1
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Change Language
For the following carbocations, the correct order of stability is

I. $$^ \oplus C{H_2} - COC{H_3}$$

II. $$^ \oplus C{H_2} - OC{H_3}$$

III. $$^ \oplus C{H_2} - C{H_3}$$
A
III < II < I
B
II < I < III
C
I < II < III
D
I < III < II
2
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let cos$$^{ - 1}\left( {{y \over b}} \right) = \log {\left( {{x \over n}} \right)^n}$$. Then
A
$${x^2}{y^2} + x{y_1} + {n^2}y = 0$$
B
$$x{y_{^2}} - x{y_1} + 2{n^2}y = 0$$
C
$${x^2}{y_{^2}} + 3x{y_1} - {n^2}y = 0$$
D
$$x{y_{^2}} + 5x{y_1} - 3y = 0$$

$$\left( {Here,\,{y_2} = {{{d^2}y} \over {d{x^2}}},\,{y_1} = {{dy} \over {dx}}} \right)$$
3
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let $$\phi (x) = f(x) + f(1 - x)$$ and $$f(x) < 0$$ in [0, 1], then
A
$$\phi $$ is monotonic increasing in $$\left[ {0,{1 \over 2}} \right]$$ and monotonic decreasing in $$\left[ {{1 \over 2}, 1} \right]$$
B
$$\phi $$ is monotonic increasing in $$\left[ {{1 \over 2}, 1} \right]$$ and monotonic decreasing in $$\left[ {0, {1 \over 2}} \right]$$
C
$$\phi $$ is neither increasing nor decreasing in any sub-interval of [0, 1]
D
$$\phi $$ is increasing in [0, 1]
4
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Change Language
$$\int {{{f(x)\phi '(x) + \phi (x)f'(x)} \over {(f(x)\phi (x) + 1)\sqrt {f(x)\phi (x) - 1} }}dx = } $$
A
$${\sin ^{ - 1}} = \sqrt {{{f(x)} \over {\phi (x)}}} + c$$
B
$${\cos ^{ - 1}}\sqrt {{{(f(x))}^2} - {{(\phi (x))}^2}} + c$$
C
$$\sqrt 2 {\tan ^{ - 1}}\sqrt {{{f(x)\phi (x) - 1} \over 2}} + c$$
D
$$\sqrt 2 {\tan ^{ - 1}}\sqrt {{{f(x)\phi (x) + 1} \over 2}} + c$$
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