Let $S$ be the set of all real values of $k$ for which the system of linear equations

$x + y + z = 2$

$2x + y - z = 3$

$3x + 2y + kz = 4$

has a unique solution. Then $S$ is :

1

If $x_1, x_2,\ldots , x_n$ and $\frac{1}{h_1}, \frac{1}{h_2},\ldots , \frac{1}{h_n}$ are two A.P.s such that $x_3 = h_2…

Topic: JEE Main 2018 (15 April Morning Shift)

2

n–digit numbers are formed using only three digits 2,5,7. The smallest value of n for which 900 such distinct numbers c…

Topic: JEE Main 2018 (15 April Morning Shift)

1

Let $A$ be a matrix such that $A \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}$ is a scalar matrix and $|3A| = 108$. The…

Topic: JEE Main 2018 (15 April Morning Shift)

2

If $\lambda \in \mathbb{R}$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2-\lambda)x + (10-…

Topic: JEE Main 2018 (15 April Morning Shift)

3

Consider the following two binary relations on the set $A = {a, b, c}$ : $R_1 = {(c, a), (b, b), (a, c), (c, c), (b, c)…

Topic: JEE Main 2018 (15 April Morning Shift)

4

The set of all $\alpha \in \mathbb{R}$ for which $w = \dfrac{1 + (1-8\alpha)z}{1-z}$ is purely imaginary number, for al…

Topic: JEE Main 2018 (15 April Morning Shift)

5

If the tangents drawn to the hyperbola $4y^{2}=x^{2}+1$ intersect the co-ordinate axes at the distinct points $A$ and $…

Topic: JEE Main 2018 (15 April Morning Shift)

6

If $\tan A$ and $\tan B$ are the roots of the quadratic equation $3x^{2}-10x-25=0$, then the value of $3\sin^{2}(A+B)-1…

Topic: JEE Main 2018 (15 April Morning Shift)

7

A box $A$ contains $2$ white, $3$ red and $2$ black balls. Another box $B$ contains $4$ white, $2$ red and $3$ black ba…

Topic: JEE Main 2018 (15 April Morning Shift)

8

The mean of set of $30$ observations is $75$. If each observation is multiplied by a non-zero number $\lambda$ and then…

Topic: JEE Main 2018 (15 April Morning Shift)

9

If $\overrightarrow a ,\,\,\overrightarrow b ,$ and $\overrightarrow C $ are unit vectors such that $\overrightarrow a…

Topic: JEE Main 2018 (15 April Morning Shift)

10

Let y = y(x) be the solution of the differential equation ${{dy} \over {dx}} + 2y = f\left( x \right),$ where $f\left( …

Topic: JEE Main 2018 (15 April Morning Shift)