Class 11th

Let A = $\left\{n\in N:H.C.F.\left(n,45\right)=1\right\}$ and Let B = $\left\{2k:k\in \left\{1,2,......,100\right\}\right\}.$ Then the sum of all the elements of $A\cup Bis..........$

If $si{n}^2\left(10^0\right)sin\left(20^0\right)sin\left(40^0\right)sin\left(50^0\right)sin\left(70^0\right)=\alpha -\frac{1}{16}sin\left(10^0\right),$ then 16 + 1 is equal to

Let the solution curve y = y(x) of the differential equation (4 + x²)dy – 2x(x² + 3y + 4)dx = 0 pass through the origin. They y(2) is equal to

Let f(x) = $max\left\{\left|x+1\right|,\left|x+2\right|,......,\left|x+5\right|\right\}.Then{\displaystyle \underset{-6}{\overset{0}{\int }}f\left(x\right)dx}$ is equal to

LE the common tangents to the curves $4\left(x^2+y^2\right)=9$ and y2 = 4x intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and $\mathcal{l}$ respectively denote the eccentricity and the length of the latus rectum of this ellipse, then $\frac{\mathcal{l}}{e^2}$ is equal to

There are ten boys B₁, B₂,…., B₁₀ and five girls G₁, G₂,…., G₅ in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B₁ and B₂ together should not be the members of a group, is………….

The sum of the cubes of all the roots of the equation $x^4-3x^3-2x^2+3x+1=0$ is

Let f(x) = $2co{s}^{-1}x+4co{t}^{-1}x-3x^2-2x+10,x\in \left[-1,1\right].If\left[a,b\right]$ is the range of the function f, then 4a – b is equal to

Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K. The depression in freezing point for 4.5 molal solution of glucose in water is 4K. The ratio of molal elevation constant to molal depression constant (K_b/K_f) is________.

2.2g of nitrous oxide (N₂O) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression of the gas from 217.1mL to 167.75mL. The change in thermal energy of the process, $\Delta U$  is '-x' J. The value of 'x' is________. [Nearest Integer]

(Given : atomic mass of N = 14 g mol^-1 and of O = 16 g mol^-1.

Molar heat capacity of N₂O is 100 J K^-1 mol^-1)