A vector $\overrightarrow a $ has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system, $\overrightarrow a $ has components p + 1 and $\sqrt {10} $, then the value of p is equal to :
Previous 10 Questions — JEE Main 2021 (18 March Morning Shift)
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If $\mathop {\lim }\limits_{x \to 0} {{{{\sin }^{ - 1}}x - {{\tan }^{ - 1}}x} \over {3{x^3}}}$ is equal to L, then the …
Topic: JEE Main 2021 (18 March Morning Shift)
The equation of one of the straight lines which passes through the point (1, 3) and makes an angles ${\tan ^{ - 1}}\lef…
Topic: JEE Main 2021 (18 March Morning Shift)
The integral $\int {{{(2x - 1)\cos \sqrt {{{(2x - 1)}^2} + 5} } \over {\sqrt {4{x^2} - 4x + 6} }}} dx$ is equal to (whe…
Topic: JEE Main 2021 (18 March Morning Shift)
The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is…
Topic: JEE Main 2021 (18 March Morning Shift)
Let $\alpha, \beta, \gamma$ be the real roots of the equation $x^3 + ax^2 + bx + c = 0$, $(a, b, c \in \mathbb{R} \text…
Topic: JEE Main 2021 (18 March Morning Shift)
The solutions of the equation $\left| {\matrix{ {1 + {{\sin }^2}x} & {{{\sin }^2}x} & {{{\sin }^2}x} \cr …
Topic: JEE Main 2021 (18 March Morning Shift)
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If the equation $a|z{|^2} + \overline {\overline \alpha z + \alpha \overline z } + d = 0$ represents a circle where a…
Topic: JEE Main 2021 (18 March Morning Shift)
For the four circles M, N, O and P, following four equations are given :Circle M : x2 + y2 = 1, Circle N : x2 + y2 $-$ …
Topic: JEE Main 2021 (18 March Morning Shift)
The real valued function $f(x) = {{\cos e{c^{ - 1}}x} \over {\sqrt {x - [x]} }}$, where [x] denotes the greatest integ…
Topic: JEE Main 2021 (18 March Morning Shift)
If the functions are defined as $f(x) = \sqrt x $ and $g(x) = \sqrt {1 - x} $, then what is the common domain of the fo…
Topic: JEE Main 2021 (18 March Morning Shift)
If $f(x) = \left\{ {\matrix{ {{1 \over {|x|}}} & {;\,|x|\, \ge 1} \cr {a{x^2} + b} & {;\,|x|\, < 1} \…
Topic: JEE Main 2021 (18 March Morning Shift)
Let $A + 2B = \left[ {\matrix{ 1 & 2 & 0 \cr 6 & { - 3} & 3 \cr { - 5} & 3 & 1 \cr …
Topic: JEE Main 2021 (18 March Morning Shift)
The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is :
Topic: JEE Main 2021 (18 March Morning Shift)
The value of $3 + {1 \over {4 + {1 \over {3 + {1 \over {4 + {1 \over {3 + ....\infty }}}}}}}}$
Topic: JEE Main 2021 (18 March Morning Shift)
