For the frequency distribution :
Variate (x) :      x₁   x₂   x₃ ....  x₁₅
Frequency (f) : f₁   f₂  f₃...... f₁₅
where 0 < x₁ < x₂ < x₃ < ... < x₁₅ = 10 and $\sum\limits_{i = 1}^{15} {{f_i}} $ > 0, the standard deviation cannot be :

1

2$\pi $ - $\left( {{{\sin }^{ - 1}}{4 \over 5} + {{\sin }^{ - 1}}{5 \over {13}} + {{\sin }^{ - 1}}{{16} \over {65}}} \r…

Topic: JEE Main 3 September 2020 (Morning)

2

Let [t] denote the greatest integer$ \le $ t. If for some $\lambda $ $ \in $ R - {1, 0}, $\mathop {\lim }\limits_{x \to…

Topic: JEE Main 3 September 2020 (Morning)

3

The solution curve of the differential equation, (1 + e-x)(1 + y2)${{dy} \over {dx}}$ = y2, which passes throughthe poi…

Topic: JEE Main 3 September 2020 (Morning)

4

If $\alpha $ and $\beta $ are the roots of the equation x2 + px + 2 = 0 and ${1 \over \alpha }$ and ${1 \over \beta }$ …

Topic: JEE Main 3 September 2020 (Morning)

5

If the number of integral terms in the expansion of (31/2 + 51/8)n is exactly 33, then the least valueof n is

Topic: JEE Main 3 September 2020 (Morning)

6

If $\Delta $ = $\left| {\matrix{ {x - 2} &amp; {2x - 3} &amp; {3x - 4} \cr {2x - 3} &amp; {3x - 4} &amp; {4x - 5}…

Topic: JEE Main 3 September 2020 (Morning)

7

The value of (2.1P0 – 3.2P1 + 4.3P2 .... up to 51th term)+ (1! – 2! + 3! – ..... up to 51th term)is equal to :

Topic: JEE Main 3 September 2020 (Morning)

8

The function, f(x) = (3x – 7)x2/3, x $ \in $ R, isincreasing for all x lying in

Topic: JEE Main 3 September 2020 (Morning)

9

If $y^{2} + \log_{e}(\cos^{2}x) = y,\; x \in \left(-\tfrac{\pi}{2}, \tfrac{\pi}{2}\right),$ then :

Topic: JEE Main 3 September 2020 (Morning)

10

$\int\limits_{ - \pi }^\pi {\left| {\pi - \left| x \right|} \right|dx} $ is equal to :

Topic: JEE Main 3 September 2020 (Morning)