Class 11th

When 600 mL of 0.2 M HNO₃ is mixed with 400 mL of 0.1 M NaOH solution in a flask, the rise in temperature of the flask is_________ * 10^-2 °C.

(Enthalpy of neutralization = 57 kJ mol^-1 and Specific heat of water = 4.2 JK^-1 g^-1)

(Neglect heat capacity of flask)

The minimum uncertainty in the speed of an electron in an one dimensional region of length 2a₀ (Where a₀ = Bohr radius 52.9 pm) is__________ km s^-1.

(Given: Mass of electron = 9.1 * 10^-31 kg, Planck's constant h = 6.63 * 10^-34 Js)

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture of constant volume is $\frac{{\alpha }^2}{4}RJ/molK;$  then the value of a will be________.

The pressure P₁ and density d₁ of diatomic gas $\left(\gamma =\frac{7}{5}\right)$  changes suddenly to P₂(>P₁) and d₂ respectively during an adiabatic process. The temperature of the gas increases and becomes ________times of its initial temperature. (given   $\frac{d_2}{d_1}=32)$

If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a dept ah(h <e) from the earth surface. The value of a will be_______.

An object is projected in the air with initial velocity u at an angle q. The projectile motion is such that the horizontal range R, in maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be_______degree.

Let x₁, x₂, x₃,…….x₂₀ be in geometric progression with x₁ = 3 and the common ratio $\frac{1}{2}.$  A new data is constructed replacing each x_i by (x_i – i)². If $\overline{x}$  is the mean of new data, then the greatest integer less than or equal to $\overline{x}$  is………….

For the hyperbola H: x² – y² = 1 and the ellipse E : $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$  a > b > 0, let the

(1) eccentricity of E be reciprocal of the eccentricity of H, and

(2) the line y = $\sqrt[]{\frac{5}{2}}x+K$  be a common tangent of E and H.

Then 4(a² + b²) is equal to…………….

If ${\displaystyle \underset{0}{\overset{\sqrt[]{3}}{\int }}\frac{15x^3}{\sqrt[]{1+x^2+\sqrt[]{{\left(1+x^2\right)}^3}}}dx=\alpha \sqrt[]{2}+\beta \sqrt[]{3},}$  where a, b are integers, then α + β is equal to……….

Let S be the set of all passwords which are six to eight characters long, where each character is either an alphabet form $\left\{A,B,C,D,E\right\}$ $$ or a number from $\left\{1,2,3,4,5\right\}$ $$ with the repetition of characters allowed. If the number of passwords in S whose at least one character is a number from $\left\{1,2,3,4,5\right\}is\alpha *5^6,$ ${}^{}$ then is equal to………….