CDS Exam (II)- 2026 - Elementary Mathematics Defence Question Paper

CDS Previous Year Question Papers Question Papers
CDS Exam (II)- 2026 - Elementary Mathematics

CDS Exam (II)- 2026 - Elementary Mathematics Defence Questions

1.
Two positive integers x and y are in the ratio 17 : 19. If the LCM of the two numbers is 1615, then what is (x + y) equal to?
A.
36
B.
180
C.
360
D.
Cannot be determined due to insufficient data
😑 View Answer Error
ANSWER :
B. 180
2.
If \( \frac{p}{q} = \frac{q}{r} = \frac{r}{s} = k \), then what is \( \frac{p^{3} + q^{3} + r^{3}}{q^{3} + r^{3} + s^{3}} \) equal to?
A.
\( \frac{p}{s} \)
B.
\( \frac{r}{q} \)
C.
\( \frac{s}{p} \)
D.
\( \frac{q}{r} \)
😑 View Answer Error
ANSWER :
A. \( \frac{p}{s} \)
3.
If \( x^{2} - 4x + 3 \) is a factor of \( x^{4} + px^{2} + q \), then what is (p - q) equal to?
A.
-19
B.
-17
C.
17
D.
19
😑 View Answer Error
ANSWER :
A. -19
4.
Suppose p and q are positive integers where q is not a perfect square. If \( \frac{1}{p + \sqrt{q}} \) is a root of a quadratic equation having integer coefficients, then which of the following statements is/are correct?
I. The sum of the roots is 2p times the product of the roots.
II. The sum of the reciprocals of the roots is equal to 2p.
Select the answer using the code given below:
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
😑 View Answer Error
ANSWER :
C. Both I and II
5.
If \( \frac{1}{2b + 2c} + \frac{1}{2c + 2a} = \frac{1}{a + b} \), then what is \( a^{2} + b^{2} + c^{2} \) equal to?
A.
\( 9c^{2} \)
B.
\( 4c^{2} \)
C.
\( 3c^{2} \)
D.
\( 2c^{2} \)
😑 View Answer Error
ANSWER :
C. \( 3c^{2} \)
6.
A train completely crossed two persons X and Y moving in the same direction as the train in 8 seconds and 8.1 seconds respectively. X is walking at a uniform speed of 3 km/hr and Y is walking at a uniform speed of 4 km/hr. What is the speed of the train?
A.
81 km/hr
B.
82 km/hr
C.
83 km/hr
D.
84 km/hr
😑 View Answer Error
ANSWER :
D. 84 km/hr
7.
A number is formed by three digits, each less by unity than the digit that follows it. If 15 is added to the number, then the sum is 30 times the sum of the digits of the number. What is the product of the digits of the number?
A.
6
B.
24
C.
60
D.
120
😑 View Answer Error
ANSWER :
C. 60
8.
Consider the following statements in respect of common logarithms:
I. The logarithm of a number greater than 100 but less than 1000 lies between 2 and 3.
II. The logarithm of a positive number less than unity is negative.
Which of the statements given above is/are correct?
A.
I only
B.
II only
C.
Both I and II
D.
Neither I nor II
😑 View Answer Error
ANSWER :
C. Both I and II
9.
What is the number of zeros immediately after the decimal point in \( (0.5)^{1000} \)?
(Given that \( \log_{10} 2 = 0.30103 \))
A.
300
B.
301
C.
302
D.
303
😑 View Answer Error
ANSWER :
B. 301
10.
If \( x = 11 + 2\sqrt{30} \), then what is the value of \( x^{\frac{1}{2}} + x^{-\frac{1}{2}} \)?
A.
\( 2\sqrt{2} \)
B.
\( 2\sqrt{3} \)
C.
\( 2\sqrt{5} \)
D.
\( 2\sqrt{6} \)
😑 View Answer Error
ANSWER :
D. \( 2\sqrt{6} \)
Prev Next page