Subject

Mathematics

Class

CBSE Class 10

Pre Boards

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Sample Papers

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CBSE Class 10 Mathematics Solved Question Paper 2018

Short Answer Type

11.

Find the sum of first 8 multiples of 3.

12.

Given that $\sqrt{2}$ is irrational, prove that $(5 + 3 \sqrt{2})$ is an irrational number.

13.

If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.

14.

If A(–5, 7), B(–4, –5), C(–1, –6) and D(4, 5) are the vertices of the quadrilateral, find the area of the quadrilateral ABCD.

15.

Find all zeroes of the polynomial (2x⁴ - 9x³ + 5x² + 3x-1) if two of its zeroes are ( 2 + √3 ) and ( 2 - √3 ).

16.
Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.

Using the factor tree for the prime factorization of
404 and 96, we have
404 = 2²× 101 and 96 = 2⁵ × 3

To find the HCF, we list common prime factors and their smallest exponent in 404 and 96 as under: Common prime factor = 2, Least exponent = 2
therefore, HCF = 2² =4

To find the LCM, we list all prime factors of 404 and 96 and their greatest exponent as follows:

Prime factors of 404 and 96	Greatest Exponent
2	5
3	1
101	1

Therefore,

LCM = 2⁵ x 3¹ x 101¹

= 2⁵ x 3¹ x 101¹

= 9696
Now,

HCF x LCM = 9696 x 4= 38784
Product of two numbers = 404 x 96
Therefore, HCF x LCM = Product of two numbers.

17.

Prove that the lengths of tangents drawn from an external point to a circle are equal.

18.

Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal.

19.

If the area of two similar triangles are equal, prove that they are congruent.

20.

A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed.