CDS MATHEMATICS QUIZ-3

Question 1:

In a triangle $A B C$, $D E$ is parallel to $B C, A D=6, B D=6$ $A E=a+3$, and $E C=8$. What is the value of ' $a$ '.

$7$

$\frac{5}{2}$

$5$

$\frac{5}{3}$

Question 2:

A cylindrical pencil of Radius $2.8 \mathrm{~cm}$ has one of its ends sharpened into a conical shape of height $4.2 \mathrm{~cm}$. Find the volume of the material removed.

$54.23 \mathrm{~cm}^{3}$

$56.36 \mathrm{~cm}^{3}$

$66.63 \mathrm{~cm}^{3}$

$68.99 \mathrm{~cm}^{3}$

Question 3:

Mohan Can do a piece of work in $10\\ \ \mathrm{days}$ and Atul can do same work in 12 days. They Started working together but Mohan left the work after 2 days, then find the time taken by Atul to complete the remaining work.

$5 \frac{3}{5} days$

$7 \frac{6}{5}$ days

$8 \frac{9}{5}$ days

$7 \frac{3}{5}$ days

Question 4:

Find the equation of a line whose intercepts are twice of the line $3 x-2 y-12=0$

$3 x-2 y=24$

$2 x-3 y=12$

$2 x-3 y=24$

None of these

Question 5:

If a and b be two rational numbers, find the value of b.

$\frac{3+\sqrt{7}}{3-\sqrt{7}}=a+b \sqrt{7}$

4

3

2

1

Question 6:

A wire when bent in the form of a square enclosed a region of area $112.36 \mathrm{~cm}^{2}$. If the same wire is bent into the form of a circle, then the area of the circle is.

$124.36 \mathrm{~cm}^{2}$

$156.38 \mathrm{~cm}^{2}$

$142.70 \mathrm{~cm}^{2}$

$120.30 \mathrm{~cm}^{2}$

Question 7:

The ratio of copper to zinc in alloys $P$ and $Q$ are $3: 4$ and $5: 9$, respectively. $P$ and $Q$ are taken in the ratio $2: 3$ and melted to form a new alloy $R$. What is the ratio of copper to zinc in $R$.

$27: 43$

$43: 17$

$29: 43$

$43: 29$

Question 8:

Premlata and Manisha enter into partnership.Premlata invests some money at beginning, Manisha invests double the amount after 4 months and Rohan invests thrice the amount after 8 months. If the annual profit be Rs. 32000 , Rohan's share is?

Rs. 12,000

Rs. 15,000

Rs. 20000

Rs. 9600

Question 9:

If $\sin \theta+\cos \theta=\frac{\sqrt{6}}{\sqrt{5}}$ then find $\sin ^{2} \theta \operatorname{cos}^{2} \theta$

$\frac{1}{5}$

$\frac{1}{25}$

$\frac{\sqrt{5}}{\sqrt{6}}$

$\frac{1}{100}$

Question 10:

In a triangle $\mathrm{ABC}, \mathrm{AC}=8 \mathrm{~cm}, \mathrm{AB}=6 \mathrm{~cm}$, and $\mathrm{BC}=12 \mathrm{~cm}$ then find the value of $\angle \mathrm{ACB}$ $=?$

$\cos ^{-1}\left(\frac{43}{48}\right)$

$\cos ^{-1}\left(\frac{47}{51}\right)$

$\cos ^{-1}\left(\frac{41}{59}\right)$

$\cos ^{-1}\left(\frac{49}{53}\right)$