Mathematics questions
18011 published questions with worked solutions.
- Let the tangents drawn from the origin to the circle, x^2+y^2-8x-4y+16=0 touch it at the points A and B. The (AB)^2 is equal to:
- The value of c in the Lagrange's mean value theorem for the function f(x)=x^3-4x^2+8x+11, when x [0,1] is:
- Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A B and B D, then A C" is:Not in JEE syllabus
- If 3+i 4-i , [0,2 ], is a real number, then an argument of +i is:
- In a workshop, there are five machines and the probability of any one of them to be out of service on a day is 1 4 . If the...
- Let X= n N: 1 n 50 . If A= n X: n is a multiple of 2 and B= n X: n is a multiple of 7 , then the number of elements in the...
- If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x.y is equal to_________.
- If the function f defined on (- 1 3 , 1 3 ) by f(x)= cases 1 x _e ( 1+3x 1-2x ), & when x 0 k, & when x=0 cases is continuous,...
- If the system of linear equations, x+y+z=6 x+2y+3z=10 3x+2y+ z= has more than two solutions, then - ^2 is equal to_________.
- If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through ( , 7, 1) is ( 5 3 , 7 3 , 17 3 ), then...
- Given : f(x)= cases x, & 0 x< 12 12, & x= 12 1-x, & 12<x 1 cases and g(x)= (x- 12 )^2, x R. Then the area (in sq. units) of the...
- Let a, b R, a 0 be such that the equation, ax^2-2bx+5=0 has a repeated root , which is also a root of the equation, x^2-2bx-10=0....
- If A= x R: |x|<2 and B= x R: |x-2| 3 ; then -
- Let a_n be the n^ th term of a G.P. of positive terms. If _ n=1 ^ 100 a_ 2n+1 =200 and _ n=1 ^ 100 a_ 2n =100, then _ n=1 ^ 200...
- If z be a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be -
- If x= _ n=0 ^ (-1)^n ^ 2n and y= _ n=0 ^ ^ 2n , for 0< < 4 , then -
- Let [t] denote the greatest integer t and _ x 0 x [ 4 x ]=A. Then the function, f(x)=[x^2] ( x) is discontinuous, when x is equal...
- Let a function f:[0,5] R be continuous, f(1) = 3 and F be defined as F(x)= _1^x t^2g(t) ,dt, where g(t)= _1^t f(u) ,du. Then for...
- A random variable X has the following probability distribution : | X | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---| | P(X) | K^2...
- If d ^2 ( 2 + 2 ) = +2 _e|f( )|+C where C is a constant of integration, then the ordered pair ( ,f( )) is equal to -