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Q:

Write in descending order: -5, -17, 10, -14 and 2.

A:
Descending order means arranging the numbers from the greatest to the smallest.
10 > 2 > -5 > -14 > -17.
Q:

A player played 14 games. Out of which he won 8 games. Write the fraction of the games he won.

A:
Fraction of games he won = Games he won/Total Games he played
= 8/14
= 4/7
Q:

What is the median of the values 27, 48, 72, 38, 14, 21, 22 ?

A:
Arranging terms in ascending order

14,21,22,27,38,48,72

Median = Medial term = 27

Q:

Form an equation if subtract 3 from a number, the result is 4.

A:
Let the number be 'x'
x- 3 = 4
Q:

Is the triangle possible if angles of the triangle are 30°, 60° and 80°?

A:
No, triangle is not possible as the sum of three angles of a triangle is not equal to 180°.
Q:

Find the supplementary angle of 75°.

A:

Sum of two supplementary angles = 180º

One of them = 75º

Another angle = 180°-75° = 105°

Q:

Rewrite in the simplest form.

A:

Q:

Subtract (-128) from the sum of 55 and (-38).

A:

{55 + (-38)} – (–128)
= (17) – (–128)
= 17 + 128
= 145.

Q:

Find the product 0.30.030.003.

A:
(0.3 0.03) 0.003
= 0.009 0.003
= 0.000027
Q:

Following are the marks obtained by students of class VI.
23, 35, 40, 49, 49.5, 15, 15.5, 17.5. Find :
1) Highest Marks
2) Lowest Marks
3) Range

A:
1) Highest Marks = 49.5
2) Lowest Marks = 15
3) Range = Maximum marks - Minimum marks
=49.5 – 15
= 34.5
Q:

Check whether x = -2 is a solution to the equation 7x + 5 = 9 or not.

A:

Here 7x + 5 = 9
Putting x = -2
LHS =7 (-2) + 5
or =-14 + 5
or =-9 RHS

x = -2 is not a solution of the given equation.

Q:

Indicate two pairs of angles which are:

(i) vertically opposite angles.
(ii) linear pairs.

A:
(i) 1 and 4; 5 and (3 + 2)

(ii) 1 and 5; 4 and 5
Q:

Find angle x in the figure given below:

A:

Sum of two interior angles = Opposite exterior angle
50 + x = 110
x = 60

Q:

If DEF BCA, write the part that corresponds to

A:

Q:

Find out the numbers if

i. 10% of number is 600

ii. 12% of number is 1080.

A:

Q:

Arrange the following in ascending order:

A:

Q:


A:

Q:

Raghu has 175 sweets out of which he gives one fifth part to his sister and out of the remaining he gives two seventh part to his youngest brother. How many sweets are left with him?

A:

Total sweets = 175
Sweets given to sister = 1/5 of 175
= 1/5 175 = 35
Remaining = 175 – 35 = 140

Sweets given to brother = 2/7 of 140
= 2/7 140 = 40
Now remaining sweets = 140 – 40 = 100

Q:

Find the mean of first five multiples of 5.

A:

First five multiples of 5 are 5, 10, 15, 20, 25.

Mean =
Mean = 15

Q:

Two-third of a number is 3 more than one-third of the number. Find the number.

A:


Thus, the number is 9.

Q:

In the given figure, decide whether l is parallel to m:

A:
(i) l is parallel to m.
(ii) l is not parallel to m.
(iii) l is parallel to m.
Q:

Find angles x and y in the following figure:

A:

In triangle PQR,

P = x ( vertically opposite angles)

Q = x

R = y = x (vertically opposite angles)

Therefore, P + Q + R = 1800

3x = 1800

x = 600.

Since, x = y (Verically opposide triangle)

Hence, y = 600.

Q:

In Fig, BD and CE are altitudes of ABC such that BD = CE.
(i) State the three pairs of equal parts in CBD and BCE.
(ii) Is CBD BCE? Why or why not?
(iii) Is DCB = EBC? Why or why not?

A:
(i) In CBD and BCE,
the three pairs of equal parts are as given below:

BEC = CDB (=90)

BD = CE (Given)

and BC= BC (Common in both)

(ii) From (i) above, CBD BCE (By RHS congruence rule)

(iii) Yes, DCB = EBC (Corresponding parts of congruent triangles)

Q:

A man buys 3 oranges for Rs. 4 and sells 4 oranges for Rs. 6. Find his Gain or loss per cent.

A:
C.P of one orange = Rs.
S.P of one orange = Rs. 3/2x3/3 = 9/6 and 4/3x2/2 = 8/6

S.P > C.P


Q:

Simplify .

A:

Q:

In a class test containing 15 questions, 3 marks are given for every correct answer and (–1) marks given for every incorrect answer.
(i) Gurpreet attempts all the questions but only 9 of her answers are correct. What is her total score?
(ii) One of her friends gets only 5 answers correct. What will be her score?

A:

Marks given for correct answer = 3
Marks given for wrong answer = - 1

Total number of questions = 15
(i) Number of correct answers of
Gurpreet = 9
Number of incorrect answers of
Gurpreet = 15 – 9
= 6
Total score of Gurpreet = 9 (3) + 6(-1)
= 27 – 6
= 21
(ii) Number of correct answers of
her friend = 5
Number of incorrect answers of
her friend = 15 – 5 = 10

Total score of Gurpreet’s friend = 5(3) + 10(-1)
=15 – 10 = 5

Q:

The following table shows the weight of 12 students in a class.

