If the system of linear equations
x + y + 3z = 0
x + 3y + k²z = 0
3x + y + 3z = 0
has a non-zero solution (x, y, z) for some k $ \in $ R,then x + $\left( {{y \over z}} \right)$ is equal to :

1

$\lim_{x \to 0} \dfrac{x \left( e^{\tfrac{\sqrt{1+x^{2}+x^{4}}-1}{x}} - 1 \right)}{\sqrt{1+x^{2}+x^{4}} - 1}$

Topic: JEE Main 5 September 2020 (Evening)

2

If a + x = b + y = c + z + 1, where a, b, c, x, y, z are non-zero distinct real numbers, then$\left| {\matrix{ x &amp…

Topic: JEE Main 5 September 2020 (Evening)

3

The value of ${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$ is :

Topic: JEE Main 5 September 2020 (Evening)

4

If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eig…

Topic: JEE Main 5 September 2020 (Evening)

5

If the mean and the standard deviation of thedata 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of…

Topic: JEE Main 5 September 2020 (Evening)

6

Let y = y(x) be the solution of the differentialequationcosx${{dy} \over {dx}}$ + 2ysinx = sin2x, x $ \in $ $\left( {0,…

Topic: JEE Main 5 September 2020 (Evening)

1

The area (in sq. units) of the region A = {(x, y) : (x – 1)[x] $ \le $ y $ \le $ 2$\sqrt x $, 0 $ \le $ x $ \le $ 2}, w…

Topic: JEE Main 5 September 2020 (Evening)

2

If L = sin2$\left( {{\pi \over {16}}} \right)$ - sin2$\left( {{\pi \over {8}}} \right)$ and M = cos2$\left( {{\pi \o…

Topic: JEE Main 5 September 2020 (Evening)

3

If $\int {{{\cos \theta } \over {5 + 7\sin \theta - 2{{\cos }^2}\theta }}} d\theta $ = A${\log _e}\left| {B\left( \the…

Topic: JEE Main 5 September 2020 (Evening)

4

If the length of the chord of the circle,x2 + y2 = r2 (r > 0) along the line, y – 2x = 3 is r,then r2 is equal to :

Topic: JEE Main 5 September 2020 (Evening)

5

If $\alpha $ and $\beta $ are the roots of the equation,7x2 – 3x – 2 = 0, then the value of${\alpha \over {1 - {\alpha…

Topic: JEE Main 5 September 2020 (Evening)

6

The derivative of ${\tan ^{ - 1}}\left( {{{\sqrt {1 + {x^2}} - 1} \over x}} \right)$ with respect to ${\tan ^{ - 1}}\l…

Topic: JEE Main 5 September 2020 (Evening)

7

If x = 1 is a critical point of the function f(x) = (3x2 + ax – 2 – a)ex, then :

Topic: JEE Main 5 September 2020 (Evening)

8

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 …

Topic: JEE Main 5 September 2020 (Evening)