JEE Main entrance exam Question Bank Solutions

Let ABC be a triangle such that ∠A = 45°, ∠B = 75° then `"a" + "c"sqrt(2)` is equal to ______. (in usual notation)

If `(tan2θ + tanθ)/(1 - tanθtan2θ)` = 0, then the general value of θ is ______.

In a triangle ABC, in usual notation, (a + b + c)(b + c – a) = λbc will be true if ______.

If sum of all the solutions of the equation `8cosx.(cos(π/6 + x).cos(π/6 - x) - 1/2)` = 1 in [0, π] is kπ, then k is equal to ______.

Consider the statement: “P(n) : n² – n + 41 is prime." Then which one of the following is true?

The positive integer just greater than (1 + 0.0001)¹⁰⁰⁰⁰ is ______.

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is ______.

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 ______.