Mathematics questions
18011 published questions with worked solutions.
- Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides and q be the...
- If the range of the function f(x) = 5-x x^2-3x+2 , x 1, 2, is (- , ] [ , ), then ^2 + ^2 is equal to :
- If the locus of Z C, such that Re ( z-1 2z+i ) + Re ( z -1 2 z -i ) = 2, is a circle of radius r and center (a, b), then 15ab r^2...
- Let a_n be the nth term of an A.P. If S_n = a_1 + a_2 + a_3 + + a_n = 700, a_6 = 7 and S_7 = 7, then a_n is equal to :
- If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth...
- Let the length of a latus rectum of an ellipse x^2 a^2 + y^2 b^2 = 1 be 10. If its eccentricity is the minimum value of the...
- Let y = y(x) be the solution of the differential equation (x^2 + 1) y' - 2xy = (x^4 + 2x^2 + 1) x, y(0) = 1. Then _ -3 ^ 3 y(x)dx...
- Consider the lines L_1 : x - 1 = y - 2 = z and L_2 : x - 2 = y = z - 1. Let the feet of the perpendiculars from the point P(5, 1,...
- The number of real roots of the equation x |x – 2| + 3|x – 3| + 1 = 0 is
- Let the system of equations x + 5y – z = 1 4x + 3y – 3z = 7 24x + y + λz = m, λ, μ ∈ **R**, have infinitely many solutions. Then...
- Let f : R → R be a polynomial function of degree four having extreme values at x = 4 and x = 5. If _ x 0 f(x) x^2 = 5, then f(2)...
- For t > – 1, let _t and _t be the roots of the equation ((t+2)^ 1/7 -1 )x^2 + ((t+2)^ 1/6 -1 )x + ((t+2)^ 1/21 -1 ) = 0. If _ t...
- The sum of the series 2 1 ^ 20 C_4 - 3 2 ^ 20 C_5 + 4 3 ^ 20 C_6 - 5 4 ^ 20 C_7 + + 18 17 ^ 20 C_ 20 , is equal to _______.
- If the function f(x) = ( x) - ( x) x - x is continuous at x = 0, then f(0) is equal to ______.
- Let A and B be two sets, then (A B)' (A' B) is equal to
- If S is a set with 10 elements and A= (x,y):x,y S, x y , then the number of elements in A is
- For any two sets A and B, if A X=B X= and A X=B X for some set X, then (AMU 2009)
- The shaded region in the figure represents
- Let X and Y be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then, n(X Y) is equal...
- A class has 175 students. The following data shows the number of students opting one or more subjects: Mathematics 100; Physics...