1
JEE Main 2021 (Online) 17th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Which of the following is true for y(x) that satisfies the differential equation

$${{dy} \over {dx}}$$ = xy $$-$$ 1 + x $$-$$ y; y(0) = 0 :
A
y(1) = 1
B
y(1) = e$$-$$$${1 \over 2}$$ $$-$$ 1
C
y(1) = e$${1 \over 2}$$ $$-$$ e$$-$$$${1 \over 2}$$
D
y(1) = e$${1 \over 2}$$ $$-$$ 1
2
JEE Main 2021 (Online) 17th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The sum of possible values of x for

tan$$-$$1(x + 1) + cot$$-$$1$$\left( {{1 \over {x - 1}}} \right)$$ = tan$$-$$1$$\left( {{8 \over {31}}} \right)$$ is :
A
$$-$$$${{{32} \over 4}}$$
B
$$-$$$${{{33} \over 4}}$$
C
$$-$$$${{{31} \over 4}}$$
D
$$-$$$${{{30} \over 4}}$$
3
JEE Main 2021 (Online) 17th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of $$4 + {1 \over {5 + {1 \over {4 + {1 \over {5 + {1 \over {4 + ......\infty }}}}}}}}$$ is :
A
2 + $${2 \over 5}\sqrt {30} $$
B
2 + $${4 \over {\sqrt 5 }}\sqrt {30} $$
C
5 + $${2 \over 5}\sqrt {30} $$
D
4 + $${4 \over {\sqrt 5 }}\sqrt {30} $$
4
JEE Main 2021 (Online) 17th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The inverse of $$y = {5^{\log x}}$$ is :
A
$$x = {5^{\log y}}$$
B
$$x = {y^{{1 \over {\log 5}}}}$$
C
$$x = {5^{{1 \over {\log y}}}}$$
D
$$x = {y^{\log 5}}$$
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