Revision Test - 1 Mark

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Questions:

Multiple Choice Question

35 x 1 = 35

The blood groups of 30 students of Class VIII are recorded as follows: A,B,O,O,AB,O,A,O,B,A,O,B,A,O,O, A,AB,O,A,A,O,O,AB,B,A,O,B,A,B,O. Find the probability that a student of Class VIII selected at random has his blood group AB.

(a)

\(\frac { 1 }{ 10 } \)

(b)

\(\frac { 1 }{ 5 } \)

(c)

\(\frac { 1 }{ 6 } \)

(d)

\(\frac { 1 }{ 3 } \)

In a blood test the following blood groups were recorded:

Blood group	No.of students
A	10
AB	15
B	11
O	3

A student is selected at random from the class. The probability that student has blood group 'AB'is:

(a)

\(\frac { 5 }{ 13 } \)

(b)

\(\frac { 7 }{ 13 } \)

(c)

\(\frac { 8 }{ 13 } \)

(d)

\(\frac { 6 }{ 13 } \)

A dice is tossed 100 times. The frequency of occurrence of numbers 1, 2, 3, 4, 5, 6 are given as under:
1 : 22, 2 : 28,3: 12,4: 14,5: 11,6: 13
A die is tossed again. The probability of an odd prime number is

(a)

0.23

(b)

0.50

(c)

0.49

(d)

0.73

A dice is thrown. What will be the probability of getting an even number?

(a)

\(\frac { 1 }{ 6 } \)

(b)

\(\frac { 1 }{ 2 } \)

(c)

\(\frac { 1 }{ 3 } \)

(d)

\(\frac { 2 }{ 3 } \)

Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows:
0 1 2 2 1 2
3 1 3 0 1 3
1 1 2 2 0 1
2 1 3 0 0 1
1 2 3 2 2 0
Find the probability of getting 3 heads is

(a)

\(\frac { 1 }{ 2 } \)

(b)

\(\frac { 1 }{ 3 } \)

(c)

\(\frac { 1 }{ 4 } \)

(d)

\(\frac { 1 }{ 6 } \)

Two coins are tossed simultaneously 1000 times and we get
Two heads: 200 times
One head: 600 times
No head: 200 times
Find the probability of getting no head is

(a)

\(\frac { 1 }{ 5 } \)

(b)

\(\frac { 1 }{ 2 } \)

(c)

\(\frac { 1 }{ 4 } \)

(d)

A dice is thrown 100 times with the frequencies for the outcomes 1,2,3,4,5 and 6 as given in the following table

Outcome	Frequency
1	10
2	20
3	10
4	20
5	25
6	15

Find the probability of outcome 5 is

(a)

\(\frac { 1 }{ 2 } \)

(b)

\(\frac { 1 }{ 3 } \)

(c)

\(\frac { 1 }{ 4 } \)

(d)

\(\frac { 1 }{ 5 } \)

In a survey of 350 women, 132 were found to be working. If a woman is selected at random, the probability that she is not working is:

(a)

\(\frac { 66 }{ 175 } \)

(b)

\(\frac { 109 }{ 175 } \)

(c)

\(\frac { 43 }{ 175 } \)

(d)

When a coin is tossed 500 times, the following outcomes were recorded:
Head: 235 times, Tail: 265 times
If now a coin is tossed once again, the probability of getting a Tail is

(a)

0.50

(b)

0.47

(c)

0.45

(d)

0.53

10.

If A and B are the only two outcomes of an event and P(A) = 0.32, then value of P(B) would be:

(a)

0.38

(b)

0.68

(c)

0.78

(d)

0.32

11.

An experiment has two outcomes E and F P(E)+P(F) is equal to:

(a)

(b)

(c)

(d)

\(\frac { 1 }{ 2 } \)

12.

The median of first 10 odd numbers is

(a)

(b)

5.5

(c)

(d)

6.5

13.

The mean wage of 5 employees of a school is Rs 3000. One employee gets retired and the mean wage of the remaining employee is Rs 3200. The wage of the retiring employee was

(a)

Rs 2200

(b)

Rs 2400

(c)

Rs 2000

(d)

Rs 2600.

14.

The mean of x + 1,x + 3,x + 4,x +8 is:

(a)

x + 1

(b)

x + 3

(c)

x + 4

(d)

x + 8

15.

The mean 1,2,3,4,5x is

(a)

(b)

(c)

x + 2

(d)

5x + 1.

16.

The ages (in years) of 10 children are given below 15,15,16,16,15,14,17,16,14,16. The modal age of the children is:

(a)

(b)

(c)

(d)

17.

