1
JEE Main 2022 (Online) 27th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let $$S = 2 + {6 \over 7} + {{12} \over {{7^2}}} + {{20} \over {{7^3}}} + {{30} \over {{7^4}}} + \,.....$$. Then 4S is equal to

A
$${\left( {{7 \over 3}} \right)^2}$$
B
$${{{7^3}} \over {{3^2}}}$$
C
$${\left( {{7 \over 3}} \right)^3}$$
D
$${{{7^2}} \over {{3^3}}}$$
2
JEE Main 2022 (Online) 27th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If a1, a2, a3 ...... and b1, b2, b3 ....... are A.P., and a1 = 2, a10 = 3, a1b1 = 1 = a10b10, then a4 b4 is equal to -

A
$${{35} \over {27}}$$
B
1
C
$${{27} \over {28}}$$
D
$${{28} \over {27}}$$
3
JEE Main 2022 (Online) 27th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If m and n respectively are the number of local maximum and local minimum points of the function $$f(x) = \int\limits_0^{{x^2}} {{{{t^2} - 5t + 4} \over {2 + {e^t}}}dt} $$, then the ordered pair (m, n) is equal to

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

Let f be a differentiable function in $$\left( {0,{\pi \over 2}} \right)$$. If $$\int\limits_{\cos x}^1 {{t^2}\,f(t)dt = {{\sin }^3}x + \cos x} $$, then $${1 \over {\sqrt 3 }}f'\left( {{1 \over {\sqrt 3 }}} \right)$$ is equal to

A
$$6 - 9\sqrt 2 $$
B
$$6 - {9 \over {\sqrt 2 }}$$
C
$${9 \over 2} - 6\sqrt 2 $$
D
$${9 \over {\sqrt 2 }} - 6$$
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