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

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CDS Exam (II)- 2026 - Elementary Mathematics

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

11.
If \( \frac{1}{x + k} + \frac{1}{x + 2k} + \frac{1}{x + 5k} = \frac{1}{k} \), then what is the solution of the equation?
A.
\( \frac{k}{3} \)
B.
\( \frac{k}{2} \)
C.
\( \frac{2k}{3} \)
D.
k
😑 View Answer Error
ANSWER :
D. k
12.
Consider the polynomial
\( p(x) = x^{5} + 2x^{4} + x^{3} - x^{2} - 2x - 1 \):
I. \( x^{2} + 2x + 1 \) is a factor of p(x).
II. \( x^{2} + x + 1 \) divides p(x).
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
13.
If 5 is a root of the equation \( x^{2} + px - 55 = 0 \) and the quadratic equation \( x^{2} + px + k = 0 \) has equal roots, then what is the value of k?
A.
3
B.
6
C.
9
D.
12
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ANSWER :
C. 9
14.
Had I walked 0.5 km/hr faster, I would have taken 8 minutes less to walk 2 km. What is my original speed?
A.
2.5 km/hr
B.
2.75 km/hr
C.
3 km/hr
D.
3.25 km/hr
😑 View Answer Error
ANSWER :
A. 2.5 km/hr
15.
If the roots of the equation \( x^{2} + mx + n = 0 \) are increased by the same quantity k, then they become the roots of the equation \( x^{2} + nx + m = 0 \). What is the value of (m + n)?
A.
-4
B.
-2
C.
2
D.
4
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ANSWER :
A. -4
16.
If \( \alpha \) and \( \beta \) are the roots of the equation \( 2x^{2} - 2(n + 1)x + (n^{2} + n + 1) = 0 \), then what is \( (2\alpha^{3} + 2\beta^{3}) \) equal to?
A.
\( n^{3} - 1 \)
B.
\( 1 - n^{3} \)
C.
\( -(n^{3} + 1) \)
D.
\( -(2n^{3} + 1) \)
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ANSWER :
C. \( -(n^{3} + 1) \)
17.
The product of two numbers is 1050. The quotient when the larger number is divided by the smaller number is 4 and the remainder is 10. What is the sum of the two numbers?
A.
70
B.
75
C.
80
D.
85
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ANSWER :
D. 85
18.
What is the HCF of \( x^{3} + x^{2}y - 10xy^{2} + 8y^{3} \) and \( x^{3} + x^{2}y - 4xy^{2} - 4y^{3} \)?
A.
(x - y)
B.
(x - 2y)
C.
(x + 2y)
D.
(x + 4y)
😑 View Answer Error
ANSWER :
B. (x - 2y)
19.
What is \( \left(\sqrt{2} + \sqrt{3} + \sqrt{5}\right)\left(\sqrt{2} + \sqrt{3} - \sqrt{5}\right)\left(\sqrt{2} - \sqrt{3} + \sqrt{5}\right)\left(-\sqrt{2} + \sqrt{3} + \sqrt{5}\right) \) equal to?
A.
60
B.
40
C.
24
D.
12
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ANSWER :
C. 24
20.
The LCM and HCF of two polynomials p(x) and q(x) are \( (x + k)^{2}(x^{2} - 7x + 6) \) and (x + k) respectively. If \( \left[x^{3} + (2k - 1)x^{2} + k(k - 2)x - k^{2}\right] \) is one of the polynomials, then which of the following statements is/are correct?
I. The other polynomial is (x + k)(x - 6) where \( k \neq -6 \).
II. (x + k) cannot be the HCF if k = -6.
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
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