The range of a$\in$R for which the function f(x) = (4a $-$ 3)(x + log_e 5) + 2(a $-$ 7) cot$\left( {{x \over 2}} \right)$ sin²$\left( {{x \over 2}} \right)$, x $\ne$ 2n$\pi$, n$\in$N has critical points, is :

1

Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, the…

Topic: JEE Main 2021 (16 March Morning Shift)

2

Let the functions f : R $ \to $ R and g : R $ \to $ R be defined as :$f(x) = \left\{ {\matrix{ {x + 2,} & {x <…

Topic: JEE Main 2021 (16 March Morning Shift)

3

The locus of the midpoints of the chord of the circle, x2 + y2 = 25 which is tangent to the hyperbola, ${{{x^2}} \over …

Topic: JEE Main 2021 (16 March Morning Shift)

4

If n is the number of irrational terms in the expansion of ${\left( {{3^{1/4}} + {5^{1/8}}} \right)^{60}}$, then (n $-…

Topic: JEE Main 2021 (16 March Morning Shift)

5

Let $A = \left[ {\matrix{ i & { - i} \cr { - i} & i \cr } } \right],i = \sqrt { - 1} $. Then, the syste…

Topic: JEE Main 2021 (16 March Morning Shift)

6

Let a complex number z, |z| $\ne$ 1, satisfy ${\log _{{1 \over {\sqrt 2 }}}}\left( {{{|z| + 11} \over {{{(|z| - 1)}^2}…

Topic: JEE Main 2021 (16 March Morning Shift)

7

The number of elements in the set {x $\in$ R : (|x| $-$ 3) |x + 4| = 6} is equal to :

Topic: JEE Main 2021 (16 March Morning Shift)

8

Let the position vectors of two points P and Q be 3$\widehat i$ $-$ $\widehat j$ + 2$\widehat k$ and $\widehat i$ + 2$\…

Topic: JEE Main 2021 (16 March Morning Shift)

9

Let ${S_k} = \sum\limits_{r = 1}^k {{{\tan }^{ - 1}}\left( {{{{6^r}} \over {{2^{2r + 1}} + {3^{2r + 1}}}}} \right)} $. …

Topic: JEE Main 2021 (16 March Morning Shift)

10

Let a vector $\alpha \widehat i + \beta \widehat j$ be obtained by rotating the vector $\sqrt 3 \widehat i + \widehat j…

Topic: JEE Main 2021 (16 March Morning Shift)

1

If for x $\in$ $\left( {0,{\pi \over 2}} \right)$, log10sinx + log10cosx = $-$1 and log10(sinx + cosx) = ${1 \over 2}$…

Topic: JEE Main 2021 (16 March Morning Shift)

2

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the…

Topic: JEE Main 2021 (16 March Morning Shift)

3

If y = y(x) is the solution of the differential equation, ${{dy} \over {dx}} + 2y\tan x = \sin x,y\left( {{\pi \over 3…

Topic: JEE Main 2021 (16 March Morning Shift)