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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.

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.

Given: Let triangles be Δ ABC and ΔDEF both triangles are similar, i.e., ΔABC ~ ΔDEF and also, areas are equal, i.e., area ΔABC = area ΔDEF

To prove: Both triangles are congruent, i.e., ΔABC ≅ ΔDEF

Proof:

As given, ΔABC ~ ΔDEF

Since two triangles are similar therefore the ratio of the area is equal to the square of the ratio of its corresponding side

$\frac{a r e a ∆ A B C}{a r e a ∆ D E F} = {(\frac{B C}{E F})}^{2} = {(\frac{A B}{D E})}^{2} = {(\frac{A C}{D F})}^{2} {(\frac{B C}{E F})}^{2} = {(\frac{A B}{D E})}^{2} = {(\frac{A C}{D F})}^{2} = 1 N o w, t a k i n g a n y o n e c a s e 1 = {(\frac{B C}{E F})}^{2} 1 = \frac{B C}{E F} E F = B C$

Similarly, we get

DE = AB

DF = AC

Since, in ΔABC and ΔDEF

EF =BC
AB = DE
AC = DF

Hence by SSS congruency
ΔABC ≅ ΔDEF

Hence proved

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.