JEE Main entrance exam Question Bank Solutions for Mathematics (JEE Main)

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?

The differential equation whose solution is Ax² + By² = 1 where A and B are arbitrary constants is of ______.

If in a ΔABC `a cos^2(C/2) + c cos^2(A/2) = (3b)/2`, then the sides a, b and c ______.

Let a triangle ABC be inscribed in the circle x² `-sqrt(2)(x + y) + y^2` = 0 such that ∠BAC = `π/2`. If the length of side AB is `sqrt(2)`, then the area of the ΔABC is equal to ______.

If one of the diameters of the circle x² + y² – 2x – 6y + 6 = 0 is a chord of another circle 'C' whose center is at (2, 1), then its radius is ______.

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 ______.

The coefficient of x²⁵⁶ in the expansion of (1 – x)¹⁰¹(x² + x + 1)¹⁰⁰ is ______.

The number of rational terms in the binomial expansion of `(4^(1/4) + 5^(1/6))^120` is ______.

The sum of the co-efficients of all even degree terms in x in the expansion of `(x + sqrt(x^3 - 1))^6 + (x - sqrt(x^3 - 1))^6, (x > 1)` is equal to ______.

If D, E, F are the mid points of the sides BC, CA and AB respectively of a triangle ABC and 'O' is any point, then, `|vec(AD) + vec(BE) + vec(CF)|`, is ______.

If the 4^th term in the expansion of `(ax + 1/x)^n` is `5/2` then the values of a and n respectively are ______.

Given, `f_n(x) = 1/n(sin^nx + cos^nx)` for n = 1, 2, 3, ....... Then the value of 24(f₄(x) – f₆(x)) is equal to ______.

The coefficient of y⁴⁹ in (y – 1)(y – 3)(y – 5) ...... (y – 99) is ______.

The number of ordered pairs (a, b), (where a, b ∈ R) satisfying the equation a²⁰⁰⁸ + b²⁰⁰⁸ = 2008 |a||b| – 2006 is equal to ______.

Let right angled isosceles triangle ABC be inscribed in a circle according to adjacent diagram vertex A is moved along the circle to reach at A' such that are \[{\stackrel\frown{AA'}}\] = `(πr)/3`, if r = `sqrt(3) + 1` then (A'C)² is ______.

If |x – 1| + |x – 2| + |x – 3| ≥ 6 then ______.

The points A(5, –1, 1); B(7, –4, 7); C(1, –6, 10) and D(–1, –3, 4) are vertices of a ______.

The middle term in the expansion of (1 – 3x + 3x² – x³)⁶ is ______.

The value of cos 255° + sin 195° is ______.

The number of solution of tan x + sec x = 2 cos x in [0, 2π] is ______.