Competitive Exams : Quantitative Aptitude - Geometry (Set 4)

Question 1

If $x + \frac{1}{x} = \sqrt{3}$, what is the value of $x^{12} + x^6 + 1$?

Accepted Answer

A) 0

Answer

B) 1

Answer

C) 3

Answer

D) -1

Question 2

In a circle, two chords ABandCDintersect at$P$. If $AP = 6 cm$, $PB = 4 cm$, and $CP = 3 cm$, what is the length of PD?

Accepted Answer

B) 8 cm

Answer

A) 7 cm

Answer

C) 9 cm

Answer

D) 12 cm

Question 3

Two athletes run on a circular track of 1500 mat speeds of15 km/hand25 km/hin opposite directions. When will they meet for the first time?

Accepted Answer

C) 135 seconds

Answer

A) 120 seconds

Answer

B) 130 seconds

Answer

D) 150 seconds

Question 4

In $ riangle ABC$, the incenter is $I$. If $\angle BAC = 80^\circ$, what is $\angle BIC$?

Accepted Answer

A) 130°

Answer

B) 100°

Answer

C) 120°

Answer

D) 140°

Question 5

The difference between the CI and SI on a sum for 2 years at $10% ext{ p.a.}$is Rs. 150. Find the principal.

Accepted Answer

B) 15000

Answer

A) 12000

Answer

C) 18000

Answer

D) 20000

Question 6

A cyclic quadrilateral ABCDhas$\angle A = 70^\circ$. What is the measure of $\angle C$?

Accepted Answer

C) 110°

Answer

A) 70°

Answer

B) 90°

Answer

D) 180°

Question 7

Find the area of a right-angled triangle with hypotenuse 13 cm and one side 5 cm.

Accepted Answer

D) 30 cm^2

Answer

A) 20 cm^2

Answer

B) 25 cm^2

Answer

C) 24 cm^2

Question 8

If the radius of a sphere is increased by 20%, by what percentage does the volume increase?

Accepted Answer

A) 72.8%

Answer

B) 60%

Answer

C) 44%

Answer

D) 80%

Question 9

The tangent PTand secantPABare drawn to a circle. If$PT = 8$and$PA = 4$, find AB.

Accepted Answer

B) 12

Answer

A) 8

Answer

C) 16

Answer

D) 20

Question 10

A chord of length 16 cm is at a distance of 6 cm from the center of the circle. Find the radius.

Accepted Answer

C) 10 cm

Answer

A) 8 cm

Answer

B) 9 cm

Answer

D) 12 cm

Question 11

The internal angle bisectors of $\angle B$and$\angle C$in$ riangle ABC$meet at$O$. If $\angle A = 50^\circ$, find $\angle BOC$.

Accepted Answer

A) 115°

Answer

B) 130°

Answer

C) 105°

Answer

D) 125°

Question 12

If each side of an equilateral triangle is 6 cm, find its altitude.

Accepted Answer

D) 3\sqrt{3}

Answer

A) 2\sqrt{3}

Answer

B) 4\sqrt{3}

Answer

C) 5\sqrt{3}

Question 13

A rectangular field has length twice its width. Area is 800. Find perimeter.

Accepted Answer

B) 120

Answer

A) 100

Answer

C) 140

Answer

D) 160

Question 14

The sum of interior angles of a polygon is $1440^\circ$. Find the number of sides.

Accepted Answer

C) 10

Answer

A) 8

Answer

B) 9

Answer

D) 12

Question 15

Find the area of an equilateral triangle with side 8 cm.

Accepted Answer

A) 16\sqrt{3}

Answer

B) 8\sqrt{3}

Answer

C) 32\sqrt{3}

Answer

D) 64\sqrt{3}

Question 16

Distance between points $(0,0)$and$(3,4)$is:

Accepted Answer

B) 5

Answer

A) 4

Answer

C) 6

Answer

D) 7

Question 17

Ratio of area of two similar triangles is 16:25. Find the ratio of their perimeters.

Accepted Answer

C) 4:5

Answer

A) 25:16

Answer

B) 5:4

Answer

D) 16:25

Question 18

What is the angle subtended by a diameter at the circumference?

Accepted Answer

D) 90°

Answer

A) 45°

Answer

B) 60°

Answer

C) 30°

Question 19

If $3\sin heta = 4\cos heta$, find $ an heta$.

Accepted Answer

A) 4/3

Answer

B) 3/4

Answer

C) 1

Answer

D) 0.5

Question 20

Volume of a cylinder with radius 7 cm and height 10 cm ($\pi = 22/7$):

Accepted Answer

B) 1540

Answer

A) 1440

Answer

C) 1640

Answer

D) 1740

Set 8Competitive Exams : Quantitative Aptitude - Geometry