Subject

Mathematics

Class

CBSE Class 10

Pre Boards

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Sample Papers

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 Multiple Choice QuestionsShort Answer Type

1.

Given ABC ~ PQR, if ABPQ = 13, then find arABCarPQR


The ratio of the area of a similar triangle is equal to the square of their proportional side

ar ABCar PQR = AB2PQ2ar ABCar PQR =132 = 19


2.

In an AP, if the common difference (d) = –4, and the seventh term (a7) is 4, then find the first term.


a7 = 4

a + 6d = 4 

as an = a + (n-1) d

but d = -4

a + (-24) = 4
a = 4 + 24 = 28
therefore first term a = 28


3.

What is the value of (Cos267o - sin2 23o)?


Cos2 67° - sin223°

as cos (90° - θ) = sin θ

Let θ = 23°

cos (90° - 23°) = sin 23°

cos 67° = sin 23°

∴ cos267° = sin223°

∴ cos267° = sin223° = 0


4.

Two different dice are tossed together. Find the probability:
(i) of getting a doublet
(ii) of getting a sum 10, of the numbers on the two dice.


The outcomes when two dice are thrown together are
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
Total number of outcomes = 36
n (s) = 36

i) A = getting a doublet
A = {(1,1), (2,2), (3,3),(4,4), (5,5), (6,6)}

n(A) = 6
 P(A) = n(A)n(S) = 636 =16

B = getting sum of numbers as 10.
B = {(6, 4), (4, 6), (5, 5)}
n(B) =3

 P (B) = n(B)n(S) = 336 = 112


5.

An integer is chosen at random between 1 and 100. Find the probability that it is :

(i) divisible by 8

(ii) not divisible by 8


An integer is chosen at random from 1 to 100
Therefore n(S) = 100
(i) Let A be the event that number chosen is divisible by 8
∴ A = { 8,16,24,32,40,48,56,64,72,80,88,96}
∴ n (A) = 12
Now, P (that number is divisible by 8)

P(A) = n(A)n(S) = 12100 = 650 = 325P (A) = 325

(ii) Let ‘A’ be the event that number is not divisible by 8.

 P (A') = 1-P(A) = 1-325P(A') = 2225


6.

What is the HCF of the smallest prime number and the smallest composite number?


Smallest prime number is 2.

Smallest composite number is  4

therefore, HCF is 2


7.

In figure, ABCD is a rectangle. Find the values of x and y.


Given figure is a rectangle i.e ABCD,

DC = AB and BC = AD

x + y = 30 ...(i)
and 

x -y = 14 ...(ii)

Adding (i) and (ii), we get

2x = 44
x = 22
Putting  value of x in equation (i)
x + y = 30
22 + y = 30
y = 30-22 
y = 8

Thus, x = 22 and y = 8


8.

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3). Hence find m.


Suppose the point P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3) in the ratio K : 1

Co-ordinates of the point,

P = 6K + 2K + 1, -3K + 3K + 1

But the co-ordinates of point P are given as (4, m)

6K + 2K+1  = 4  ....(i)-3K + 3K+1 = m ..... (ii)6K + 2 = 4K +42K =2K =1Putting K =1 in equ. (2)-3(1) + 31 + 1 = m m = 0Ratio is 1:1 and m = 0i.e P is the mid point of AB 


9.

If x = 3 is one root of the quadratic equation x2-2kx -6 =0, the find the value of k.


x = 3 is one of the root of x2-2kx -6 =0

(3)2 -2k(3) - 6 =0

9-6k - 6 = 0
3 - 6k = 0
3 = 6k
k = 3/6 = 1/2


10.

Find the distance of a point P(x, y) from the origin.


Given point is P(x,y)

Origin point is O (0,0)

Using distance formula

PO = (x2-x1)2 + (y2-y1)2 = (x-0)2 + (y-0)2= x2 +y2