Let a be an integer such that $\mathop {\lim }\limits_{x \to 7} {{18 - [1 - x]} \over {[x - 3a]}}$ exists, where [t] is greatest integer $\le$ t. Then a is equal to :

1

The number of distinct real roots of x4 $-$ 4x + 1 = 0 is :

Topic: JEE Main 2022 (27 June Morning Shift)

2

If ${\cos ^{ - 1}}\left( {{y \over 2}} \right) = {\log _e}{\left( {{x \over 5}} \right)^5},\,|y| < 2$, then :

Topic: JEE Main 2022 (27 June Morning Shift)

3

If $\int {{{({x^2} + 1){e^x}} \over {{{(x + 1)}^2}}}dx = f(x){e^x} + C} $, where C is a constant, then ${{{d^3}f} \over…

Topic: JEE Main 2022 (27 June Morning Shift)

4

The value of the integral $\int\limits_{ - 2}^2 {{{|{x^3} + x|} \over {({e^{x|x|}} + 1)}}dx} $ is equal to :

Topic: JEE Main 2022 (27 June Morning Shift)

5

If ${{dy} \over {dx}} + {{{2^{x - y}}({2^y} - 1)} \over {{2^x} - 1}} = 0$, x, y > 0, y(1) = 1, then y(2) is equal to :

Topic: JEE Main 2022 (27 June Morning Shift)

6

In an isosceles triangle ABC, the vertex A is (6, 1) and the equation of the base BC is 2x + y = 4. Let the point B lie…

Topic: JEE Main 2022 (27 June Morning Shift)

7

Let the eccentricity of an ellipse ${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$, $a > b$, be ${1 \over 4}$. …

Topic: JEE Main 2022 (27 June Morning Shift)

8

If two straight lines whose direction cosines are given by the relations $l + m - n = 0$, $3{l^2} + {m^2} + cnl = 0$ ar…

Topic: JEE Main 2022 (27 June Morning Shift)

9

Let $\overrightarrow a = \widehat i + \widehat j - \widehat k$ and $\overrightarrow c = 2\widehat i - 3\widehat j + 2…

Topic: JEE Main 2022 (27 June Morning Shift)

10

Five numbers ${x_1},{x_2},{x_3},{x_4},{x_5}$ are randomly selected from the numbers 1, 2, 3, ......., 18 and are arrang…

Topic: JEE Main 2022 (27 June Morning Shift)