If the system of linear equations

$x + ay + z = 3$

$x + 2y + 2z = 6$

$x + 5y + 3z = b$

has no solution, then :

1

If $a$, $b$, $c$ are in A.P. and $a^{2}$, $b^{2}$, $c^{2}$ are in G.P. such that $a < b < c$ and $a + b + c = \dfrac{3}…

Topic: JEE Main 2018 (15 April Evening Shift)

1

If $|z - 3 + 2i| \le 4$ then the difference between the greatest value and the least value of $|z|$ is :

Topic: JEE Main 2018 (15 April Evening Shift)

2

The number of four letter words that can be formed using the letters of the word $\text{BARRACK}$ is :

Topic: JEE Main 2018 (15 April Evening Shift)

3

Suppose $A$ is any $3\times 3$ non-singular matrix and $(A-3I)(A-5I)=0$ where $I=I_{3}$ and $O=O_{3}$. If $\alpha A+\be…

Topic: JEE Main 2018 (15 April Evening Shift)

4

Let $f\colon A\to B$ be a function defined as $f(x)=\dfrac{x-1}{x-2}$, where $A=\mathbb{R}-{2}$ and $B=\mathbb{R}-{1}$.…

Topic: JEE Main 2018 (15 April Evening Shift)

5

If $f(x)$ is a quadratic expression such that $f(1)+f(2)=0$, and $-1$ is a root of $f(x)=0$, then the other root of $f(…

Topic: JEE Main 2018 (15 April Evening Shift)

6

If the position vectors of the vertices $A$, $B$ and $C$ of a $\triangle ABC$ are respectively $4\hat{i}+7\hat{j}+8\hat…

Topic: JEE Main 2018 (15 April Evening Shift)

7

If the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$, then the variance of this data is :

Topic: JEE Main 2018 (15 April Evening Shift)

8

A player $X$ has a biased coin whose probability of showing heads is $p$ and a player $Y$ has a fair coin. They start p…

Topic: JEE Main 2018 (15 April Evening Shift)

9

An angle between the lines whose direction cosines are given by the equations $l + 3m + 5n = 0$ and $5lm - 2mn + 6nl = …

Topic: JEE Main 2018 (15 April Evening Shift)

10

Tangents drawn from the point $(-8,0)$ to the parabola $y^{2} = 8x$ touch the parabola at $P$ and $Q$. If $F$ is the fo…

Topic: JEE Main 2018 (15 April Evening Shift)