CDS MATHEMATICS QUIZ-5

Question 1:

The present age of a father is equal to sum of the ages of his 4 children. After ten years ,the sum of the ages of the children will be $1.6$ times the age of their father. What is the present age of father?

36 years

40 years

42 years

45 years

Question 2:

How many three digit numbers are divisible by 6 ?

151

150

157

153

Question 3:

A pole on the ground leans at $60^{\circ}$ with the vertical. At a point $x$ metre away from the base of the pole on the ground, two halves of the pole subtend the same angle. If the pole and the point are in the same vertical plane, then what is the length of the pole?

$\sqrt{2} x$ metre

$\sqrt{3} x$ metre

$2 x$ metre

$2 \sqrt{2} x$ metre

Question 4:

Nandan scored $80 \%$ marks in five subjects together Hindi,Social Science, Biology, English and Sanskrit, where the maximum marks of each subject were 110 . How many marks did Nandan scored in Social Science, if she scored 89 marks in Hindi 92 marks in Sanskrit, 98 marks in Biology and 81 marks in English?

80

75

65

70

Question 5:

A sector is cut from a circle of radius $21 \mathrm{~cm}$. If the length of the arc of the sector is $55 \mathrm{~cm}$, then what is the area of the sector?

$577 \cdot 5 \mathrm{~cm}^{2}$

$612.5 \mathrm{~cm}^{2}$

$705 \cdot 5 \mathrm{~cm}^{2}$

$725.5 \mathrm{~cm}^{2}$

Question 6:

Evaluate

$(4 / 9) \times 1701+(2 / 11) \times 1386=?$

180

1080

1008

1800

Question 7:

A sphere of diameter $6 \mathrm{~cm}$ is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is $6 \mathrm{~cm}$. If the sphere is completely submerged in water, then by how much will the surface level of water be raised?

$0.5 \mathrm{~cm}$

$1 \mathrm{~cm}$

$1.5 \mathrm{~cm}$

$2 \mathrm{~cm}$

Question 8:

Let $A B C$ be a triangle right angled at $C$, then what is $\tan A+\tan B$ equal to?

$\frac{a}{b c}$

$\frac{a^{2}}{b c}$

$\frac{b^{2}}{c a}$

$\frac{c^{2}}{a b}$

Question 9:

A wire of length $2.5$ meters was measured as $2.55$ metres by mistake. What will be the value of error percent?

$25 \%$

$30 \%$

$22.5 \%$

$20 \%$

Question 10:

What is the value of $a^{3}+b^{3}+c^{3}-3 a b c$, when $a=95, b=96$ and $c=97$.

896

764

832

864