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

Among the following the number of state variables is ______________.

Internal energy (U)

Volume (V)

Heat (q)

Enthalpy (H)

Your input ____
2
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$ \text { Let } S=\left\{x \in[-6,3]-\{-2,2\}: \frac{|x+3|-1}{|x|-2} \geq 0\right\} \text { and } $$

$$T=\left\{x \in \mathbb{Z}: x^{2}-7|x|+9 \leq 0\right\} \text {. } $$

Then the number of elements in $$\mathrm{S} \cap \mathrm{T}$$ is :

A
7
B
5
C
4
D
3
3
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\alpha$$, $$\beta$$ be the roots of the equation $$x^{2}-\sqrt{2} x+\sqrt{6}=0$$ and $$\frac{1}{\alpha^{2}}+1, \frac{1}{\beta^{2}}+1$$ be the roots of the equation $$x^{2}+a x+b=0$$. Then the roots of the equation $$x^{2}-(a+b-2) x+(a+b+2)=0$$ are :

A
non-real complex numbers
B
real and both negative
C
real and both positive
D
real and exactly one of them is positive
4
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\mathrm{A}$$ and $$\mathrm{B}$$ be any two $$3 \times 3$$ symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?

A
$$\mathrm{A}^{4}-\mathrm{B}^{4}$$ is a smmetric matrix
B
$$\mathrm{AB}-\mathrm{BA}$$ is a symmetric matrix
C
$$\mathrm{B}^{5}-\mathrm{A}^{5}$$ is a skew-symmetric matrix
D
$$\mathrm{AB}+\mathrm{BA}$$ is a skew-symmetric matrix
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