Mathematics questions
18011 published questions with worked solutions.
- Let = _ x R 8^ 2 3x .4^ 4 3x and = _ x R 8^ 2 3x .4^ 4 3x . If 8x^2+bx+c=0 is a quadratic equation whose roots are ^ 1/5 and ^...
- Let f:[0, ) [0,3] be a function defined by f(x)= cases t:0 t x , & 0 x 2+ x, & x> cases Then which of the following is true ?
- Let N be the set of natural number and a relation R on N be defined by R= (x,y) N N:x^3-3x^2y-xy^2+3y^2=0
- Which of the following is the negation of the statement "for all M > 0, then exists x such that x " ?Not in JEE syllabus
- Consider a circle C which touches the y-axis at (0, 6) and cuts off an intercept 6 5 on the x-axis. Then the radius of the circle...
- Let a , b , c be vectors such that a = b ( b c ). If magnitudes of the vectors a , b and c are 2,1 and 2 respectively and the...
- Let A and B be two 3 × 3 real matrices such that (A^2-B^2) is invertible matrix. If A^5=B^5 and A^3B^2=A^2B^3, then the value of...
- Let f : (a,b) R be twice differentiable function such that f(x)= _a^xg(t)dt for a differentiable function g(x). If f(x) = 0 has...
- Let a =(1,- , ), b =(3, ,- ) and c =(- ,-2,1); , I be three vectors such that a =( b c ). If magnitudes of the vectors a , b and...
- The distance of the point P(3, 4, 4) from the point of intersection of the line joining the points Q(3, –4, –5) and R(2, –3, 1)...
- Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its center at (3, –4), one focus at (4, –4) and one...
- If _0^ ( ^3x)e^ - ^2x dx= - e _0^1 te^tdt, then the value of + is equal to_____.
- Let y = y(x) be the solution of the differential equation dy dx =e^ x+y ; N. If y( _e2)= _e2 and y(0)= _e ( 1 2 ), then the value...
- Let n be a non-negative integer. Then the number of divisors of the form "4n + 1" of the number (10)^ 10 .(11)^ 11 .(13)^ 13 is...
- If A= bmatrix 1&0&1 0&1&1 0&0&1 bmatrix and M = A + A^2 + A^3 + .... + A^ 20 then the sum of all the elements of the matrix M is...
- If for x, y P, x > 0, y= _ 10 x+ _ 10 x^ 1/3 + _ 10 x^ 1/9 + upto terms and 2+4+6+ +2y 3+6+9 .3y = 4 _ 10 x , then the ordered...
- Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisector of AB...
- If the matrix A = pmatrix 0&2 &-1 pmatrix satisfies A(A^3+3I) = 2I, then the value of K is :
- The distance of the point (1, –2, 3) from the plane x – y + z = 5 measured parallel to a line, whose direction ratios are 2, 3,...
- If S= z C: z-i z+2i R , then :