Practice questions
88551 published questions with worked solutions.
- If the set of all a R, for which the equation 2x^2 + (a-5)x + 15 = 3a has no real root, is the interval ( , ), and X = x Z : < x...
- If x + ^2x = 1, x (0, 2 ), then ( ^ 12 x + ^ 12 x) + 3( ^ 10 x + ^ 10 x + ^8x + ^8x) + ( ^6x + ^6x) is equal to
- Let the area enclosed between the curves |y| = 1 - x^2 and x^2 + y^2 = 1 be . If 9 = + ; , are integers, then the value of | - |...
- If the domain of the function _5(18x - x^2 - 77) is ( , ) and the domain of the function _ (x-1) ( 2x^2+3x-2 x^2-3x-4 ) is ( , ),...
- Let a straight line L pass through the point P(2, –1, 3) and be perpendicular to the lines x-1 2 = y+1 1 = z-3 -2 and x-3 1 = y-2...
- Let S = N 0 . Define a relation R from S to R by : R = (x,y): _e y = x _e ( 2 5 ), x S, y R Then, the sum of all the elements in...
- 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...