Practice questions
88551 published questions with worked solutions.
- If 0<x_1<x_2< satisfy 1+ x+ ^2x+ =4+2 3, find |[x_1-x_2]|, where [ ] represents the greatest integer function.Not in JEE Main syllabus
- Consider the equation 3^ x +3^ x =2 3^ -1/ 2 , x (0,2 ), and let x denote the least integer x. Find of the roots of the equation .Not in JEE Main syllabus
- Evaluate | 2 7 4 7 + 4 7 8 7 + 8 7 2 7 |.
- If x+y+z= , x z=3 and z y=15, find ^2z.
- Evaluate 8 36^ 72^ 108^ 144^ .
- If 30( ^2x- ^2x)+7 2x+20=0, then evaluate 2 2x-1.
- Evaluate ^25^ + ^210^ + ^215^ + + ^285^ + ^290^ .
- If 2 1- - = 45, then evaluate 1- + -1 .
- How many solutions does the equation ^4x+ ^4x= x x have in [ ,5 ]?Not in JEE Main syllabus
- Consider the equation x (x+ 3 ) (x- 3 )+ 14=0, x [0,3 ]. The sum of the values of x that satisfy the equation is ( m n ) , where...Not in JEE Main syllabus
- Find the number of integral values of k for which the equation 9 x+40 x=2k+1 has a solution.Not in JEE Main syllabus
- If 8 , x, 3 8 are in A.P. and 8 , y, 4 are in A.P., then find y x .
- In (- 2 , 2 ), it is given that 2 2x>3 x. The set of all values of x that satisfy the inequality is (m ,n ) (0,p ), where m,n<0...Not in JEE Main syllabus
- Given that 4 x y=1 and ^2x+ ^2y 32, evaluate ^2x+ ^2y.
- Consider the inequality x- 3x 0, x [0,2 ]. Apart from isolated points, the solution set is [0,a ] [b ,2 ]. Find b-a.Not in JEE Main syllabus
- If 75^ and 15^ are the roots of the quadratic equation x^2+Px+Q=0, then evaluate Q-P.
- How many solutions does the equation ^5x+ ^4x=1, -2 <x<2 , have?Not in JEE Main syllabus
- How many solutions does the equation ^ 10 x- ^ 10 x=1 have in [-3 ,3 ]?Not in JEE Main syllabus
- If (7 12^ )= ab + a+ b+a, where a,b are positive integers, then find b a .
- Evaluate ^288^ + ^228^ - 88^ 28^ .