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

Suppose $$f:R \to R$$ be given by $$f(x) = \left\{ \matrix{ 1,\,\,\,\,\,\,\,\,\,\,\mathrm{if}\,x = 1 \hfill \cr {e^{({x^{10}} - 1)}} + {(x - 1)^2}\sin {1 \over {x - 1}},\,\mathrm{if}\,x \ne 1 \hfill \cr} \right.$$

then

A
f'(1) does not exist
B
f'(1) exists and is zero
C
f'(1) exist and is 9
D
f'(1) exists and is 10
2
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
3
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
4
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
$$A = {x^2},B = 3x,C = 2n$$
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