JEE Advanced questions
859 published questions with worked solutions.
- Match the compounds in LIST-I with the observations in LIST-II, and choose the correct option. LIST-I (I) Aniline (II) o-Cresol...
- Let and be real numbers such that - 4 < < 0 < < 4 . If ( + ) = 1 3 and ( - ) = 2 3 , then the greatest integer less than or equal...
- If y(x) is the solution of the differential equation x ,dy - (y^2 - 4y) ,dx = 0 for x > 0, y(1) = 2, and the slope of the curve y...
- The product of all positive real values of x satisfying the equation x^ (16( _5 x)^3 - 68 _5 x ) = 5^ -16 is _____.
- If = _ x 0 e^ x^3 - (1 - x^3)^ 1 3 + ((1 - x^2)^ 1 2 - 1 ) x x ^2 x , then the value of 6 is _____.
- Let be a real number. Consider the matrix A = pmatrix & 0 & 1 2 & 1 & -2 3 & 1 & -2 pmatrix . If A^7 - ( - 1)A^6 - A^5 is a...
- Consider the hyperbola x^2 100 - y^2 64 = 1 with foci at S and S_1, where S lies on the positive x-axis. Let P be a point on the...
- Consider the functions f, g: R R defined by f(x) = x^2 + 5 12 and g(x) = cases 2 (1 - 4|x| 3 ), & |x| 3 4 , 0, & |x| > 3 4 ....
- Let PQRS be a quadrilateral in a plane, where QR = 1, PQR = QRS = 70°, PQS = 15° and PRS = 40°. If RPS = °, PQ = and PS = , then...
- Let z denote the complex conjugate of a complex number z. If z is a non-zero complex number for which both real and imaginary...
- Let G be a circle of radius R > 0. Let G_1, G_2, , G_n be n circles of equal radius r > 0. Suppose each of the n circles G_1,...
- Let i , j and k be the unit vectors along the three positive coordinate axes. Let a = 3 i + j - k , b = i + b_2 j + b_3 k , b_2,...
- For x R , let the function y(x) be the solution of the differential equation dy dx + 12y = ( 12 x ), y(0) = 0. Then, which of the...
- Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many...
- If M = pmatrix 5 2 & 3 2 - 3 2 & - 1 2 pmatrix , then which of the following matrices is equal to M^ 2022 ?
- Suppose that Box-I contains 8 red, 3 blue and 5 green balls, Box-II contains 24 red, 9 blue and 15 green balls, Box-III contains...
- For positive integer n, define f(n) = n + 16 + 5n - 3n^2 4n + 3n^2 + 32 + n - 3n^2 8n + 3n^2 + 48 - 3n - 3n^2 12n + 3n^2 + + 25n...
- In a radioactive decay chain reaction, ^ 230 _ 90 Th nucleus decays into ^ 214 _ 84 Po nucleus. The ratio of the number of to...
- In a particular system of units, a physical quantity can be expressed in terms of the electric charge e, electron mass m_e,...
- On a frictionless horizontal plane, a bob of mass m = 0.1 kg is attached to a spring with natural length l_0 = 0.1 m. The spring...