Let $f(x) = \int\limits_0^x {{e^t}f(t)dt + {e^x}} $ be a differentiable function for all x$\in$R. Then f(x) equals :

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If 0 < a, b < 1, and tan$-$1a + tan$-$1b = ${\pi \over 4}$, then the value of $(a + b) - \left( {{{{a^2} + {b^2}…

Topic: JEE Main 2021 (26 February Evening Shift)

2

A natural number has prime factorization given by n = 2x3y5z, where y and z are such that y + z = 5 and y$-$1 + z$-$1 …

Topic: JEE Main 2021 (26 February Evening Shift)

3

Consider the following system of equations : x + 2y $-$ 3z = a 2x + 6y $-$ 11z = bx $-$ 2y + 7z = c, where a, b and c a…

Topic: JEE Main 2021 (26 February Evening Shift)

4

Let f(x) be a differentiable function at x = a with f'(a) = 2 and f(a) = 4. Then $\mathop {\lim }\limits_{x \to a} {{xf…

Topic: JEE Main 2021 (26 February Evening Shift)

5

Let A(1, 4) and B(1, $-$5) be two points. Let P be a point on the circle (x $-$ 1)2 + (y $-$ 1)2 = 1 such that (PA)2 +…

Topic: JEE Main 2021 (26 February Evening Shift)

1

For x > 0, if $f(x) = \int\limits_1^x {{{{{\log }_e}t} \over {(1 + t)}}dt} $, then $f(e) + f\left( {{1 \over e}} \ri…

Topic: JEE Main 2021 (26 February Evening Shift)

2

Let $A = \{ 1,2,3,....,10\} $ and $$f:A \to A$$ be defined as $f(k) = \left\{ {\matrix{ {k + 1} & {if\,k\,is\,odd…

Topic: JEE Main 2021 (26 February Evening Shift)

3

Let A1 be the area of the region bounded by the curves y = sinx, y = cosx and y-axis in the first quadrant. Also, let A…

Topic: JEE Main 2021 (26 February Evening Shift)

4

Let $f(x) = {\sin ^{ - 1}}x$ and $g(x) = {{{x^2} - x - 2} \over {2{x^2} - x - 6}}$. If $g(2) = \mathop {\lim }\limits_{…

Topic: JEE Main 2021 (26 February Evening Shift)

5

Let f : R $ \to $ R be defined as $f(x) = \left\{ \matrix{ 2\sin \left( { - {{\pi x} \over 2}} \right),if\,x < - 1…

Topic: JEE Main 2021 (26 February Evening Shift)

6

If the locus of the mid-point of the line segment from the point (3, 2) to a point on the circle, x2 + y2 = 1 is a circ…

Topic: JEE Main 2021 (26 February Evening Shift)

7

If vectors $\overrightarrow {{a_1}} = x\widehat i - \widehat j + \widehat k$ and $\overrightarrow {{a_2}} = \widehat …

Topic: JEE Main 2021 (26 February Evening Shift)

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A seven digit number is formed using digits 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed is divisible by…

Topic: JEE Main 2021 (26 February Evening Shift)