If the system of linear equations

2x + y $-$ z = 7

x $-$ 3y + 2z = 1

x + 4y + $\delta$z = k, where $\delta$, k $\in$ R has infinitely many solutions, then $\delta$ + k is equal to:

1

The area enclosed by y2 = 8x and y = $\sqrt2$ x that lies outside the triangle formed by y = $\sqrt2$ x, x = 1, y = 2$\…

Topic: JEE Main 2022 (29 June Morning Shift)

2

Let $\overrightarrow a = \alpha \widehat i + 3\widehat j - \widehat k$, $\overrightarrow b = 3\widehat i - \beta \wid…

Topic: JEE Main 2022 (29 June Morning Shift)

3

Let $f:R \to R$ be a function defined by :$f(x) = \left\{ {\matrix{ {\max \,\{ {t^3} - 3t\} \,t \le x} & ; & {x \le 2…

Topic: JEE Main 2022 (29 June Morning Shift)

4

Let the solution curve of the differential equation$x{{dy} \over {dx}} - y = \sqrt {{y^2} + 16{x^2}} $, $y(1) = 3$ be $…

Topic: JEE Main 2022 (29 June Morning Shift)

5

The probability that a randomly chosen 2 $\times$ 2 matrix with all the entries from the set of first 10 primes, is sin…

Topic: JEE Main 2022 (29 June Morning Shift)

1

Let $\alpha$ and $\beta$ be the roots of the equation x2 + (2i $-$ 1) = 0. Then, the value of |$\alpha$8 + $\beta$8| is…

Topic: JEE Main 2022 (29 June Morning Shift)

2

Let $A = [{a_{ij}}]$ be a square matrix of order 3 such that ${a_{ij}} = {2^{j - i}}$, for all i, j = 1, 2, 3. Then, th…

Topic: JEE Main 2022 (29 June Morning Shift)

3

Let a set $A = A_1 \cup A_2 \cup \cdots \cup A_k$, where $A_i \cap A_j = \phi$ for $i \ne j$, $1 \le i, j \le k$. Defin…

Topic: JEE Main 2022 (29 June Morning Shift)

4

The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A' B (where B i…

Topic: JEE Main 2022 (29 June Morning Shift)

5

A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an…

Topic: JEE Main 2022 (29 June Morning Shift)

6

The domain of the function ${\cos ^{ - 1}}\left( {{{2{{\sin }^{ - 1}}\left( {{1 \over {4{x^2} - 1}}} \right)} \over \pi…

Topic: JEE Main 2022 (29 June Morning Shift)

7

If the constant term in the expansion of ${\left( {3{x^3} - 2{x^2} + {5 \over {{x^5}}}} \right)^{10}}$ is 2k.l, where l…

Topic: JEE Main 2022 (29 June Morning Shift)

8

$\int_0^5 {\cos \left( {\pi \left( {x - \left[ {{x \over 2}} \right]} \right)} \right)dx} $,where [t] denotes greatest …

Topic: JEE Main 2022 (29 June Morning Shift)

9

Let PQ be a focal chord of the parabola y2 = 4x such that it subtends an angle of ${\pi \over 2}$ at the point (3, 0).…

Topic: JEE Main 2022 (29 June Morning Shift)

10

Let the mean and the variance of 5 observations $x_1, x_2, x_3, x_4, x_5$ be $\dfrac{24}{5}$ and $\dfrac{194}{25}$ resp…

Topic: JEE Main 2022 (29 June Morning Shift)