CDS MATHEMATICS QUIZ-9

If $\sin 2 \theta=\frac{1}{2}$, then the value of $\cos \left(75^{\circ}-\theta\right)$ is.

A tub is in the shape of a frustum of a cone. The radii of two circular ends of the tub are $105 \mathrm{~cm}$ and $42 \mathrm{~cm}$. If the vertical height of the tub is $16 \mathrm{~cm}$, what is its slant height ?

If $1+4 r^{2}+16 r^{4}=256$ and $1+2 r+4 r^{2}=32$, then find the value of $\frac{1}{r} + \frac{1}{r^{2}}$.

The maximum value of $\sin \theta+\cos \theta$ is:

In a triangle $\mathrm{ABC}, \mathrm{AC}=10 \mathrm{~cm}, \mathrm{BC}=x \mathrm{~cm}$ and $\angle \mathrm{C}=60^{\circ}, \angle \mathrm{B}=45^{\circ}$ then find the value of $x$.

In world cup Champions, Rohit scored an average of 120 runs per match in the first 3 match and an average of 140 runs per match in the last four match. What is Rohit's average runs for the first match and the last two match if his average runs per match for all the five match is 122 and total number of matches are 5 ?

A wire is in the form of a circle of radius $70 \mathrm{~cm}$. If it is bent in the form of a rhombus, then what is its side length? (Take $\pi=\frac{22}{7}$ )

The ratio of present age of Ram and Shivam is $7: 9$ if 12 years ago, the ratio of their ages Was $5: 7$. Then find the ratio of their 10 Years from now?

5 pencils, 6 notebooks and 7 erasers cost RS. 250; whereas 6 pencils, 4 notebooks and 2 erasers cost RS. 180 . What is the cost of 2 notebooks and 4 erasers?