# CDS Maths(1) Questions and answers

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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.

31). The LCM of two integers is 1237. What is their HCF?
 A). 37 B). 19 C). 1 D). Cannot be determined
32). What is $$\Large \frac{1}{a-b}$$-$$\Large \frac{1}{a+b}$$-$$\Large \frac{2b}{a^{2}+b^{2}}$$-$$\Large \frac{4b^{3}}{a^{4}+b^{4}}$$-$$\Large \frac{8b^{7}}{a^{8}-b^{8}}$$
 A). $$a+b$$ B). $$a-b$$ C). $$1$$ D). $$0$$
33). A man rides one third of the distances from A to B at the rate of $$x$$km/hr and the remainder at the rate of $$2y$$ km/hr. If he had travelled at a uniform rate of $$6z$$ km/hr, he could have ridden from A to B and back again in he same time Which one of the following is correct?
 A). $$z$$ = $$x$$ + $$y$$ B). $$3 z$$ = $$x$$ + $$y$$ C). $$\Large \frac{1}{z}$$ = $$\Large \frac{1}{x}$$+$$\Large \frac{1}{y}$$ D). $$\Large \frac{1}{2z}$$ = $$\Large \frac{1}{x}$$+$$\Large \frac{1}{y}$$
34). If $$ax$$ + $$by$$ - $$2$$ = 0 and $$axby$$ = $$1$$, where $$a$$ $$\ne$$$$0$$,$$b$$ $$\ne$$$$0$$ then what is $$\left( a^{2} x + b^{2 y}\right)$$ equal to?
 A). $$a$$ +$$b$$ B). $$2ab$$ C). $$a^{3}$$ +$$b^{3}$$ D). $$a^{4}$$ +$$b^{4}$$
35). Consider the following statements :
1. $$\left( a - b - c \right)$$ is one of the factors of $$3abc$$ + $$b^{3}$$ + $$c^{3}$$ - $$a^{3}$$
2. $$\left( b + c - 1 \right)$$ is one of the factors of $$3abc$$ + $$b^{3}$$ + $$c^{3}$$ - $$1$$
Which of the above statements is/are correct?

 A). 1 only B). 2 only C). Both 1 and 2 D). Neither 1 nor 2

36). $$7^{10}$$ - $$5^{10}$$ is divisible by
 A). 10 B). 7 C). 5 D). 11
37). Consider the following statements in respect of four spheres A, B, C and D having respective radii 6, 8, 10 and 12 cm :
1. The surface area of sphere C is equal to the sum of surface areas of spheres A and B.
2. The volume of sphere D is equal to the sum of volumes of spheres A, B and C.
Which of the above statements is/are correct?

 A). 1 only B). 2 only C). Both 1 and 2 D). Neither 1 nor 2
38). What is the number of divisors of 360?
 A). 12 B). 18 C). 24 D). None of these
39). The multiplication of a three-digit number $$XY5$$with digit $$Z$$ yields $$X215.$$What is $$X + Y + Z$$equal to?
 A). 13 B). 15 C). 17 D). 18
40). If the equation $$x^{2}$$ + $$2$$$$\left( 1+k\right)$$$$x$$ + $$k^{2}$$ = $$0$$ has equal roots, then what is the value of k?
 A). $$\Large \frac{1}{2}$$ B). -$$\Large \frac{1}{2}$$ C). $$1$$ D). $$-1$$
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