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1

WB JEE 2022

MCQ (Single Correct Answer)
English
Bengali

The maximum value of $$f(x) = {e^{\sin x}} + {e^{\cos x}};x \in R$$ is

A
2e
B
$$2\sqrt e $$
C
$$2{e^{{1 \over {\sqrt 2 }}}}$$
D
$$2{e^{ - {1 \over {\sqrt 2 }}}}$$

$$f(x) = {e^{\sin x}} + {e^{\cos x}};x \in R$$ এর সর্বোচ্চ মান হবে

A
2e
B
$$2\sqrt e $$
C
$$2{e^{{1 \over {\sqrt 2 }}}}$$
D
$$2{e^{ - {1 \over {\sqrt 2 }}}}$$
2

WB JEE 2022

MCQ (Single Correct Answer)
English
Bengali

Let $$f(n) = {2^{n + 1}}$$, $$g(n) = 1 + (n + 1){2^n}$$ for all $$n \in N$$. Then

A
$$f(n) > g(n)$$
B
$$f(n) < g(n)$$
C
f(n) and g(n) are not comparable.
D
$$f(n) > g(n)$$ if n be even and $$f(n) < g(n)$$ if n be odd.

মনে কর সকল $$n \in N$$ এর জন্য $$f(n) = {2^{n + 1}}$$, $$g(n) = 1 + (n + 1){2^n}$$ । তবে

A
$$f(n) > g(n)$$
B
$$f(n) < g(n)$$
C
f(n) and g(n) এর মধ্যে কোন তুলনা করা যায় না।
D
যদি n যুগ্ম হয় তবে $$f(n) > g(n)$$ ও যদি n অযুগ্ম হয় তবে $$f(n) < g(n)$$ হবে।
3

WB JEE 2022

MCQ (Single Correct Answer)
English
Bengali

Let $$f(x) = {(x - 2)^{17}}{(x + 5)^{24}}$$. Then

A
f does not have a critical point at x = 2
B
f has a minimum at x = 2
C
f has neither a maximum nor a minimum at x = 2
D
f has a minimum at x = 2

মনে কর $$f(x) = {(x - 2)^{17}}{(x + 5)^{24}}$$ । সেক্ষেত্রে

A
x = 2 রেখার উপর f(x) এর কোন সন্ধিবিন্দু নেই
B
x = 2 রেখায় f(x) এর ক্ষুদ্রতম মান আছে
C
x = 2 রেখার উপর f(x) এর সর্বনিম্ন বা সর্বোচ্চ বিন্দু কোনটাই নেই
D
x = 2 রেখায় f(x) এর সর্বোচ্চ বিন্দু আছে
4

WB JEE 2022

MCQ (Single Correct Answer)
English
Bengali

Domain of $$y = \sqrt {{{\log }_{10}}{{3x - {x^2}} \over 2}} $$ is

A
x < 1
B
2 < x
C
1 $$\le$$ x $$\le$$ 2
D
2 < x < 3

Explanation

$${\log _{10}}\left( {{{3x - {x^2}} \over 2}} \right) \ge 0$$

$$ \Rightarrow {{3x - {x^2}} \over 2} \ge {10^0}$$

$$ \Rightarrow {{3x - {x^2}} \over 2} \ge 1$$

$$ \Rightarrow 3x - {x^2} \ge 2$$

$$ \Rightarrow {x^2} - 3x + 2 \le 0$$

$$ \Rightarrow (x - 2)(x - 1) \le 0$$

$$\therefore$$ $$x \in [1,2]$$ ...... (1)

Also, $${{3x - {x^2}} \over 2} > 0$$

$$ \Rightarrow {x^2} - 3x < 0$$

$$ \Rightarrow x(x - 3) < 0$$

$$ \Rightarrow x \in (0,3)$$ ...... (2)

$$\therefore$$ Intersection of (1) and (2) is $$x \in [1,2]$$

$$y = \sqrt {{{\log }_{10}}{{3x - {x^2}} \over 2}} $$ অপেক্ষকের সংজ্ঞার অঞ্চল হবে

A
x < 1
B
2 < x
C
1 $$\le$$ x $$\le$$ 2
D
2 < x < 3

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