Previous Year Maths Question of Chapter Real number (Class X)

 

Previous Year Mathematics Questions of Class 10 Chapter {Real Number} for Examination 2023

One mark Questions

     1.  The sum of exponents of prime factors in the prime factorization of 196 is             …......                                 (CBSE 2020)
2. Euclid’ division lemma states that for 2 positive integer a and b, there exists         unique integer q and r satisfying a = bq + r and ……………       (CBSE 2020)
3. The decimal expansion of 23/2⁵ x 5² will terminate after how many places of        decimal?                             (CBSE 2020)
4. If H.C.F of two numbers is 27 and their L.C.M is 162. If one of the number of         54 then find the other number. (CBSE 2020)
5.  2√3 is …………                              (CBSE 2020)
6. If H.C.F (336, 54) = 6, find L.C.M (336, 54).                   (CBSE 2019)
7.  What is the H.C.F of smallest prime number and the Smallest composite                 number.                                     (CBSE 2018)
8.  Explain why 7 x 11 x 13 + 13 is a composite number.
9.  Without actually performing the long division write 15/1600 in decimal form.
10.   Express 5050 as product of its prime factors, is it unique?
11.   Three measuring rods are 64 cm, 80 cm, and 96 cm in length, the least length       of cloth that can be measured an exact number of times, using any of the rods.

Two mark Questions

1.       Write the smallest number which is divisible by both 306 and 657.

2.       Given that √2 is an irrational. Prove that 5 + 3√2 is an irrational number.

3.       Prove that 1/√2 is an irrational number.

4.       Show that 5 - 3√2 is irrational.

5.       Show that any positive integer is of the form 3q or 3q + 1 or 3q + 2 for some         integer q.

7.       Using Euclid’s division algorithm, find the largest number that divides 1251,             9377 and 15628 leaving remainders 1, 2 and 3 respectively.

8.       Find the greatest number of 6 digit exactly divisible by 24, 15 and 36.

9.       Prove that √3 + √7 is irrational.

Three/ Four mark Questions

1.       Prove the √3 is an irrational number.                               (CBSE 2020)

2.       Prove the √5 is an irrational number.                               (CBSE 2020)

3.       Using Euclid algorithm, find the HCF of 271 and 1032. (CBSE 2020)

4.       Prove that 2 + 5√3 is an irrational numbers, given that √3 is an irrational                      number.                                                                                 (CBSE 2019)

5.       Using Euclid’s Algorithm, find the H.C.F of 2048 and 960.   (CBSE 2018)

6.       Find H.C.F and L.C.M of 404 and 96 and verify that H.C.F X L.C.M = Product             of the two given numbers.

7.     Prove that the square of any positive integer of the form 5q + 1 is of the same                 form.

8.      If d is the H.C.F of 56 and 72, find x, y satisfying d = 56x + 72y. Also show that x             and y are not Unique.

9.   In the morning walk three Persons step off together, their steps measure 80 cm, 85             cm and 90 cm respectively. What is the minimum distance each should walk, So             that he can cover the distance in complete step?