Mathematics questions
18011 published questions with worked solutions.
- The probability that two randomly selected subsets of the set 1, 2, 3, 4, 5 have exactly two elements in their intersection, is :
- For integers n and r, let n r = cases ^nC_r, & if n r 0 0, & otherwise cases The maximum value of k for which the sum _ i=0 ^k 10...
- Let be an integer. If the shortest distance between the lines x – =2y – 1 = –2z and x = y + 2 = z – is 7 2 2 , then the value of...
- Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (–5, 0). If the locus of...
- If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle (x-2)^2+(y-3)^2=25 at the...
- If the variance of 10 natural numbers 1, 1, 1, ...., 1, k is less than 10, then the maximum possible value of k is _______.
- The sum of first four terms of a geometric progression (G.P.) is 65 12 and the sum of their respective reciprocals is 65 18 . If...
- The students S_1, S_2, ...., , S_ 10 are to be divided into 3 groups A, B and C such that each group has at least one student and...
- Let i = -1 . If (-1+i 3)^ 21 (1-i)^ 24 + (1+i 3)^ 21 (1+i)24 =k, and n = [|k|] be the greatest integral part of |k|. Then _ j=0 ^...
- The number of the real roots of the equation (x+1)^2+|x-5|= 27 4 is _________.
- A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes...
- The equation of the plane passing through the point (1, 2, –3) and perpendicular to the planes 3x + y – 2z = 5 and 2x – 5y – z =...
- The population P = P(t) at time 't' of a certain species follows the differential equation dP dt =0.5P-450. If P(0) = 850, then...
- The system of linear equations 3x – 2y – kz = 10, 2x – 4y – 2z = 6, x + 2y – z = 5m is inconsistent if :
- If f:R R is a function defined by f(x)=[x-1] ( 2x-1 2 ) , where [.] denotes the greatest integer function, then f is :
- The distance of the point (1, 1, 9) from the point of intersection of the line x-3 1 = y-4 2 = z-5 2 and the plane x + y + z = 17...
- If the tangent to the curve y = x^3 at the point P(t,t^3) meets the curve again at Q, then the ordinate of the point which...
- If x- x 8- 2x dx=a ^ -1 ( x+ x b )+c, where c is a constant of integration, then the ordered pair (a, b) is equal to :
- The value of -^ 15 C_1+2.^ 15 C_2-3.^ 15 C_3+ -15.^ 15 C_ 15 +^ 14 C_1+^ 14 C_3+^ 14 C_5+ +^ 14 C_ 11 is :
- The function f(x)= 4x^3-3x^2 6 -2 x+(2x-1) x :