Practice questions
88551 published questions with worked solutions.
- In ABC, if b+c=3a, then the value of ( B 2 ) ( C 2 ) is ____.Not in JEE syllabus
- If in ABC, A a = B b = C c , side a=2 and the area of ABC is S, then the value of [S], where [ ] represents the greatest integer...Not in JEE syllabus
- Two straight roads intersect at an angle of 60^ . A bus on one road is 6 km away from the intersection point and a car on the...Not in JEE syllabus
- Let x+ 1x=2 and y+ 1y=-2, and ^ -1 x+ ^ -1 y=m . Then the value of m is ____.
- Let x 0. If ^ -1 (1-x)-2 ^ -1 x= 2 , then the sum of the values of x is ____.
- Taking 2=1.41, the value of 1 ( 14 ^ -1 63 8 ) is ____.
- If ^ -1 x+ ^ -1 y+ ^ -1 z=3 , then the value of x^ 100 +y^ 100 +z^ 100 - 9 x^ 101 +y^ 101 +z^ 101 is ____.
- In a triangle ABC, the lengths of the two larger sides are 10 and 5 3. If the angles A, B, C are in AP, then the length of the...Not in JEE syllabus
- The inradius of the triangle having sides 26, 28 and 30 units is ____.Not in JEE syllabus
- Let 0<A,B< 2 . If A= ^ -1 ( x 3 2k-x ) and B= ^ -1 ( 2x-k k 3 ), then the value of A-B (in degrees) is ____.
- The number of real solutions of the equation ^ -1 x(x+1) + ^ -1 x^2+x+1 = 2 is ____.
- Let x,y,z,r>0 with x^2+y^2+z^2=r^2. If ^ -1 ( xy zr )+ ^ -1 ( yz xr )+ ^ -1 ( zx yr )=m , then the value of m is ____.
- Points D, E on BC of ABC are such that BD=DE=EC. If BAD=x, DAE=y and EAC=z, then the value of (x+y) (y+z) x z is ____.Not in JEE syllabus
- If ^ -1 ( 2 11 )+ ^ -1 ( 12 )= 12 ^ -1 ( p q ), where p and q are positive integers with (p,q)=1, then the value of q-2p is ____.
- If ^ -1 x=a and ^ -1 (2x 1-x^2 )+ ^ -1 ( 1 2x^2-1 )= 2 3 , where 1 2 <x<1, then the value of ^ -1 (2x) (in degrees) is ____.
- The value of ^ -1 ( ^ -1 2+ 3 4 + ^ -1 ( 16 8 )+ ^ -1 2 ) is ____.
- If 3 ^ -1 ( 1 2+ 3 )- ^ -1 ( 1x )= ^ -1 ( 13 ), then the value of x is ____.
- The value of ^ -1 ( ( 53 5 ) )- ^ -1 ( ( 10 3 ) ) (in degrees) is ____.
- If x= (2 ^ -1 2) and y= ( 12 ^ -1 ( 43 ) ), then the value of x+y^2 is ____.
- Let 0<x< 14 and ^ -1 ( 6x 1+9x^2 )+ ^ -1 ( 1-16x^2 1+16x^2 )= 2 . If x satisfies the equation px^2+qx+r=0, where p,q,r are...