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

Let three vectors `veca, vecb` and `vecc` be such that `vecc` is coplanar with `veca` and `vecb, vecc,` = 7 and `vecb` is perpendicular to `vecc` where `veca = -hati + hatj + hatk` and `vecb = 2hati + hatk`, then the value of `2|veca + vecb + vecc|^2` is ______.

Let a complex number z, |z| ≠ 1, satisfy `log_(1/sqrt(2))((|z| + 11)/(|z| - 1)^2) ≤ 2`. Then, the largest value of |z| is equal to ______.

Let z and ω be two complex numbers such that ω = `zbarz - 2z + 2,|(z + i)/(z - 3i)|` = 1 and Re(ω) has minimum value. Then, the minimum value of n∈N for which ωⁿ is real, is equal to ______.

If z and ω are two complex numbers such that |zω| = 1 and arg(z) – arg(ω) = `(3π)/2`, then `"arg"((1 - 2barzω)/(1 + 3barzω))` is ______. (Here arg(z) denotes the principal argument of complex number z)

The equation arg `((z - 1)/(z + 1)) = π/4` represents a circle with ______. 

Let `veca = hati + hatj + hatk` and `vecb = hatj - hatk`. If `vecc` is a vector such that `veca.vecc = vecb` and `veca.vecc` = 3, then `veca.(vecb.vecc)` is equal to ______.

`int (sin  (5x)/2)/(sin  x/2)dx` is equal to ______. (where C is a constant of integration).

Which one of the following is a fallacy?

`int(log(logx) + 1/(logx)^2)dx` = ______.

`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.

Set of values of x satisfying the inequality `((x - 3)^2(2x + 5)(x - 7))/((x^2 + x + 1)(3x - 6)^2)` ≤ 0 is [a, b) ∪ (b, c] then 2a + b + c is equal to ______.

A function y = f(x) satisfies the differential equation `(dy)/(dx) + x^2y` = –2x, f(1) = 1. the value of |f"(1)| is ______.

The value of `intsinx/(sinx - cosx)dx` equals ______.

If z and ω are two non-zero complex numbers such that |zω| = 1 and Arg(z) – Arg(ω) = `π/2`, then `barzω` is equal to ______.

If x = `sum_(n = 0)^∞a^n`, y = `sum_(n = 0)^∞b^n`, z = `sum_(n = 0)^∞c^n` where a, b , c are in A.P. and |a| < 1, |b| < 1, |c| < 1 then x, y, z are in ______.

If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ²) is ______.

The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.

The value of `lim_(x → ∞) ((x^2 - 1)sin^2(πx))/(x^4 - 2x^3 + 2x - 1)` is equal to ______.

The total number of four-digit numbers such that each of first three digits is divisible by the last digit is equal to ______.

Let M be any 3 × 3 matrix with entries from the set {0, 1, 2}. The maximum number of such matrices, for which the sum of diagonal elements of M^TM is seven, is ______.