A rational number lying between -3 and 3 is:

1

(a)

0

(b)

-4.3

(c)

-3.4

(d)

1.101 1001 10001...

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

1

(a)

0.75

(b)

\(\sqrt { 6 } \)

(c)

0.750 7500 75000...

(d)

0.7512

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

1

(a)

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

(b)

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

(c)

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

(d)

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

(0.001)^1/3 is equal to

1

(a)

0.1

(b)

0.001

(c)

0.01

(d)

0.0001

A linear polynomial

1

(a)

has one and only one zero

(b)

may have no zero

(c)

may have one zero

(d)

may have more than one zero

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

1

(a)

1

(b)

11

(c)

\(-\sqrt{11}\)

(d)

\(\sqrt{11}\)

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

1

(a)

-3

(b)

3

(c)

-2

(d)

1

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

1

(a)

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

(b)

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

(c)

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

(d)

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

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

1

(a)

0

(b)

1

(c)

0

(d)

50

The value of 549²-548² is:

1

(a)

1087

(b)

1077

(c)

1097

(d)

1

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

1

(a)

II quadrant

(b)

III quadrant

(c)

IV quadrant

(d)

 I quadrant

Point (0,4) lies:

1

(a)

in I quadrant

(b)

on x - axis

(c)

on y - axis

(d)

in IV quadrant

Write the coordinates of P

1

(a)

(-2,-2)

(b)

(2,2)

(c)

(2,-2)

(d)

(-2,2)

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

1

(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)

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

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?

1

(a)

43.2 kg

(b)

86.4 kg

(c)

21.6 kg

(d)

None of these

Facts or information collected with a definite purpose are called:

1

(a)

Median

(b)

Mode

(c)

Data

(d)

Histogram

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

1

(a)

95

(b)

25

(c)

70

(d)

60

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

1

(a)

2

(b)

3

(c)

5

(d)

1

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

1

(a)

7

(b)

4

(c)

3

(d)

1.

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:

1

(a)

4

(b)

15

(c)

16

(d)

17

The mean 1,2,3,4,5x is 

1

(a)

3

(b)

5

(c)

x + 2

(d)

5x + 1.

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

1

(a)

x + 1

(b)

x + 3

(c)

x + 4

(d)

x + 8

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

1

(a)

Rs 2200

(b)

Rs 2400

(c)

Rs 2000

(d)

Rs 2600.

The median of first 10 odd numbers is

1

(a)

5

(b)

5.5

(c)

6

(d)

6.5

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

1

(a)

1

(b)

0

(c)

2

(d)

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

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

1

(a)

0.38

(b)

0.68

(c)

0.78

(d)

0.32

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

1

(a)

0.50

(b)

0.47

(c)

0.45

(d)

0.53

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:

1

(a)

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

(b)

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

(c)

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

(d)

1

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

1

(a)

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

(b)

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

(c)

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

(d)

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

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

1

(a)

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

(b)

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

(c)

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

(d)

1

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

1

(a)

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

(b)

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

(c)

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

(d)

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

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

1

(a)

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

(b)

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

(c)

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

(d)

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

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

1

(a)

0.23

(b)

0.50

(c)

0.49

(d)

0.73

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:

1

(a)

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

(b)

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

(c)

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

(d)

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

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.

1

(a)

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

(b)

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

(c)

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

(d)

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

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

1

(a)

\(\frac{58}{1000}\)= 0.058 (Decimal point is shifted three places to the left)

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

1

(a)

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

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

1

(a)

Not a polynomial.

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

1

(a)

Degree of x³+5 = 3
Degree of 4-x⁵ = 5
Degree of (x³-5) (4-x⁵) = 3+5 = 8.

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

1

(a)

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).

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

1

(a)

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.

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

1

(a)

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.

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.

1

(a)

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

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.

1

(a)

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

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

1

(a)

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