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#### Question 1:

Write the following numbers in words.

(a) 3,81,742

(b) 7,80,65,043

(a) Three lakhs eighty-one thousand seven hundred and forty-two

(b) Seven crores eighty lakhs sixty-five thousand and forty-three

#### Question 2:

Write the numbers using comma in International system.

(a) 804321

(b) 9705064

(a) 804,321

(b) 9,705,064

#### Question 3:

Write the numerals for the following

(a) Forty six lakh, five thousands, seven hundred and ninety

(b) Fifty three crore, four lakh, three thousand and eight.

(a) 46,05,790

(b) 53,04,03,008

#### Question 4:

Express the following in powers of 10.

(a) 6,54,320

(b) 76,40,321

(a)

(b)

#### Question 5:

Express the following standard form.

(a) 5 × 106 + 4 × 105 + 2 × 103 + 9 × 102 + 6 × 100

(b) 4 × 105 + 8 ×103 + 7 × 101

(a) 54, 02, 906

(b) 4,08,070

#### Question 6:

Express the following numbers in Roman number system.

(a) 46

(b) 564

(c) 1,257

(a) 46 = 40 + 6 = XL + VI = XLVI

(b) 564 = 500 + 60 + 4 = D + LX + IV = DLXIV

(c) 1257 = 1000 + 200 + 50 + 7 = M + CC + L + VII = MCCLVII

#### Question 7:

Convert the following numbers into base 5 system.

(a) 19

(b) 37

(c) 48

(a)

(b)

(c)

#### Question 8:

Convert the Base 5 numerals into Base 10.

(a) 41(5)

(b) 132(5)

(c) 204(5)

(a)

(b)

(c)

#### Question 9:

Express the following in exponential form.

(a) 3 × 3 × 3 × 3

(b) 5 × 5 × 5

(a)

(b)

#### Question 10:

Expand the following exponents.

(a) 24

(b) 42

(c) 65

(a)

(b)

(c)

#### Question 11:

Find the value of

(a) 52

(b) 34

(a)

(b)

#### Question 12:

Simplify:

(a) 6,048 + 36 + 8 + 769

(b) 4,670 − 3,294

(c) 6,847 + 3,521 − 4,053 − 3,082

(d) 5,609 × 84

(e) 4,536 ÷ 42

(a)

(b)

(c)

(d)

(e)

#### Question 13:

Group the following numbers which are divisible by 3, 4 and 5

296, 312, 145, 720, 48, 375, 600

A given number is divisible by 3 if the sum of all the digits is divisible by 3.

A given number is divisible by 4 if the number formed by the last two digits is divisible by 4.

A given number is divisible by 5 if it ends with 0 or 5.

The numbers divisible by 3 are 312, 720, 48, 375, and 600.

The numbers divisible by 4 are 296, 312, 720, 48, and 600.

The numbers divisible by 5 are 145, 720, 375, and 600.

#### Question 14:

Write all the factors of

(a) 68

(b) 125

(a) 1, 2, 4, 17, 34, 68

(b) 1, 5, 25, 125

#### Question 15:

Find the H.C.F of

(a) 45, 60

(b) 54, 27

(a) H.C.F. = 15

(b) H.C.F. = 27

#### Question 16:

Find the L.C.M. of

(a) 10, 12

(b) 30, 46

(a) L.C.M. = 60

(b) L.C.M. = 690

#### Question 17:

Write next three equivalent fractions of

(a)

(b)

(a)

The next three equivalent fractions of are, and.

(b)

The next three equivalent fractions of are, and.

#### Question 18:

Reduce the following to their lowest terms.

(a)

(b)

(c)

(a)

(b)

(c)

#### Question 19:

Simplify the following

(a) 12 + [{1 + (15 − 3)} × 4]

(b)

(c)

(d)

(e)

(a)

(b)

(c)

(d)

(e)

#### Question 20:

Simplify the following

(a) 9.52 + 0.082 + 3.4156

(b) 7.35 − 1.026

(a)

(b)

#### Question 21:

Nandini scored 552 marks out of 600 in the 7th standard annual examination. Find the percentage of marks scored by her.

Percentage of marks scored by Nandini

#### Question 22:

Gowtham bought a bicycle for Rs 2,700. If the marked price of the bicycle is Rs 3,000, find the rate of discount.

Cost price = Rs.2,700

Marked price = Rs.3,000

Rate of discount

#### Question 23:

Hussain bought a television set for Rs 15,000. After some days he sold it for Rs 12,000. Find the percentage of loss.

Cost price = Rs.15,000

Selling price = Rs.12,000

Loss percentage

#### Question 24:

Sophia deposited Rs 8,000 in a post office for 5 years at the rate of 9% p.a. simple interest. Find the interest earned.

Principal = Rs.8,000

Time= 5 years

Rate = 9% p.a.

Simple Interest

#### Question 25:

Somappa and Hanumappa started a partnership business investing Rs 24,000 and Rs 32,000 respectively. Find the ratio of their investments.

Ratio of their investments

#### Question 26:

Find the value of x in each of the following:

(a) x : 3 :: 15 : 5

(b) 10 : x :: 2 : 3

(a)

(b)

#### Question 27:

(a) Write the set in Roster method. X = {months in a year}

(b) Write the set in Rule method. Y = {1, 4, 9, 16, 25}

(a)

(b)

#### Question 28:

Write the equivalent and the equal symbol for the following sets.

