Mathematics questions
18011 published questions with worked solutions.
- A plane passing through the point (3, 1, 1) contains two lines whose direction ratios are 1, –2, 2 and 2, 3, –1 respectively. If...
- Let E^C denote the complement of an event E. Let E_1, E_2 and E_3 be any pairwise independent events with P(E_1)>0 and P(E_1 E_2...
- Let A= X=(x,y,z)^T: PX=0 and x^2+y^2+z^2=1 where P= pmatrix 1&2&1 -2&3&-4 1&9&-1 pmatrix , then the set A :
- Consider a region R= (x,y) R^2: x^2 y 2x . If a line y= divides the area of region R into two equal parts, then which of the...
- If a curve y = f(x), passing through the point (1, 2), is the solution of the differential equation, 2x^2dy=(2xy+y^2)dx, then f (...
- Let S be the sum of the first 9 terms of the series: x+ka + x^2+(k+2)a + x^3+(k+4)a + x^4+(k+6)a + where a 0 and x 1. If S= x^ 10...
- The set of all possible values of in the interval (0, ) for which the points (1, 2) and ( , ) lie on the same side of the line x...
- If the variance of the terms in an increasing A.P., b_1, b_2, b_3,....b_ 11 is 90, then the common difference of this A.P....
- If y= _ k=1 ^ 6 k ^ -1 3 5 kx- 4 5 kx , then dy dx at x = 0 is ___________.
- Let the position vectors of points 'A' and 'B' be i + j + k and 2 i + j +3 k , respectively. A point 'P' divides the line segment...
- For a positive integer n, (1+ 1 x )^n is expanded in increasing powers of x. If three consecutive coefficients in this expansion...
- Let [t] denote the greatest integer less than or equal to t. Then the value of _1^2|2x-[3x]| ,dx is __________.
- Let A = 1, 2, 3, 4, 5 . Let R be a relation on A defined by xRy if and only if 4x ≤ 5y. Let m be the number of elements in R and...
- If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to...
- Suppose the solution of the differential equation dy dx = (2 + )x - y + 2 x - 2 y - ( - 4 ) represents a circle passing through...
- If the locus of the point, whose distances from the point (2, 1) and (1, 3) are in the ratio 5 : 4, is ax² + by² + cxy + dx + ey...
- _ n (1^2 - 1)(n - 1) + (2^2 - 2)(n - 2) + + ((n - 1)^2 - (n - 1)) 1 (1^3 + 2^3 + + n^3) - (1^2 + 2^2 + + n^2) is equal to
- A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the...
- If z₁, z₂ are two distinct complex number such that | z_1 - 2z_2 12 - z_1 z_2 | = 2, then
- If the function f(x) = ( 1x )^ 2x ; x > 0 attains the maximum value at x = 1e then: