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SSC CHSL Exam SSC CHSL Quantative Aptitude Study Material

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Mensuration

A metal sphere of radius 5 cm is melted to make a cone with base of the same radius. What is the height of the cone ?

a) 10 cm
b) 15 cm
c) 20 cm
d) 5 cm

✔Answer

✔Solution

Correct Answer Is : 20 cm

Solution Is : Let height of a cone made from sphere be h cm, then Given, 1/3 * π * (5)² * h = 4/3 * π * (5)³ h = 4 * 5 = 20 cm

A person standing on the bank of river observes that the angle of elevation of the top of tree standing on the opposite bank is 60

a) 36.64 m
b) 38.64 m
c) 42.64 m
d) 34.64 m

✔Answer

✔Solution

Correct Answer Is : 34.64 m

Solution Is :

From the top of a cliff 90 m high, the angles of depression of the top and bottom of a tower are observed to be 30

a) 45 m
b) 60 m
c) 75 m
d) 30 m

✔Answer

✔Solution

Correct Answer Is : 60 m

Solution Is :

The area of rectangle is 108 m² and the ratio of length and width is 3 : 4, then find the value of A0

a) 7.5 m
b) 8 m
c) 8.7 m
d) 7 m

✔Answer

✔Solution

Correct Answer Is : 7.5 m

Solution Is :
Let the two sides of a rectangle be 3x and 4x. According to question 3x * 4x = 108 x² = 108/12 = 9 x = √9 = 3 AB = 9 m, AD = 12 m In Δ ABC, BD² = AB² + AD² BD² = 9² + 12² BD² = 15 cm, DO = BD/2 = 15/2 = 7.5 m ⇒ AB² + AD² = 2 DO² + 2 AO² 81 + 144 = 2 * (7.5)² + 2 AO² 225 = 112.5 -2 * AO² ⇒ AO² = 225 - 112.5/2 = 56.25 AO = √56.25 = 7.5 m

The least value of (4 sec²θ + 9 cosec²θ) is

a) 1
b) 19
c) 25
d) 7

✔Answer

✔Solution

Correct Answer Is : 25

Solution Is : 4 sec² θ + 9 cosec² θ =4( 1 + tan² θ) + 9 ( 1 + cot² θ) 13 + ( 4 tan² θ + 9 cot² θ) AM ? GM 4 tan² θ + 9 cot² θ/2 ? √ 4 tan² θ . 9 cot² θ ⇒ 4 tan² θ + 9 cot² θ = 2 * √36 ? 12 ⇒ minimum value of 4 sec² θ + 9 cosec² θ = 13 + 12 = 25.

The radius of a circle is 13 cm and xy is a chord which is at a distance of 12 cm from the centre. The length of the chord is

a) 12 cm
b) 10 cm
c) 20 cm
d) 15 cm

✔Answer

✔Solution

Correct Answer Is : 10 cm

Solution Is :

If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, then the diameter of the new sphere will be

a) 12 cm
b) 24 cm
c) 30 cm
d) 36 cm

✔Answer

✔Solution

Correct Answer Is : 24 cm

Solution Is : (B) Let R be the radius of the new sphere. ∴4/3 π r^(3 ) = 4/3 π ? (6^3 (?8)^3 (?10)^3 ) ? R^3=216+512+1000=1728 ?R=12 Therefore, Diameter of the new sphere=24 cm.

Two circular metallic discs have a thickness of 15 mm. Their areas are in the ratio of 9 : 1. The smaller dia disc is pressed against the bigger disc and rotated around it on a flat surface. How many times will the small disc rotate before it completes one circle of the bigger disc?

a) 3
b) 3π
c) π
d) None of these

✔Answer

✔Solution

Correct Answer Is : 3

Solution Is : (A) The radii of the circular discs are in the ratio 3 : 1. Therefore, the smaller disc will rotate three times before it completes one circle of the bigger disc.

A metallic cuboid weighs kg. How much would a miniature cuboid of metal weigh, if all the dimensions are reduced to 1/4th of the original?

a) 0.50 kg
b) 0.25 kg
c) 0.75 kg
d) 1.0 kg

✔Answer

✔Solution

Correct Answer Is : 0.25 kg

Solution Is : (B) If radius of the cube = 1 cm, then its volume = 1 cu.cm => 1 cu.cm weighs 16 kg. If side of the cube becomes 1/4 cm, then its volume = 1/64 cu.cm Therefore, 1/64 cu.cm. weighs 0.25 kg.

ABCD are midpoints of the rectangle. AB= 10 cm, If one of the sides of the rectangle is 12 cm, then what is the area of ABCD?

a) 100 sq cm
b) 96 sq cm
c) 195 sq cm
d) 154 sq cm

✔Answer

✔Solution

SSC CHSL Exam SSC CHSL Quantative Aptitude Study Material

Mensuration

A metal sphere of radius 5 cm is melted to make a cone with base of the same radius. What is the height of the cone ?

Correct Answer Is : 20 cm

Solution Is : Let height of a cone made from sphere be h cm, then Given, 1/3 * π * (5)2 * h = 4/3 * π * (5)3 h = 4 * 5 = 20 cm

A person standing on the bank of river observes that the angle of elevation of the top of tree standing on the opposite bank is 60

Correct Answer Is : 34.64 m

Solution Is :

From the top of a cliff 90 m high, the angles of depression of the top and bottom of a tower are observed to be 30

Correct Answer Is : 60 m

Solution Is :

The area of rectangle is 108 m2 and the ratio of length and width is 3 : 4, then find the value of A0

Correct Answer Is : 7.5 m

The least value of (4 sec2θ + 9 cosec2θ) is

Correct Answer Is : 25

Solution Is : 4 sec2 θ + 9 cosec2 θ =4( 1 + tan2 θ) + 9 ( 1 + cot2 θ) 13 + ( 4 tan2 θ + 9 cot2 θ) AM ? GM 4 tan2 θ + 9 cot2 θ/2 ? √ 4 tan2 θ . 9 cot2 θ ⇒ 4 tan2 θ + 9 cot2 θ = 2 * √36 ? 12 ⇒ minimum value of 4 sec2 θ + 9 cosec2 θ = 13 + 12 = 25.

The radius of a circle is 13 cm and xy is a chord which is at a distance of 12 cm from the centre. The length of the chord is

Correct Answer Is : 10 cm

Solution Is :

If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, then the diameter of the new sphere will be

Correct Answer Is : 24 cm

Solution Is : (B) Let R be the radius of the new sphere. ∴4/3 π r^(3 ) = 4/3 π ? (6^3 (?8)^3 (?10)^3 ) ? R^3=216+512+1000=1728 ?R=12 Therefore, Diameter of the new sphere=24 cm.

Two circular metallic discs have a thickness of 15 mm. Their areas are in the ratio of 9 : 1. The smaller dia disc is pressed against the bigger disc and rotated around it on a flat surface. How many times will the small disc rotate before it completes one circle of the bigger disc?

Correct Answer Is : 3

Solution Is : (A) The radii of the circular discs are in the ratio 3 : 1. Therefore, the smaller disc will rotate three times before it completes one circle of the bigger disc.

A metallic cuboid weighs kg. How much would a miniature cuboid of metal weigh, if all the dimensions are reduced to 1/4th of the original?

Correct Answer Is : 0.25 kg

Solution Is : (B) If radius of the cube = 1 cm, then its volume = 1 cu.cm => 1 cu.cm weighs 16 kg. If side of the cube becomes 1/4 cm, then its volume = 1/64 cu.cm Therefore, 1/64 cu.cm. weighs 0.25 kg.

ABCD are midpoints of the rectangle. AB= 10 cm, If one of the sides of the rectangle is 12 cm, then what is the area of ABCD?

Correct Answer Is : 100 sq cm

Solution Is :

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Solution Is : Let height of a cone made from sphere be h cm, then Given, 1/3 * π * (5)² * h = 4/3 * π * (5)³ h = 4 * 5 = 20 cm

The area of rectangle is 108 m² and the ratio of length and width is 3 : 4, then find the value of A0

The least value of (4 sec²θ + 9 cosec²θ) is

Solution Is : 4 sec² θ + 9 cosec² θ =4( 1 + tan² θ) + 9 ( 1 + cot² θ) 13 + ( 4 tan² θ + 9 cot² θ) AM ? GM 4 tan² θ + 9 cot² θ/2 ? √ 4 tan² θ . 9 cot² θ ⇒ 4 tan² θ + 9 cot² θ = 2 * √36 ? 12 ⇒ minimum value of 4 sec² θ + 9 cosec² θ = 13 + 12 = 25.