Mathematics questions
18011 published questions with worked solutions.
- Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card...
- Let S be the set of all R for which the system of linear equations 2x-y+2z=2 x-2y+ z=-4 x+ y+z=4 has no solution. Then the set S
- Let A be a 2 × 2 real matrix with entries from 0, 1 and |A| ≠ 0. Consider the following two statements : (P) If A ≠ I_2, then |A|...
- The contrapositive of the statement "If I reach the station in time, then I will catch the train" is :Not in JEE syllabus
- Let y = y(x) be the solution of the differential equation, 2+ x y+1 dy dx =- x, y > 0, y(0) = 1. If y( ) = a and dy dx at x = is...
- Let X = x ∈ N : 1 ≤ x ≤ 17 and Y = ax + b: x ∈ X and a, b ∈ R, a > 0 . If mean and variance of elements of Y are 17 and 216...
- If the tangent to the curve y = x + sin y at a point (a, b) is parallel to the line joining (0, 3 2 ) and ( 1 2 ,2 ), then:
- Let P(h, k) be a point on the curve y = x² + 7x + 2, nearest to the line, y = 3x – 3. Then the equation of the normal to the...
- The plane passing through the points (1, 2, 1), (2, 1, 2) and parallel to the line, 2x = 3y, z = 1 also passes through the point :
- If R = (x, y) : x, y ∈ Z, x^2+3y^2 8 is a relation on the set of integers Z, then the domain of R^ -1 is:
- The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in :
- A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola x^2 4 - y^2 2 =1 at the point (x_1, y_1). Then...
- The domain of the function f(x)= ^ -1 ( |x|+5 x^2+1 ) is (- ,-a] [a, ). Then a is equal to:
- The value of ( 1+ 2 9 +i 2 9 1+ 2 9 -i 2 9 )^3 is:
- If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0)...
- The integral _0^2 ||x-1|-x |dx is equal to___________.
- Let a , b and c be three unit vectors such that | a - b |^2+| a - c |^2=8. Then | a +2 b |^2+| a +2 c |^2 is equal to __________.
- If _ x 1 x+x^2+x^3+ +x^n-n x-1 =820, (n ∈ N) then the value of n is equal to_________.
- If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a...
- The number of integral values of k for which the line, 3x + 4y = k intersects the circle, x^2+y^2-2x-4y+4=0 at two distinct...