The mode of the distribution 3,5,7,4,2,1,4,3,4 is

(a)

(b)

(c)

(d)

18.

In the following distribution, the number of schools with result more than 60% is

Result of (in percent)	Number of schools
0-20	4
20-40	7
40-60	5
60-80	3
80-100	2

(a)

(b)

(c)

(d)

19.

Range of the following data is:
53,36,95,73,60,42,25,78,75,62

(a)

(b)

(c)

(d)

20.

Facts or information collected with a definite purpose are called:

(a)

Median

(b)

Mode

(c)

Data

(d)

Histogram

21.

My garden is in the form of a trapezium whose parallel sides are 20 m and 16 m long respectively and the distance between them is 12 m.How much manure do I require for my garden if 1 m² requires 200 g of manure?

(a)

43.2 kg

(b)

86.4 kg

(c)

21.6 kg

(d)

None of these

22.

The area of an isosceles triangle whose base is 'a' and equal sides are of length 'b' is

(a)

\(\frac { a }{ 4 } \sqrt { 4{ b }^{ 2 }-{ a }^{ 2 } } \)

(b)

\(\frac { b }{ 4 } \sqrt { 4{ b }^{ 2 }-{ a }^{ 2 } } \)

(c)

\(\frac { b }{ 2 } \sqrt { 4{ b }^{ 2 }-{ a }^{ 2 } } \)

(d)

\(\frac { a }{ 2 } \sqrt { 4{ b }^{ 2 }-{ a }^{ 2 } } \)

23.

Write the coordinates of P

(a)

(-2,-2)

(b)

(2,2)

(c)

(2,-2)

(d)

(-2,2)

24.

Point (0,4) lies:

(a)

in I quadrant

(b)

on x - axis

(c)

on y - axis

(d)

in IV quadrant

25.

If x is negative and y is positive, then the point (x,y) lies in

(a)

II quadrant

(b)

III quadrant

(c)

IV quadrant

(d)

I quadrant

26.

The value of 549²-548² is:

(a)

1087

(b)

1077

(c)

1097

(d)

27.

If \(x^{31}+51 \) is divided by (x+1), the remainder is:

(a)

(b)

(c)

(d)

28.

Find \(p(\frac{1}{3})\) for \(p(t)=t^2-t+2\)

(a)

\(\frac{22}{9}\)

(b)

\(\frac{14}{9}\)

(c)

\(\frac{16}{9}\)

(d)

\(\frac{15}{9}\)

29.

The coefficient of x in the product of (x-1)(1-2x) is:

(a)

-3

(b)

(c)

-2

(d)

30.

In the polynomial \(1-\sqrt{11} x,\) the coefficient of x is:

(a)

(b)

(c)

\(-\sqrt{11}\)

(d)

\(\sqrt{11}\)

31.

A linear polynomial

(a)

has one and only one zero

(b)

may have no zero

(c)

may have one zero

(d)

may have more than one zero

32.

(0.001)^1/3 is equal to

(a)

0.1

(b)

0.001

(c)

0.01

(d)

0.0001

33.

Rationalization of the denominator of \(\frac { 1 }{ \sqrt { 5 } +\sqrt { 2 } } \) gives:

(a)

\(\frac { 1 }{ \sqrt { 10 } } \)

(b)

\(\sqrt { 5 } +\sqrt { 2 } \)

(c)

\(\sqrt { 5 } -\sqrt { 2 } \)

(d)

\(\frac { \left( \sqrt { 5 } -\sqrt { 2 } \right) }{ 3 } \)

34.

An irrational number between \(\frac { 5 }{ 7 } \) and \(\frac { 7 }{ 9 } \)

(a)

0.75

(b)

\(\sqrt { 6 } \)

(c)

0.750 7500 75000...

(d)

0.7512

35.

A rational number lying between -3 and 3 is:

(a)

(b)

-4.3

(c)

-3.4

(d)

1.101 1001 10001...

1 Marks

10 x 1 = 10

36.

A die is thrown, what will be the probability of getting an even number?

37.

The points scored by a basketball team in a series of matches are as follows: 17,2,7,17,25,514,18,10. Find range.

38.

The number of children in 10 families of a locality are: 2,4,3,4,2,0,3,5,1,6. Find the mean number of children per family.

39.

Write the factors of polynomial 4x²+y²+4xy+8x+4y+4

40.

Find the value of k, if x-2 is a factor of p(x)=2x²+3x-k.

41.

If f(x) be a polynomial such that \(f\left( -\frac { 1 }{ 3 } \right) \)=0, then calculate one factor of f(x).

42.

Write the sum of \(0.\bar{3}\) and \(0.\bar{4}\)

43.

Find the decimal expansion of \(\frac{58}{1000}\)

44.

What is the degree of the polynomial (x³+5) (4-x⁵)?

45.

What is x+\(\frac { 1 }{ x } \)?

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Answers Key:

Multiple Choice Question

35 x 1 = 35

Required probability=\(\frac { 3(number\ of\ AB's) }{ 30 } =\frac { 1 }{ 10 } \)

Required probability=\(\frac { 15 }{ 10+15+11+3 } \)

(a)
0.23

Even numbers are 2, 4, 6, (Three)
Required probability =3/6

Required probability=\(\frac { 5(Number\ of\ Threes) }{ 30 } =\frac { 1 }{ 6 } \)

Required probability=\(\frac { 200 }{ 1000 } =\frac { 1 }{ 5 } \)

Required probability= \(\frac { 25 }{ 100 } =\frac { 1 }{ 4 } \)

Required probability= \(1-\frac { 132 }{ 350 } \)

Required probability=\(\frac { 265 }{ 500 } =0.53\)

10.

P(A)+P(b)=1

11.

P(E)+P(F)=1

12.

n = 10,n/2 = 5,n/2 + 1 = 6
= 5.5

13.

\(5 \times 3000 = 15000\)
\(4 \times 3200 =128000\)
15000 - 12800 = 2200.

14.

Mean \(= \frac {(x+1)+(x+3)+(x+4)+(x+8)}{4}\)
= x + 4

15.

\(\overset{-}{x}=\frac{1+2+3+4+5x}{2}=x + 2.\)

16.

The observation 16 occurs most frequently (4 times)
\(\therefore\) Modal age = 16

17.

Frequency of 4 is maximum (3).

18.

Required number = 3 + 2 = 5.

19.

Range = Highest value - Lowest value
= 95 - 25 = 70

20.

Definition of data.

21.

Area = \(\frac { (20+16)\times 12 }{ 2 } \) = 216 m²
\(\therefore \) Manure required = 216\(\times \)200 g = 43.2 kg

22.

(a)
\(\frac { a }{ 4 } \sqrt { 4{ b }^{ 2 }-{ a }^{ 2 } } \)

23.

(a)
(-2,-2)

24.

25.

(a)
II quadrant

26.

549²-548²
=(549+548)(549-548)=1097

27.

By remainder theorem,
Remainder\(=(-1)^{31}+51=-1+51\)
\(=50 \quad |x+1=0\ \Rightarrow \ x=-1\)

28.

\(p(\frac{1}{3})=(\frac{1}{3})^2-(\frac{1}{3})+2=\frac{16}{9}\)

29.

Coefficient of x=1+2=3

30.

Evident

31.

A characteristic of a linear polynomial

32.

(a)
0.1

33.

(d)
\(\frac { \left( \sqrt { 5 } -\sqrt { 2 } \right) }{ 3 } \)

34.

35.

(a)
0

1 Marks

10 x 1 = 10

36.

()
Favourable number of outcomes = 3(2,4,6)
Total number of outcomes = 6
Required probability\(=\frac{3}{6}=\frac{1}{2}\)

37.

()
Range = highest point-lowest point
= 27 - 2 = 25

38.

()
Mean number of children per family =\(\frac{2+4+3+4+2+0+3+5+1+6}{10}=\frac{30}{10}\) = 3

39.

()
4x²+y²+4xy+8x+4y+4 = (2x)²+(y)²+(2)²+2\(\times\)2x\(\times\)y+2\(\times\)2x\(\times\)2+2\(\times\)y\(\times\)2
= (2x+y+2)².
Factor is 2x + y + 2.

40.

()
x-2 is a factor of p(x), then p(2) = 0
p(2)= 2\(\times\)(2)²+3\(\times\)2-k=0
\(\Rightarrow\) 8+6-k = 0
\(\therefore\) k = 14.

41.

()
Since, \(f\left( -\frac { 1 }{ 3 } \right) \) =0
\(\therefore -\frac { 1 }{ 3 } \) is a zero of polynomial f(x)
So, x+\(\frac { 1 }{ 3 } \)or 3x+1 is a factor of f(x).

42.

()
\(0.\bar{3}+0.\bar{4}\)=(0.333...) + (0.444...)
= 0.777...
Let x = 0.777...
10x = 7.777...
⇒ 10x - x = (7.777...) - (0.777...)
⇒ 9x = 7.0
⇒ x = \(\frac{7}{9}\)

43.