H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Model Test Paper, Exercise 1: SECTION

Show that every positive even integer is of the form $2q$ and every positive odd integer is of the form $(2q+1),$ where $q$ is some integer. 

For what value of $k$ the quadratic polynomial $x^2+kx+k$ has equal zeroes [with condition $k$ should be more than $1$]. 

Find the value of $\cos 2°\cos 4°\cos 6°\dots \cos 100°$.

For what value of ${}^{\text{'}}k^{\text{'}}$ the quadratic equation: $x^2-2kx+k^2=0$ has real and unequal roots. 
 

If perimeter of quadrant of a circle is equal area of same quadrant of same circle of radius ${}^{\text{'}}r^{\text{'}},$ then its diameter is $\frac{4\pi +k}{\pi }$.Find $k$

Evaluate: $\frac{{\sin }^{2}11°+{\sin }^{2}79°}{{cosec}^{2}20°-{\tan }^{2}70°}$

In a right angled $∆ABC$, $\angle B=90°$, then find the value of ${\sin }^{2}A+{\sin }^{2}C$.

The wheel of a car are of diameter $80 \mathrm{cm}$ each. How many complete revolutions does each wheel will make in $10 \mathrm{minutes}$ if speed of car is $66 \mathrm{km}/\mathrm{h}$?