(a) Equivalent AB

(b) Equal P = Q

#### Question 29:

Classify the following as finite, infinite or null sets.

(a) Set of odd numbers

(b) Set of persons living for three hundred years

(c) Set of letters in the word ‘TEACHER’

(a) Infinite set

(b) Null set

(c) Finite set

#### Question 30:

Classify the following into monomial, binomial and trinomial expression.

(a) 5abc

(b) xy + z

(c) ab + bc

(d) ab × d

(e) 5x + 1

(f) 6m + 7n − 10

(a) Monomial

(b) Trinomial

(c) Binomial

(d) Monomial

(e) Binomial

(f) Trinomial

#### Question 31:

(a) 2m, 6m, m

(b) 2pq, 4pq, 8pq, pq

(c) 7x, 4y, 3x, 2y

(d) 8xyz, 12yzx

(e) 4ab, 5bc

(a)

(b)

(c)

(d)

(e)

#### Question 32:

Subtract:

(a) 4ax from 8ax

(b) 7pqr from 12 pqr

(a)

(b)

#### Question 33:

Find the product of

(a) 6a × 4a

(b) 5x × 7y

(c) 4m2n × 6mn

(d) 3p × 2q × 2r

(e) 5x2y × 4x3y2 × 2z

(a)

(b)

(c)

(d)

(e)

#### Question 34:

Divide:

(a) 10a2b ÷ 5ab

(b) 18x3y2 ÷ 6x2y2

(a)

(b)

#### Question 35:

(a) (m × 4m) − (3m4 ÷ m2)

(b) (x5 ÷ x3) + 3x2

(a)

(b)

#### Question 36:

Solve the following

(a) P + 4 = 15

(b) m − 9 = 4

(c) x + 2x + 1 = 4x + 6

(d) 9a − 3a − 4a − 6 = 0

(a)

(b)

(c)

(d)

#### Question 37:

What is the frequency denoted by these tallies.

(a)

(b)

(c)

(d)

(a) 5

(b) 6

(c) 13

(d) 17

#### Question 38:

Find the Range of the following scores.

(a) 18, 23, 19, 25, 22, 14, 21, 30

(b) 45, 39, 40, 36, 42, 48, 39

(a) Range = Highest number − Lowest number = 30 − 14 = 16

(b) Range = Highest number − Lowest number = 48 − 36 = 12

#### Question 39:

Find the size of the class interval in the following:

(a) 11 − 20

(b) 31 − 35

(c) 41 − 49

(a) Size of the class interval = (20 11) + 1 = 10

(b) Size of the class interval = (35 31) + 1 = 5

(c) Size of the class interval = (49 − 41) + 1 = 9

#### Question 40:

Prepare a frequency distribution table for the following scores. (size of the CI is 5)

 14 19 24 35 16 11 18 25 29 19 21 23 29 33

 Class Interval (C.I) Frequency (f) 10 − 15 2 15 − 20 4 20 − 25 3 25 − 30 3 30 − 35 2

#### Question 41:

(a) Write the complementary angle of 20°

(b) Write the supplementary angle of 108°

(a) Complementary angle of

(b) Supplementary angle of

#### Question 42:

Find the remaining angles in the following figure.

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

#### Question 43:

Draw a line AB = 5.5 cm. Mark a point X and construct an angle of 60° by using compass at X.

#### Question 44:

Construct a triangle PQR in which PQ = 6.4 cm, PR = QR = 5 cm

Construction of triangle PQR:

(i) Draw a line segment PQ of length 6.4 cm.

(ii) With P as centre, draw an arc of radius 5 cm.

(iii) With Q as centre, draw another arc of radius 5 cm.

(iv) The two arcs intersect at a point R.

(v) Join PR and QR.

#### Question 45:

Construct the triangle MNO, NO = 4.8 cm, and measure the two sides of the triangle.

Construction of triangle MNO:

(i) Draw a line segment NO of length 4.8 cm.

(ii) With N as centre, draw , using compass.

(iii) With O as centre, draw , using compass.

(iv) Mark the intersection of the two sides of the triangle as M.

By measuring, we get

cm and cm.

#### Question 46:

Observe the figure and fill in the blanks:

(a) ‘O’ = ……….

(b) OA = ……….

(c) BOC = ……..

(d) DE = ……….

(1) ‘O’= Centre of the circle

(3) BOC= Diameter

(4) DE = Chord

#### Question 47:

Write the two properties of the following quadrilaterals.

(a) rectangle

(b) trapezium

(c) rhombus

(a) Properties of a rectangle:

(i) Opposite sides of a rectangle are parallel and equal.

(ii) Each angle of a rectangle is a right angle.

(b) Properties of a trapezium:

(i) At least one pair of opposite sides is parallel.

(ii) The sum of all the angles of a trapezium is .

(c) Properties of a rhombus:

(i) The adjacent sides of a rhombus are equal.

(ii) The diagonals of a rhombus bisect each other.

#### Question 48:

Find the sum of the interior angles of the followings:

(a) triangle

(a)

(b)

#### Question 49:

Name of the following polygons.

(a) 8 sided polygon

(b) 7 sided polygon

(a) Octagon

(b) Heptagon

#### Question 50:

Write the formula to find the area of:

(a) a triangle

(b) a rectangle