Let C be the set of all complex numbers. Let ${S_1} = \{ z \in C||z - 3 - 2i{|^2} = 8\} $ ${S_2} = \{ z \in C|{\mathop{\rm Re}\nolimits} (z) \ge 5\} $ and ${S_3} = \{ z \in C||z - \overline z | \ge 8\} $. Then the number of elements in ${S_1} \cap {S_2} \cap {S_3}$ is equal to :

1

The value of the definite integral$ \int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {{{dx} \over {(1 + {e^{x\cos x}})(…

Topic: JEE Main 2021 (27 July Morning Shift)

2

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

Topic: JEE Main 2021 (27 July Morning Shift)

3

If the mean and variance of the following data : 6, 10, 7, 13, a, 12, b, 12 are 9 and ${{37} \over 4}$ respectively, t…

Topic: JEE Main 2021 (27 July Morning Shift)

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If the area of the bounded region $R = \left\{ {(x,y):\max \{ 0,{{\log }_e}x\} \le y \le {2^x},{1 \over 2} \le x \le 2…

Topic: JEE Main 2021 (27 July Morning Shift)

2

A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this…

Topic: JEE Main 2021 (27 July Morning Shift)

3

If the coefficients of x7 in ${\left( {{x^2} + {1 \over {bx}}} \right)^{11}}$ and x$-$7 in ${\left( {{x} - {1 \over {bx…

Topic: JEE Main 2021 (27 July Morning Shift)

4

If $\sin \theta + \cos \theta = {1 \over 2}$, then 16(sin(2$\theta$) + cos(4$\theta$) + sin(6$\theta$)) is equal to :

Topic: JEE Main 2021 (27 July Morning Shift)

5

Let $A = \left[ {\matrix{ 1 & 2 \cr { - 1} & 4 \cr } } \right]$. If A$-$1 = $\alpha$I + $\beta$A, $\alp…

Topic: JEE Main 2021 (27 July Morning Shift)

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Let $f:\left( { - {\pi \over 4},{\pi \over 4}} \right) \to R$ be defined as $f(x) = \left\{ {\matrix{ {{{(1 + |\sin…

Topic: JEE Main 2021 (27 July Morning Shift)

7

Let y = y(x) be solution of the differential equation ${\log _{}}\left( {{{dy} \over {dx}}} \right) = 3x + 4y$, with y(…

Topic: JEE Main 2021 (27 July Morning Shift)

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Let f : R $\to$ R be a function such that f(2) = 4 and f'(2) = 1. Then, the value of $\mathop {\lim }\limits_{x \to 2} …

Topic: JEE Main 2021 (27 July Morning Shift)

9

Let $P$ and $Q$ be two distinct points on a circle which has center at $C(2,3)$ and which passes through origin $O$. If…

Topic: JEE Main 2021 (27 July Morning Shift)

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Let $\alpha$, $\beta$ be two roots of the equation x2 + (20)1/4x + (5)1/2 = 0. Then $\alpha$8 + $\beta$8 is equal to

Topic: JEE Main 2021 (27 July Morning Shift)