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

$$ \text { Let } f(x)=a x^{2}+b x+c \text { be such that } f(1)=3, f(-2)=\lambda \text { and } $$ $$f(3)=4$$. If $$f(0)+f(1)+f(-2)+f(3)=14$$, then $$\lambda$$ is equal to :

A
$$-$$4
B
$$\frac{13}{2}$$
C
$$\frac{23}{2}$$
D
4
3
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The function $$f: \mathbb{R} \rightarrow \mathbb{R}$$ defined by

$$f(x)=\lim\limits_{n \rightarrow \infty} \frac{\cos (2 \pi x)-x^{2 n} \sin (x-1)}{1+x^{2 n+1}-x^{2 n}}$$ is continuous for all x in :

A
$$R-\{-1\}$$
B
$$ \mathbb{R}-\{-1,1\}$$
C
$$R-\{1\}$$
D
$$R-\{0\}$$
4
JEE Main 2022 (Online) 28th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The function $$f(x)=x \mathrm{e}^{x(1-x)}, x \in \mathbb{R}$$, is :

A
increasing in $$\left(-\frac{1}{2}, 1\right)$$
B
decreasing in $$\left(\frac{1}{2}, 2\right)$$
C
increasing in $$\left(-1,-\frac{1}{2}\right)$$
D
decreasing in $$\left(-\frac{1}{2}, \frac{1}{2}\right)$$
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