**Mathematics For Class 10**

**TEST PAPER**

**Real Numbers**

1. Why is 7x11x13+7 a composite integer?

**2.**

**Without actual division, state whether 13 by 2**

^{0 }x 5^{7} is a terminating or a non terminating rational number.

3.

**Identify whether**√**16 is a rational number.****4.**

**what is the conjugate number of 2+**√

**5?**

5.

**Express 140 as the product of its prime factors.**6.

**Determine whether 875/10**^{3}**is a terminating or a non-terminating decimal.****7.**

**Q 7** HCF of two integers 26, 91 is 13, what will be its LCM?

8.

**If f(x) is divisble by q(x), what will be the value of r(x), where f(x) = g(x)q(x) + r(x)?**9.

**Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.**10.

**Use the division algorithm to find the quotient***q***(***y***) and remainder***r***(***y***), when***f***(***y***) = 8***y*^{4}**– 12***y*^{3}**– 2***y*^{2}**+ 15***y***– 4 is divided by***g***(***y***) = 2***y*^{2}**– 3***y***+ 1.**11.

**Show that 3√2** is irrational.**12.**

**Show that 5 –**√

**3**

is irrational.

**13.**

**Prove that**√

**2**

is irrational number?

14.

**Express 32760 as the product of its prime factors.**15.

**Find the HCF and LCM of 6, 72 and 120, using the prime factorisation method.** **16.**

**Find the HCF of 96 and 404 by the prime factorisation method. Hence, find their LCM.**

17.

**Find the LCM and HCF of 6 and 20 by the prime factorisation method.**18.

**A sweet seller has 420 Kaju burfis and 130 Badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the maximum number of burfis that can be placed in each stack for this purpose?**19.

**Use** Euclid ’s division algorithm to find the HCF of 4052 and 12576.20.

**Find the largest number that will divide 2053 and 967 and leaves a remainder of 5 and 7 respectively.**
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