1
JEE Main 2023 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let the vectors $$\vec{a}, \vec{b}, \vec{c}$$ represent three coterminous edges of a parallelopiped of volume V. Then the volume of the parallelopiped, whose coterminous edges are represented by $$\vec{a}, \vec{b}+\vec{c}$$ and $$\vec{a}+2 \vec{b}+3 \vec{c}$$ is equal to :

A
3 V
B
2 V
C
6 V
D
V
2
JEE Main 2023 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

If the tangents at the points $$\mathrm{P}$$ and $$\mathrm{Q}$$ on the circle $$x^{2}+y^{2}-2 x+y=5$$ meet at the point $$R\left(\frac{9}{4}, 2\right)$$, then the area of the triangle $$\mathrm{PQR}$$ is :

A
$$\frac{13}{8}$$
B
$$\frac{5}{8}$$
C
$$\frac{5}{4}$$
D
$$\frac{13}{4}$$
3
JEE Main 2023 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f(x)$$ be a function satisfying $$f(x)+f(\pi-x)=\pi^{2}, \forall x \in \mathbb{R}$$. Then $$\int_\limits{0}^{\pi} f(x) \sin x d x$$ is equal to :

A
$$\pi^{2}$$
B
$$\frac{\pi^{2}}{2}$$
C
$$2 \pi^{2}$$
D
$$\frac{\pi^{2}}{4}$$
4
JEE Main 2023 (Online) 6th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Among the statements

(S1) : $$(p \Rightarrow q) \vee((\sim p) \wedge q)$$ is a tautology

(S2) : $$(q \Rightarrow p) \Rightarrow((\sim p) \wedge q)$$ is a contradiction

A
neither (S1) and (S2) is True
B
only (S2) is True
C
both $$(\mathrm{S} 1)$$ and $$(\mathrm{S} 2)$$ are True
D
only (S1) is True
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