Mathematics questions
18011 published questions with worked solutions.
- Let the equation of the pair of lines, y = px and y = qx, can be written as (y – px) (y – qx) = 0. Then the equation of the pair...
- Let y = y (x) be the solution of the differential equation xdy = (y + x^3 x)dx with y( )=0, then y ( 2 ) is equal to :
- Let n N and [x] denote the greatest integer less than or equal to x. If the sum of (n + 1) terms ^nC_0, 3.^nC_1, 5.^nC_2,...
- Consider the function f(x) cases P(x) (x-2) , & x 2 7, & x=2 cases Where P(x) is a polynomial such that P"(x) is always a...
- The equation of a circle is Re(z^2)+2(Im(z))^2+2Re(z)=0, where z = x + iy. A line which passes through the center of the given...
- If ( a +3 b ) is perpendicular to (7 a -5 b ) and ( a -4 b ) is perpendicular to (7 a -2 b ), then the angle between a and b (in...
- Let a curve y = f(x) pass through the point (2, ( _e2)^2) and have slope 2y x _ex for all positive real value of x. Then the...
- A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. The minimum value of n...
- If the co-efficient of x^7 and x^8 in the expansion of (2+ x 3 )^n are equal, then the value of n is equal to________.
- If the lines x-k 1 = y+2 2 = z+3 3 are co-planar, then the value of k is________.
- A spherical gas balloon of radius 16 meter subtends an angle 60° at the eye of the observer A while the angle of elevation of its...Not in JEE syllabus
- Let f(x)=3 ^4x+10 ^3x+6 ^2x-3, x [ 6 , 2 ]. Then, f is :
- Let S_n be the sum of the first n terms of an arithmetic progression. If S_ 3n =3S_ 2n , then the value of S_ 4n S_ 2n is :
- The locus of the centroid of the triangle formed by any point P on the hyperbola 16x^2-9y^2+32x+36y-164=0, and its foci is :
- Let the vectors (2+a+b) i +(a+2b+c) j +(b+c) k , (1+b) i +2b j -b k and (2+b) i +2b j +(1-b) k , b,c R be co-planar. Then which...
- Let f:R R be defined as f(x)= cases |x^2-5x+6| (5x-x^2-6) , & x<2 ^ ( x-2 x-[x] ) , & x>2 , & x=2 cases where [x] is the greatest...
- The value of the definite integral _ /24 ^ 5 /24 ( 2x)^ 1/3 ( 2x)^ 1/3 +( 2x)^ 1/3 dx is :
- If b is very small as compared to the value of a, so that the cube and other higher powers of b a can be neglected in the...
- Let y = y(x) be solution of the differential equation dy dx =1+xe^ y-x , - 2<x< 2, y(0)=0, then, the minimum value of y(x), x (-...
- The Boolean expression (p q) (q p) is equivalent to :Not in JEE syllabus