The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to :

1

Let $\overrightarrow a = \widehat i + \widehat j + 2\widehat k$, $\overrightarrow b = 2\widehat i - 3\widehat j + \wi…

Topic: JEE Main 2022 (26 June Evening Shift)

2

The locus of the mid point of the line segment joining the point (4, 3) and the points on the ellipse ${x^2} + 2{y^2} =…

Topic: JEE Main 2022 (26 June Evening Shift)

3

f the solution of the differential equation ${{dy} \over {dx}} + {e^x}\left( {{x^2} - 2} \right)y = \left( {{x^2} - 2x}…

Topic: JEE Main 2022 (26 June Evening Shift)

4

If $y = y(x)$ is the solution of the differential equation $x{{dy} \over {dx}} + 2y = x\,{e^x}$, $y(1) = 0$ then the lo…

Topic: JEE Main 2022 (26 June Evening Shift)

5

If $\int {{1 \over x}\sqrt {{{1 - x} \over {1 + x}}} dx = g(x) + c} $, $g(1) = 0$, then $g\left( {{1 \over 2}} \right)$…

Topic: JEE Main 2022 (26 June Evening Shift)

6

The area of the region bounded by y2 = 8x and y2 = 16(3 $-$ x) is equal to:

Topic: JEE Main 2022 (26 June Evening Shift)

7

Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a co…

Topic: JEE Main 2022 (26 June Evening Shift)

8

Let f(x) = min {1, 1 + x sin x}, 0 $\le$ x $\le$ 2$\pi $. If m is the number of points, where f is not differentiable a…

Topic: JEE Main 2022 (26 June Evening Shift)

9

$\mathop {\lim }\limits_{x \to 0} {{\cos (\sin x) - \cos x} \over {{x^4}}}$ is equal to :

Topic: JEE Main 2022 (26 June Evening Shift)

10

If the system of equations$\alpha$x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = $\beta$has infinitely many solutions, t…

Topic: JEE Main 2022 (26 June Evening Shift)

1

$16\sin (20^\circ )\sin (40^\circ )\sin (80^\circ )$ is equal to :

Topic: JEE Main 2022 (26 June Evening Shift)

2

If the inverse trigonometric functions take principal values then ${\cos ^{ - 1}}\left( {{3 \over {10}}\cos \left( {{{\…

Topic: JEE Main 2022 (26 June Evening Shift)

3

The area of the polygon, whose vertices are the non-real roots of the equation $\overline z = i{z^2}$ is :

Topic: JEE Main 2022 (26 June Evening Shift)

4

Let the system of linear equations $x + 2y + z = 2$, $\alpha x + 3y - z = \alpha $, $ - \alpha x + y + 2z = - \alpha $…

Topic: JEE Main 2022 (26 June Evening Shift)

5

$x = \sum\limits_{n = 0}^\infty {{a^n},y = \sum\limits_{n = 0}^\infty {{b^n},z = \sum\limits_{n = 0}^\infty {{c^n}} …

Topic: JEE Main 2022 (26 June Evening Shift)