1
JEE Main 2022 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Suppose $$a_{1}, a_{2}, \ldots, a_{n}$$, .. be an arithmetic progression of natural numbers. If the ratio of the sum of first five terms to the sum of first nine terms of the progression is $$5: 17$$ and , $$110 < {a_{15}} < 120$$, then the sum of the first ten terms of the progression is equal to

A
290
B
380
C
460
D
510
2
JEE Main 2022 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be a function defined as

$$f(x)=a \sin \left(\frac{\pi[x]}{2}\right)+[2-x], a \in \mathbb{R}$$ where $$[t]$$ is the greatest integer less than or equal to $$t$$. If $$\mathop {\lim }\limits_{x \to -1 } f(x)$$ exists, then the value of $$\int\limits_{0}^{4} f(x) d x$$ is equal to

A
$$-$$1
B
$$-$$2
C
1
D
2
3
JEE Main 2022 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$ I=\int_{\pi / 4}^{\pi / 3}\left(\frac{8 \sin x-\sin 2 x}{x}\right) d x $$. Then

A
$${\pi \over 2} < I < {{3\pi } \over 4}$$
B
$${\pi \over 5} < I < {{5\pi } \over {12}}$$
C
$${{5\pi } \over {12}} < I < {{\sqrt 2 } \over 3}\pi $$
D
$${{3\pi } \over 4} < I < \pi $$
4
JEE Main 2022 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The area of the smaller region enclosed by the curves $$y^{2}=8 x+4$$ and $$x^{2}+y^{2}+4 \sqrt{3} x-4=0$$ is equal to

A
$$\frac{1}{3}(2-12 \sqrt{3}+8 \pi)$$
B
$$\frac{1}{3}(2-12 \sqrt{3}+6 \pi)$$
C
$$\frac{1}{3}(4-12 \sqrt{3}+8 \pi)$$
D
$$\frac{1}{3}(4-12 \sqrt{3}+6 \pi)$$
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