1
JEE Main 2022 (Online) 28th July Evening Shift
Numerical
+4
-1
Change Language

Let $$\mathrm{z}=a+i b, b \neq 0$$ be complex numbers satisfying $$z^{2}=\bar{z} \cdot 2^{1-z}$$. Then the least value of $$n \in N$$, such that $$z^{n}=(z+1)^{n}$$, is equal to __________.

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2
JEE Main 2022 (Online) 28th July Evening Shift
Numerical
+4
-1
Change Language

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let $$\mathrm{X}$$ be the number of white balls, among the drawn balls. If $$\sigma^{2}$$ is the variance of $$\mathrm{X}$$, then $$100 \sigma^{2}$$ is equal to ________.

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3
JEE Main 2022 (Online) 28th July Evening Shift
Numerical
+4
-1
Change Language

The value of the integral $$\int\limits_{0}^{\frac{\pi}{2}} 60 \frac{\sin (6 x)}{\sin x} d x$$ is equal to _________.

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4
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Consider the efficiency of carnot's engine is given by $$\eta=\frac{\alpha \beta}{\sin \theta} \log_e \frac{\beta x}{k T}$$, where $$\alpha$$ and $$\beta$$ are constants. If T is temperature, k is Boltzmann constant, $$\theta$$ is angular displacement and x has the dimensions of length. Then, choose the incorrect option :

A
Dimensions of $$\beta$$ is same as that of force.
B
Dimensions of $$\alpha^{-1} x$$ is same as that of energy.
C
Dimensions of $$\eta^{-1} \sin \theta$$ is same as that of $$\alpha \beta$$.
D
Dimensions of $$\alpha$$ is same as that of $$\beta$$.
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