Embibe Experts Solutions for Chapter: Sample Paper, Exercise 1: Exercise

If the vertices of a parallelogram $PQRS$taken in order are $P(3,4), Q(-2,3)$ and $R(-3,-2)$ then the coordinates of its fourth vertex $S$ are

If $49x+51y= 499, 51x+49y= 501$, then find the value of $x\text{ and} y$

In the given figure, $O$ is the centre of circle. Find $\angle AQB$, given that $PA \mathrm{and} PB$ are tangents to the circle and $\angle APB= 75°$.

If $\sin \left(A+B\right)=1$ and $\cos \left(A-B\right)=\frac{\sqrt{3}}{2}$, $0°<A+B\le 90°$ and $A>B$, then find the measures of angles $A$ and $B$.

If the zeroes of the polynomial $x^2+px+q$ are double in value to the zeroes of the polynomial $2x^2-5x-3$, then find the values of $p \text{and }q$

Anuj had some chocolates and he divided them into two lots $A \text{and} B$. He sold the first lot at the rate of $₹2$ for $3$ chocolates and the second lot at the rate of $₹1$per chocolate, and got a total of $₹400$. If he had sold the first lot at a rate of$₹1$ per chocolate and the second lot at the rate of $₹4$ for $5$ chocolates, his total collection would have been $₹ 460$. Find the total number of chocolates he had.

Prove the following that:

$\frac{{\tan }^3\theta }{1+{\tan }^2\theta }+\frac{{\displaystyle {\cot }^3\mathrm{\theta }}}{{\displaystyle 1+{\cot }^2\mathrm{\theta }}}=sec\theta \cos ec\theta -2\sin \theta \cos \theta$

Due to heavy floods in a state, thousands were rendered homeless. $50$ schools collectively offered to the state government to provide place and the canvas for 1500 tents to be fixed by the government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius $2.8 \mathrm{m}$ and height $3.5 \mathrm{m}$, with conical upper part of same base radius but of height $2.1 \mathrm{m}$. If the canvas used to make the tents costs $₹120$ per ${\mathrm{m}}^2$, find the amount shared by each school to set up the tents.