Mathematics questions
18011 published questions with worked solutions.
- If x + y = 109 is the equation of the chord of the ellipse x^2 9 + y^2 4 =1, whose mid point is ( 5 2 , 1 2 ) then + is equal to
- If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then...
- Let , ( ) be the values of m, for which the equations x + y + z = 1; x + 2y + 4z = m and x + 4y + 10z = m^2 have infinitely many...
- Let A = [a_ ij ] be a matrix of order 3 × 3, with a_ ij = ( 2 )^ i+j . If the sum of all the elements in the third row of A^2 is...
- Let P be the foot of the perpendicular from the point (1, 2, 2) on the line L : x-1 1 = y+1 -1 = z-2 2 . Let the line r = (- i+...
- Let A = [a_ ij ] be a 2 × 2 matrix such that a_ ij 0, 1 for all i and j. Let the random variable X denote the possible values of...
- The remainder, when 7^ 103 is divided by 23, is equal to:
- Let f(x) = _0^x t(t^2-9t+20) ,dt, 1 x 5. If the range of f is [ , ], then 4( + ) equals :
- If for the solution curve y = f(x) of the differential equation dy dx +( x)y= 2+ x (1+2 x)^2 , x ( - 2 , 2 ), f ( 3 )= 3 10 ,...
- If 24 _0^ /4 ( | (4x- 12 ) |+[2 x] )dx = 2 + , where [.] denotes the greatest integer function, then is equal to _____.
- If _ t 0 ( _0^1(3x+5)^t ,dx )^ 1/t = 5e ( 8 5 )^ 2/3 , then is equal to _____.
- Let a_1, a_2, , a_ 2024 be an Arithmetic Progression such that a_1 + (a_5+a_ 10 +a_ 15 + +a_ 2020 )+a_ 2024 =2233. Then...
- Let integers a, b [–3, 3] be such that a + b 0. Then the number of all possible ordered pairs (a, b), for which | z-a z+b |=1 and...
- Let y^2=12x the parabola and S be its focus. Let PQ be a focal chord of the parabola such that (SP)(SQ)= 147 4 . Let C be the...
- If _ x 0 (2x) + a (4x) - b x^4 is finite, then (a + b) is equal to :
- If _ r=0 ^ 10 ( 10^ r+1 -1 10^r ) ^ 11 C_ r+1 = ^ 11 -11^ 11 10^ 10 , then is equal to :
- Let (a, b) be the point of intersection of the curve x^2 = 2y and the straight line y - 2x - 6 = 0 in the second quadrant. Then...
- If [- 7 6 , 4 3 ], then the number of solutions of 3 ^2 - 2( 3 -1) - 4 = 0, is equal to :Not in JEE Main syllabus
- If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then a + b + ab is equal to :
- If the domain of the function f(x) = 1 10+3x-x^2 + 1 x+|x| is (a, b), then (1+a)^2 + b^2 is equal to :