Mathematics questions
18011 published questions with worked solutions.
- Coefficient of x^ 11 in the expansion of (1 + x^2)^4(1 + x^3)^7(1 + x^4)^ 12 is
- The common tangents to the circle x^2 + y^2 = 2 and the parabola y^2 = 8x touch the circle at the points P, Q and the parabola at...
- For x ∈ (0, π), the equation sin x + 2 sin 2x − sin 3x = 3 hasNot in JEE Main syllabus
- In a triangle the sum of two sides is x and the product of the same two sides is y. If x^2 - c^2 = y, where c is the third side...Not in JEE syllabus
- Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains...
- Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than...
- The quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then the equation p(p(x)) = 0 has
- Let z_k = ( 2k 10 ) + i ( 2k 10 ); k = 1, 2, …, 9. List I P. For each z_k there exists a z_j such that z_k z_j = 1 Q. There...
- List I P. The number of polynomials f(x) with non-negative integer coefficients of degree ≤ 2, satisfying f(0) = 0 and _0^1f(x)...
- List I P. Let y(x) = (3 ^ -1 x), x ∈ [−1, 1], x 3 2 . Then 1 y(x) (x^2 - 1) d^2y(x) dx^2 + x dy(x) dx equals Q. Let A_1, A_2, ,...
- Let f_1 : R R , f_2 : [0, ) R , f_3 : R R and f_4 : R [0, ) be defined by f_1(x) = cases |x| & if x < 0, e^x & if x 0; cases...
- The number of distinct solutions of the equation 5 4 ^2 2x+ ^4x+ ^4x+ ^6x+ ^6x=2 in the interval [0,2 ] isNot in JEE Main syllabus
- The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least...
- Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively...
- If the normals of the parabola y^2=4x drawn at the end points of its latus rectum are tangents to the circle (x-3)^2+(y+2)^2=r^2,...
- Let f: R R be a function defined by f(x)= cases [x], & x 2 0, & x>2 cases , where [x] is the greatest integer less than or equal...
- A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of...
- Let X and Y be two arbitrary, 3 3, non-zero, skew-symmetric matrices and Z be an arbitrary 3 3, non-zero, symmetric matrix. Then...
- Which of the following values of satisfy the equation vmatrix (1+ )^2 & (1+2 )^2 & (1+3 )^2 (2+ )^2 & (2+2 )^2 & (2+3 )^2 (3+ )^2...
- In R ^3, consider the planes P_1:y=0 and P_2:x+z=1. Let P_3 be a plane, different from P_1 and P_2, which passes through the...