Section A (CBSE 10^th 2019 Mathematics)

Each carries one mark.

1. In figure 1 PS=3 cm , QS=4 cm , PRQ=Ɵ, PQR=90⁰ , PQRQ and RQ=9cm. Evaluate tan Ɵ

Solution

In  PSQ, PSQ=90⁰

According to Pythagoras theorem

PQ²=PS²+SQ²

=3²+4²

=9+16

=25

PQ=√25= 5cm

 

 

 

OR

If tan α=5/12 Find the value of sec α

Solution

 

 

 

 

 

 

 

 

 

 

2.Two concentric circles of radii a and b(a>b) are given. Find the length of the larger circle which touches the smaller circle.

Solution

Let the chord length =x

 

 

 

 

 

3.Find the values(s) of x, if the distance between the points A(0,0) and B(x,-4) is 5 units.

The points are A(0,0) and B(x,-4).

A(0,0) is origin

 

 

 

 

 

 

 

 

 

 

 

X²=25-16

X²=9

X=+3 or X=-3

 

 

 

4.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The number will terminate after four places.

OR

Express 429 as a product of its prime factors

 

 

 

 

 

 

 

Prime factorization of 429=3X13X11

5.Write the discriminant of the quadratic equation (x+5)²=2(5x-3)

Solution:

Discriminant=b²-4ac

(x+5)²=2(5x-4)

x²+10x+25=10x-6

x²+19=0

a=1, b=0, c=31

D= b²-4ac

=0-4x1x31

=-124

6.Find the sum of first 10 multiples of 3

Solution:

First 10 multiples of 3

3,6,9,……….30

This is an arithmetic progression

a=3 , d=3, n=10