JEE Advanced questions
3844 published questions with worked solutions.
- Let 2^ a_1 + 3^ a_2 + 5^ a_3 + 7^ a_4 + 9^ a_5 be divisible by 4, where a_1, a_2, a_3, a_4, a_5 are digits. The largest possible...
- A plane exists which is perpendicular to the line x 3 = y-1 5 = z+1 7 and passes through the line x+3 10 = y-1 -20 = z+1 k . Then...
- The curve C is the locus of a point whose sum of distances from the points S( 3 , 0) and S'(- 3 , 0) is 4. STATEMENT-1: The curve...
- STATEMENT-1: _0^ /2 dx 1 + ^3 x = 4 . STATEMENT-2: _0^a f(x) ,dx = _0^a f(x + a) ,dx where f(x) is an integrable function.
- Let F(x) = _1^ x^2 t ,dt. STATEMENT-1: F'(x) = x. STATEMENT-2: If f(x) = _a^x (t) ,dt then f'(x) = (x).
- a_1, a_2, a_3, , a_n are in AP. STATEMENT-1: 1 a_1a_n + 1 a_2a_ n-1 + 1 a_3a_ n-2 + + 1 a_na_1 = 2 a_1 + a_n ( 1 a_1 + 1 a_2 + 1...
- ABCD is a quadrilateral in which a circle is inscribed. STATEMENT-1: The lengths of the sides of the quadrilateral can be in AP....
- a, b, c are three unequal positive numbers. STATEMENT-1: The product of their sum and the sum of their reciprocals exceeds 9....
- z is a unimodular complex number. STATEMENT-1: (z^2 + z) = z. STATEMENT-2: z = ( z) - i ( z)
- Let (1 + x)^ 36 = a_0 + a_1x + a_2x^2 + + a_ 36 x^ 36 . STATEMENT-1: a_0 + a_3 + a_6 + + a_ 36 = 2 3 (2^ 35 + 1) STATEMENT-2: a_0...
- Let a, b, c be real such that ax^2 + bx + c = 0 and x^2 + x + 1 = 0 have a common root. STATEMENT-1: a = b = c. STATEMENT-2: Two...
- Given in ABC, a : b : c = A : B : C. STATEMENT-1: ABC is equilateral. STATEMENT-2: A = b^2 + c^2 - a^2 2bc , B = c^2 + a^2 - b^2...Not in JEE syllabus
- STATEMENT-1: [ , b c ; ; c a ; ; a b ,] = 0. STATEMENT-2: If p, q, r are linearly dependent vectors then they are coplanar.
- STATEMENT-1: The probability of getting a tail most of the time in 10 tosses of a unbiased coin is 12 1 - 10! 2^ 10 ,5! ,5! ....
- STATEMENT-1: The probability of solving a new problem by 3 students are 12, 13 and 14 respectively. The probability that the...
- Let A and B are two independent events. STATEMENT-1: If P(A) = 0.3 and P(A B) = 0.8 then P(B) is 27. STATEMENT-2: P( E) = 1 -...
- The equations of two straight lines are x-1 2 = y+3 1 = z-2 -3 and x-2 1 = y-1 -3 = z+3 2 . STATEMENT-1: The given lines are...
- Given two straight lines whose equations are x-3 1 = y-5 -2 = z-7 1 and x+1 7 = y+1 -6 = z+1 1 . STATEMENT-1: The line of...
- STATEMENT-1: The cubic equation 4x^3 - 15x^2 + 14x - 5 = 0 has a root in the interval (2, 3). STATEMENT-2: If f(x) = 0 is a...
- The value of _ j=0 ^ n ( ^ 4n+1 C_ j + ^ 4n+1 C_ 2n-j ) is