Mathematics questions
18011 published questions with worked solutions.
- Let A_1 be the area of the region bounded by the curves y = sinx, y = cosx and y-axis in the first quadrant. Also, let A_2 be the...
- A seven digit number is formed using digits 3,3,4,4,4,5,5. The probability, that number so formed is divisible by 2, is :
- Let z be those complex numbers which satisfy |z+5| 4 and z(1+i)+ z(1-i) -10, i= -1 . If the maximum value of |z+1|^2 is + 2, then...
- Let the normals at all the points on a given curve pass through a fixed point (a, b). If the curve passes through (3, –3) and...
- If I_ m,n = _0^1x^ m-1 (1-x)^ n-1 dx, for m, n 1 and _0^1 x^ m-1 +x^ n-1 (1+x)^ m+n dx= I_ m,n , R, then equals________.
- If the arithmetic mean and geometric mean of the p^ th and q^ th terms of the sequence –16, 8, –4, 2, ... satisfy the equation...
- Let L be a common tangent line to the curves 4x^2+9y^2=36 and (2x)^2+(2y)^2=31. Then the square of the slope of the line L...
- Let X_1, X_2, ........, X_ 18 be eighteen observations such that _ i=1 ^ 18 (X_i- )=36 & _ i=1 ^ 18 (X_i- )=90, where and are...
- If the matrix A= bmatrix 1&0&0 0&2&0 3&0&-1 bmatrix satisfies the equation A^ 20 + A^ 19 + A= bmatrix 1&0&0 0&4&0 0&0&1 bmatrix...
- A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads,...
- Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A^2 is 1, then the possible...
- In a increasing geometric series, the sum of the second and the sixth term is 25 2 and the product of the third and fifth term is...
- The sum of the infinite series 1+ 2 3 + 7 3^2 + 12 3^3 + 17 3^4 + 22 3^5 + equal to
- The value of _ h 0 2 3 ( 6 +h )- ( 6 +h ) 3h( 3 - ) is
- The maximum value of the term independent of 't' in the expansion of (tx^ 1/5 + (1-x)^ 1/10 t )^ 10 where x (0,1) is
- If (1, 5, 35), (7, 5, 5), (1, , 7) and (2 , 1, 2) are coplanar, then the sum of all possible values of is
- If ^ -1 x a = ^ -1 x b = ^ -1 y c ; 0 < x < 1, then the value of ( c a+b ) is
- The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1,2 and 3 only is
- The maximum slope of the curve y= 1 2 x^4-5x^3+18x^2-19x occurs at the point
- Consider the three planes P_1: 3x + 15y + 21z = 9, P_2: x – 3y – z = 5, and P_3: 2x + 10y + 14z = 5 Then, which one of the...