CDS Maths(1) Questions and answers

Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

Exams

These are the list of questions asked in the previous year CDS Maths Exams. You can practice these questions as real time exam in this link.

81). What is the maximum distance between two points of a cube of side 2 cm?

A). \( \sqrt{3}\)cm

B). \( 2\sqrt{3}\)cm

C). \( 4\sqrt{3}\)cm

D). \( 2\sqrt{2}\)cm

View Answer

Correct Answer: \( 2\sqrt{3}\)cm

Maximum distance between two points of cube is length of diagonal

Length of diagonal

\( \Large \sqrt{l^{2} + b^{2} + h^{2} } = \sqrt{2^{2} + 2^{2} + 2^{2}} \)

= \( \Large \sqrt{ 4 + 4 + 4} \)

= \( \Large \sqrt{12} = 2\sqrt{3}\)

Option (c) is correct

82). The areas of the three adjacent faces of a cuboidal box are at, x, 4x and 9x square unit. What is the volume of the box?

A). \(6 x^{2}\)

B). \(6 x^{3/2}\)

C). \(3 x^{3/2}\)

D). \(2 x^{3/2}\)

View Answer

Correct Answer: \(6 x^{3/2}\)

Let lb = x, bh = 4x and lh = 9x

\( \Large l = \frac{3\sqrt{x}}{2}\),

\( \Large b = \frac{2\sqrt{x}}{3}\),

\( \Large h = 6\sqrt{x}\)

Now volume of box = \( \Large l \times b \times h \)

\( \Large = \frac{3\sqrt{x}}{2} \times \frac{2\sqrt{x}}{3} \times 6\sqrt{x} \)

\( \Large = 6x^{\frac{3}{2}} \) cubic unit

Option b is correct

83). A cylinder circumscribes a sphere. What is the ratio of volume of the sphere to that of the cylinder?

A). 2 : 3

B). 1 : 2

C). 3 : 4

D). 3 : 2

View Answer

Correct Answer: 2 : 3

Here height of cylinder (h) = 2r

Volume of sphere = \( \Large \frac{4}{3} \pi r^{3} \)

and Volume of cylinder = \( \Large \pi r^{2}h \)

= \( \Large \pi r^{2}(2r) \)

= \( \Large 2 \pi r^{3} \)

Ratio of volume of sphere to volume of cylinder

\( \Large =\frac{4 . \pi r^{3}}{3 . 2 \pi r^{2}} = 2 : 3 \)

Option (A)is correct

84). If for a triangle the radius of the circumcircle is double the radius of the inscribed circle, then which one of the following is correct?

A). The triangle is right angled

B). The triangle is isosceles

C). The triangle is equilateral

D). None of these

View Answer

85). What is the total surface area of the toy?

A). \( 132 \pi cm^{2}\)

B). \( 112 \pi cm^{2}\)

C). \( 96 \pi cm^{2}\)

D). \( 66 \pi cm^{2}\)

View Answer

Correct Answer: \( 132 \pi cm^{2}\)

Total surface area of toy = Curved surface area of cone + surface area of hemisphere

\( \Large = \pi rl + 2 \pi r^{2} \)

\( \Large = \pi(6 \times 10 + 2 \pi 6^{2}) \)

\( \Large = \pi(60 + 72) \)

\( \Large 132 \pi cm^{2} \)

Option (A) is correct.

86). What is the volume of the toy?

A). \( 180 \pi cm^{2}\)

B). \( 240 \pi cm^{2}\)

C). \( 300 \pi cm^{2}\)

D). \( 320 \pi cm^{2}\)

View Answer

Correct Answer: \( 240 \pi cm^{2}\)

Volume of toy = \( \Large \frac{1}{3} \pi r^{2}h + \frac{2}{3} \pi r^{3} \)

\( \Large \frac{1}{3} \pi r^{2}( h + r)\)

\( \Large \frac{1}{3} \pi 6^{2}( 8 + 2 x 6)\)

\( \Large \frac{1}{3} \pi \times 36 \times 20 \)

\( \Large =240 \pi cm^{3}\)

Option (B) is correct.

87). What is the volume of the double cone so formed?

A). \( 3124 cm^{2}\)

B). \( 3424 cm^{2}\)

C). \( 3768 cm^{2}\)

D). \( 3924 cm^{2}\)

View Answer

88). What is the surface area of the double cone so formed?

A). \( 1101.2 cm^{2}\)

B). \( 1111.4 cm^{2}\)

C). \( 1310.4 cm^{2}\)

D). \( 13118.8 cm^{2}\)

View Answer

89). Consider the following statements :
1. The volume of the cone generated when the triangle is made to revolve about its longer leg is same as the volume of the cone generated when the triangle is made to revolve about its shorter leg.
2. The sum of the volume of the cone generated when the triangle is made to revolve about its longer leg and the volume of the cone generated when the triangle is made to revolve about its shorter leg is equal to the volume of the double cone generated when the triangle is .made to revolve about its hypotenuse.
Which of the above statements is/are correct?

A). 1 only

B). 2 only

C). Both 1 and 2

D). Neither 1 nor 2

View Answer

90). What is the area of the parallelogram?

A). \( 63 m^{2}\)

B). \( 96 m^{2}\)

C). \( 126 m^{2}\)

D). \( 125 m^{2}\)

View Answer

Correct Answer: \( 125 m^{2}\)

Perimeter = 2(a + b)

86 = 2(a + b)

43 = a + b ... (i)

Now length of one side exceeds other by 13m

a - b= 13 ..(ii)

Solving equation (i) and (ii) we get

a = 28 and b = 15

Area of \( \Large \vartriangle ABC = \sqrt{s(s-a)(s-b)(s-c)} \)

= \( \Large \sqrt{42(42-41)(42-28)(42-15)} \)

\( \Large = \sqrt{42 x 14 x 27} \)

= 7 x 2 x 3 x 3

= 126

Area of Parallelogram = 2 x Area of \( \Large \vartriangle ABC \)

= 2 x 126

= \( \Large 252 m^{3} \)

Option (D)is correct.

6	7	8	9	10

Go to :

Total Pages : 10