1
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$f:[1,3] \to R$$ be continuous and be derivable in (1, 3) and $$f'(x) = {[f(x)]^2} + 4\forall x \in (1,3)$$. Then

A
$$f(3) - f(1) = 5$$ holds
B
$$f(3) - f(1) = 5$$ does not hold
C
$$f(3) - f(1) = 3$$ holds
D
$$f(3) - f(1) = 4$$ holds
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

f(x) is a differentiable function and given $$f'(2) = 6$$ and $$f'(1) = 4$$, then $$L = \mathop {\lim }\limits_{h \to 0} {{f(2 + 2h + {h^2}) - f(2)} \over {f(1 + h - {h^2}) - f(1)}}$$

A
does not exist
B
equal to $$-3$$
C
equal to 3
D
equal to 3/2
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $${\cos ^{ - 1}}\left( {{y \over b}} \right) = {\log _e}{\left( {{x \over n}} \right)^n}$$, then $$A{y_2} + B{y_1} + Cy = 0$$ is possible for, where $${y_2} = {{{d^2}y} \over {d{x^2}}},{y_1} = {{dy} \over {dx}}$$

A
$$A = 2,B = {x^2},C = n$$
B
$$A = {x^2},B = x,C = {n^2}$$
C
$$A = x,B = 2x,C = 3n + 1$$
D
$$A = {x^2},B = 3x,C = 2n$$
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $$I = \int {{{{x^2}dx} \over {{{(x\sin x + \cos x)}^2}}} = f(x) + \tan x + c} $$, then $$f(x)$$ is

A
$${{\sin x} \over {x\sin x + \cos x}}$$
B
$${1 \over {{{(x\sin x + \cos x)}^2}}}$$
C
$${{ - x} \over {\cos x(x\sin x + \cos x)}}$$
D
$${1 \over {\sin x(x\cos x + \sin x)}}$$
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