-1 _ e (|x-2|)=0 Then the number of onto functions f: A B is...
- The system of linear equations x+y+z=6 2x+5y+az=36 x+2y+3z=b has
- The sum of all the real solutions of the equation _ (x+3) (6x^2+28x+30) = 5-2 _ (6x+10) (x^2+6x+9) is equal to :
- Let a , b , c be three vectors such that a b = 2( a c ). If | a | = 1, | b | = 4, | c | = 2, and the angle between b and c is 60^...
- The least value of ( ^2 - 6 + 3 ^2 + 2) is
- Let I(x) = 3dx (4x+6)( 4x^2+8x+3 ) and I(0) = 3 4 +20. If I ( 1 2 ) = a 2 b +c, where a, b, c N , gcd(a,b)=1, then a+b+c is equal...
- The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is
- Let A = 0,1,2,...,9 . Let R be a relation on A defined by (x,y) R if and only if |x-y| is a multiple of 3. Given below are two...
- If z = 3 2 + i 2 , i = -1 , then (z^ 201 - i)^8 is equal to
- If the mean and the variance of the data Class 4 - 8 8 - 12 12 - 16 16 - 20 Frequency 3 4 7 are and 19 respectively, then the...
- Let _ k=1 ^ n a_k = n^2 + n. If a_ 10 = 59 and a_6 = 7a_1 then + is equal to
- If the solution curve y = f(x) of the differential equation (x^2-4)y' - 2xy + 2x(4-x^2)^2 = 0, x > 2, passes through the point...
- The number of elements in the set S = x : x [0,100] and _0^x t^2 (x-t) ,dt = x^2 is.....
- Let A = bmatrix 0 & 2 & -3 -2 & 0 & 1 3 & -1 & 0 bmatrix and B be a matrix such that B(I - A) = I + A. Then the sum of the...
- Let S denote the set of 4-digit numbers abcd such that a > b > c > d and P denote the set of 5-digit numbers having product of...
- If the function f(x) = e^x(e^ x - x -1) + _e( x + x) - x x - x is Continuous at x=0, then the value of f(0) is equal to
- Let a circle of radius 4 pass through the origin O, the points A(- 3 a, 0) and B(0, - 2 b), where a and b are real parameters and...
- Let the lines L_1: r = i +2 j +3 k + (2 i +3 j +4 k ), R and L_2: r = (4 i + j )+ (5 i +2 j + k ), R , intersect at the point R....
- Let 729, 81, 9, 1, be a sequence and P_n denote the product of the first n terms of this sequence. If 2 _ n=1 ^ 40 (P_n)^ 1 n =...
- Let a = 2 i + j -2 k , b = i + j and c = a b . Let d be a vector such that | d - a | = 11 , | c d | = 3 and the angle between c...