JEE Main questions
34495 published questions with worked solutions.
- The number of solutions of the equation 2 2 + 5 2 = 2 ^3 5 2 in [- 2 , 2 ] is :Not in JEE Main syllabus
- If the orthocenter of the triangle formed by the lines y = x + 1, y = 4x – 8 and y = mx + c is at (3, –1), then m – c is:
- Let a and b be the vectors of the same magnitude such that | a + b |+| a - b | | a + b |-| a - b | = 2 +1. Then | a + b |^2 | a...
- If the area of the region (x, y) : 1 + x^2 y min x + 7, 11 – 3x is A, then 3A is equal to
- Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides and q be the...
- If the range of the function f(x) = 5-x x^2-3x+2 , x 1, 2, is (- , ] [ , ), then ^2 + ^2 is equal to :
- If the locus of Z C, such that Re ( z-1 2z+i ) + Re ( z -1 2 z -i ) = 2, is a circle of radius r and center (a, b), then 15ab r^2...
- Let a_n be the nth term of an A.P. If S_n = a_1 + a_2 + a_3 + + a_n = 700, a_6 = 7 and S_7 = 7, then a_n is equal to :
- If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth...
- Let the length of a latus rectum of an ellipse x^2 a^2 + y^2 b^2 = 1 be 10. If its eccentricity is the minimum value of the...
- Let y = y(x) be the solution of the differential equation (x^2 + 1) y' - 2xy = (x^4 + 2x^2 + 1) x, y(0) = 1. Then _ -3 ^ 3 y(x)dx...
- Consider the lines L_1 : x - 1 = y - 2 = z and L_2 : x - 2 = y = z - 1. Let the feet of the perpendiculars from the point P(5, 1,...
- The number of real roots of the equation x |x – 2| + 3|x – 3| + 1 = 0 is
- Let the system of equations x + 5y – z = 1 4x + 3y – 3z = 7 24x + y + λz = m, λ, μ ∈ **R**, have infinitely many solutions. Then...
- Let f : R → R be a polynomial function of degree four having extreme values at x = 4 and x = 5. If _ x 0 f(x) x^2 = 5, then f(2)...
- For t > – 1, let _t and _t be the roots of the equation ((t+2)^ 1/7 -1 )x^2 + ((t+2)^ 1/6 -1 )x + ((t+2)^ 1/21 -1 ) = 0. If _ t...
- The sum of the series 2 1 ^ 20 C_4 - 3 2 ^ 20 C_5 + 4 3 ^ 20 C_6 - 5 4 ^ 20 C_7 + + 18 17 ^ 20 C_ 20 , is equal to _______.
- If the function f(x) = ( x) - ( x) x - x is continuous at x = 0, then f(0) is equal to ______.
- The unit of 2I _0 c is : (I = intensity of an electromagnetic wave, c : speed of light)
- Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) :...