1
JEE Main 2023 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Which of the following statements is a tautology?

A
$$\mathrm{p\vee(p\wedge q)}$$
B
$$(\mathrm{p\wedge(p\to q))\to\,\sim q}$$
C
$$\mathrm{p\to (p\wedge (p\to q))}$$
D
$$(\mathrm{p\wedge q)\to(\sim (p)\to q)}$$
2
JEE Main 2023 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

For the system of linear equations $$\alpha x+y+z=1,x+\alpha y+z=1,x+y+\alpha z=\beta$$, which one of the following statements is NOT correct?

A
It has infinitely many solutions if $$\alpha=1$$ and $$\beta=1$$
B
It has infinitely many solutions if $$\alpha=2$$ and $$\beta=-1$$
C
$$x+y+z=\frac{3}{4}$$ if $$\alpha=2$$ and $$\beta=1$$
D
It has no solution if $$\alpha=-2$$ and $$\beta=1$$
3
JEE Main 2023 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$y(x)=x^{x},x > 0$$, then $$y''(2)-2y'(2)$$ is equal to

A
$$4(\log_{e}2)^{2}+2$$
B
$$8\log_{e}2-2$$
C
$$4\log_{e}2+2$$
D
$$4(\log_{e}2)^{2}-2$$
4
JEE Main 2023 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The value of the integral

$$\int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {{{x + {\pi \over 4}} \over {2 - \cos 2x}}dx} $$ is :

A
$${{{\pi ^2}} \over {6\sqrt 3 }}$$
B
$${{{\pi ^2}} \over 6}$$
C
$${{{\pi ^2}} \over {3\sqrt 3 }}$$
D
$${{{\pi ^2}} \over {12\sqrt 3 }}$$
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