Mathematics questions
18011 published questions with worked solutions.
- Let the position vectors of two points P and Q be 3 i - j +2 k and i +2 j -4 k , respectively. Let R and S be two points such...
- Let the functions F:R R and g:R R be defined as : f(x)= cases x+2, & x<0 ^2, & x 0 cases , g(x)= cases x^3, & x<1 3x-2, & x 1...
- Let a complex number z, |z| 1, satisfy _ 1 2 ( |z|+11 (|z|-1)^2 ) 2 Then, the largest value of |z| is equal to _____ .
- If n is the number of irrational terms in the expansion of (3^ 1/4 +5^ 1/8 )^ 60 , then (n–1) is divisible by :
- Let P be a plane x+my+nz=0 containing the line, 1-x 1 = y+4 2 = z+2 3 . If plane P divides the line segment AB joining A(–3, –6,...
- The range of a∈R for which the function f(x) = (4a – 3)(x + _e5) + 2(a – 7) ( x 2 ) ^2 ( x 2 ), x 2n , n , has critical points,...
- A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing...
- Let [x] denote greatest integer less than or equal to x. If for n N, (1-x+x^3)^n= _ j=0 ^ 3n a_jx^j then _ j=0 ^ [ 3n 2 ] a_ 2j...
- If y = y(x) is the solution of the differential equation, dy dx +2y x= x, y ( 3 )=0, then the maximum value of the function y(x)...
- The locus of the midpoints of the chord of the circle, x^2+y^2=25 which is tangent to the hyperbola, x^2 9 - y^2 16 =1 is :
- The number of roots of the equation, (81)^ ^2x +(81)^ ^2x =30 in the interval [0, ] is equal to :Not in JEE Main syllabus
- Let S_k= _ r=1 ^k ^ -1 ( 6^r 2^ 2r+1 +3^ 2r+1 ). then _ k S_k is equal to -
- Consider an arithmetic series and a geometric series having four initial terms from the set 11, 8, 21, 16, 26, 32, 4 . If the...
- Let f:(0,2) R be defined as f(x)= _2 (1+ ( x 4 ) ). Then, _ n 2 n (f ( 1 n )+f ( 2 n )+.....+f(1) ) is equal to _______.
- Let ABCD be a square of side of unit length. Let a circle C_1 centered at A with unit radius is drawn. Another circle C_2 which...
- If _ x 0 ae^x-b x+ce^ -x x x =2, then a + b + c is equal to _______.
- If the normal to the curve y(x)= _0^x(2t^2-15t+10)dt at a point (a, b) is parallel to the line x + 3y = –5, a > 1, then the value...
- Let the curve y = y(x) be the solution of the differential equation, dy dx =2(x+1). If the numerical value of area bounded by the...
- Let f:R R be a continuous function such that f(x) + f(x + 1) = 2, for all x . If I_1= _0^8f(x)dx I_2= _ -1 ^3f(x)dx, then the...
- Let z and w be two complex numbers such that w=z z -2z+2, | z+i z-3i |=1 and Re(w) has minimum value. Then, the minimum value of...