CDS Exam (II)- 2023 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (II)- 2023 - Elementary Mathematics

CDS Exam (II)- 2023 - Elementary Mathematics Defence Questions

41.
Consider the following for the next two (02) items that follow:
A line segment AB is bisected at C and semi-circles \( S_{1} \), \( S_{2} \) and \( S_{3} \) are drawn respectively on AB, AC and CB as diameters such that they all lie on same side of AB. A circle S is drawn touching internally \( S_{1} \) and externally \( S_{2} \) and \( S_{3} \).

If r is the radius of S and R is the radius of \( S_{2} \), then which one of the following is correct?
A.
\( R = 3r \)
B.
\( R = 2r \)
C.
\( 3R = 4r \)
D.
\( 2R = 3r \)
😑 View Answer Error
ANSWER :
D. \( 2R = 3r \)
42.
If m is the area of the circle S and n is the area of semi-circle \( S_{1} \), then which one of the following is correct?
A.
\( 9m = 2n \)
B.
\( 9m = 4n \)
C.
\( 3m = 2n \)
D.
\( 7m = 3n \)
😑 View Answer Error
ANSWER :
A. \( 9m = 2n \)
43.
Consider the following for the next two (02) items that follow:
Let \( \frac{(x - a)(x - b)}{(x - ma)(x - mb)} = \frac{(x + a)(x + b)}{(x + ma)(x + mb)} \); \( m, a, b > 0 \), \( m \neq 1 \), \( x \neq 0 \).

What is \( \frac{x^{2} + ab}{x^{2} + m^{2}ab} \) equal to?
A.
\( -\frac{1}{m^{2}} \)
B.
\( \frac{1}{m^{2}} \)
C.
\( \frac{2}{m} \)
D.
\( \frac{1}{m} \)
😑 View Answer Error
ANSWER :
D. \( \frac{1}{m} \)
44.
What is x equal to?
A.
\( \pm \sqrt{mab} \)
B.
\( \pm \sqrt{ab} \)
C.
\( \pm \sqrt{2mab} \)
D.
\( \pm \sqrt{2ab} \)
😑 View Answer Error
ANSWER :
A. \( \pm \sqrt{mab} \)
45.
Consider the following for the next two (02) items that follow:
The total monthly electricity bill for a house consists of the sum of two parts, one part is proportional to number of rooms and the other part is proportional to number of units consumed. ₹ 400 is the monthly electricity bill for a house with 8 rooms and consuming 240 units and ₹ 320 is the monthly electricity bill for a house with 6 rooms and consuming 200 units.

What is the monthly electricity bill for a house with m rooms and consuming n units?
A.
₹ \( (40m + n) \)
B.
₹ \( (20m + n) \)
C.
₹ \( \frac{(40m + n)}{2} \)
D.
₹ \( \frac{(30m + n)}{2} \)
😑 View Answer Error
ANSWER :
B. ₹ \( (20m + n) \)
46.
What is the monthly electricity bill for a house with 7 rooms consuming 300 units?
A.
₹ 500
B.
₹ 440
C.
₹ 340
D.
₹ 300
😑 View Answer Error
ANSWER :
B. ₹ 440
47.

Consider the following for the next two (02) items that follow:
A grouped frequency distribution is given below:

Weekly wages in Rupees (₹) Numbers of workers
2050 – 2550 5
2550 – 3050 10
3050 – 3550 k
3550 – 4050 8
4050 – 4550 2
4550 – 5050 10


If average weekly wages earned by a worker is ₹ 3,520, then what is the value of k?

A.

10

B.

12

C.

15

D.

20

😑 View Answer Error
ANSWER :

C. 15

48.
What is the median (approximate value) of the distribution?
A.
₹ 3,263
B.
₹ 3,383
C.
₹ 3,413
D.
₹ 3,483
😑 View Answer Error
ANSWER :
B. ₹ 3,383
49.
Consider the following for the next two (02) items that follow:
A quadratic equation is given by \( (a + b + c)x^{2} - (2a + 2b)x + (a + b - c) = 0 \); where a, b and c are real and distinct.

What are the roots of the equation?
A.
\( 1, \frac{(a + b - c)}{(a + b + c)} \)
B.
\( 1, \frac{(a - b + c)}{(a + b + c)} \)
C.
\( -1, \frac{(-a - b + c)}{(a + b + c)} \)
D.
\( -1, \frac{(a + b - c)}{(a + b + c)} \)
😑 View Answer Error
ANSWER :
A. \( 1, \frac{(a + b - c)}{(a + b + c)} \)
50.
Consider the following statements:
1. One of the roots of the equation is always less than 1 if a, b and c are all positive.
2. One of the roots of the equation is always negative if a, b and c are all negative.
Which of the statements given above is/are correct?
A.
1 only
B.
2 only
C.
Both 1 and 2
D.
Neither 1 nor 2
😑 View Answer Error
ANSWER :
A. 1 only
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