Weight (in Kg )

48

50

52

54

58

No. of students

4

3

2

2

1

Find the Median of the weights.

A:

Weight(x)

No. of students (f)

Cummalative frequency

48

4

4

50

3

7

52

2

9

54

2

11

58

1

12

N =f = 12 (even number)

Median

Q:

Solve the following equations:
(i)2y+5/2=37/2 (ii)(5x)/2=25/2,
(iii)6z+10=-2, (iv)(a/4)+7=5.

A:
(i)


(ii)


(iii)


(iv)


Q:

If 35 shirts of equal size can be stitched from 49/2 metres of cloth, what is the length of the cloth required for each shirt? Find the length of cloth required for 4 shirts of equal size.

A:
Length of cloth used in 35 equal shirts = 49/2 m
Length of cloth used in 1 shirts = (49/2)/35 m
= 49/70
= 0.7 m
Length of cloth used for 4 equal shirts = 4×0.7 m
= 2.8 m
Thus, cloth required for 4 equal shirts is 2.8 m.
Q:

The diagonals of a rhombus measure 10 cm and 24 cm. Find its perimeter.

A:
ABCD is a rhombus and its diagonals bisect at O.
AC = 12 cm and BD = 10 cm
So, OA = 24/2 = 12 cm, OB = 10/2 = 5 cm
In AOB, AOB = 90°
Using Pythagoras Theorem,

 AB2 = AO2 + OB2
 AB2 = (12)2 + (5)2
 = 144 + 25
= 169
AB = 13 cm.
So, the perimeter of rhombus = 4× 13 cm
= 52 cm
Q:

In triangle ABC, AB = AC and ADBC. Prove that B = C.

A:


AB = AC and ADBC
To Prove: B = C
Proof: In ABD and ACD,
AB = AC [Given]
ADB = ADC [Each 90°]
AD = AD [Common]
ABD ACD [By RHS]
So, B = C [By CPCT]

Q:

If INR 1250 is to be divided amongst Raj, Pallavi and Ronit such that Raj gets two parts, Pallavi three parts and Ronit five parts. How much money will each get? What will it be in percentage?

A:

Q:

Write in descending order: -5, -17, 10, -14 and 2.

A:
Descending order means arranging the numbers from the greatest to the smallest.
10 > 2 > -5 > -14 > -17.
Q:

A player played 14 games. Out of which he won 8 games. Write the fraction of the games he won.

A:
Fraction of games he won = Games he won/Total Games he played
= 8/14
= 4/7
Q:

What is the median of the values 27, 48, 72, 38, 14, 21, 22 ?

A:
Arranging terms in ascending order

14,21,22,27,38,48,72

Median = Medial term = 27

Q:

Form an equation if subtract 3 from a number, the result is 4.

A:
Let the number be 'x'
x- 3 = 4
Q:

Is the triangle possible if angles of the triangle are 30°, 60° and 80°?

A:
No, triangle is not possible as the sum of three angles of a triangle is not equal to 180°.
Q:

Find the supplementary angle of 75°.

A:

Sum of two supplementary angles = 180º

One of them = 75º

Another angle = 180°-75° = 105°

Q:

Rewrite in the simplest form.

A:

Q:

Subtract (-128) from the sum of 55 and (-38).

A:

{55 + (-38)} – (–128)
= (17) – (–128)
= 17 + 128
= 145.

Q:

Find the product 0.30.030.003.

A:
(0.3 0.03) 0.003
= 0.009 0.003
= 0.000027
Q:

Following are the marks obtained by students of class VI.
23, 35, 40, 49, 49.5, 15, 15.5, 17.5. Find :
1) Highest Marks
2) Lowest Marks
3) Range

A:
1) Highest Marks = 49.5
2) Lowest Marks = 15
3) Range = Maximum marks - Minimum marks
=49.5 – 15
= 34.5
Q:

Check whether x = -2 is a solution to the equation 7x + 5 = 9 or not.

A:

Here 7x + 5 = 9
Putting x = -2
LHS =7 (-2) + 5
or =-14 + 5
or =-9 RHS

x = -2 is not a solution of the given equation.

Q:

Indicate two pairs of angles which are:

(i) vertically opposite angles.
(ii) linear pairs.

A:
(i) 1 and 4; 5 and (3 + 2)

(ii) 1 and 5; 4 and 5
Q:

Find angle x in the figure given below:

A:

Sum of two interior angles = Opposite exterior angle
50 + x = 110
x = 60

Q:

If DEF BCA, write the part that corresponds to

A:

Q:

Find out the numbers if

i. 10% of number is 600

ii. 12% of number is 1080.

A:

Q:

Arrange the following in ascending order:

A:

Q:


A:

Q:

Raghu has 175 sweets out of which he gives one fifth part to his sister and out of the remaining he gives two seventh part to his youngest brother. How many sweets are left with him?

A:

Total sweets = 175
Sweets given to sister = 1/5 of 175
= 1/5 175 = 35
Remaining = 175 – 35 = 140

Sweets given to brother = 2/7 of 140
= 2/7 140 = 40
Now remaining sweets = 140 – 40 = 100

Q:

Find the mean of first five multiples of 5.

A:

First five multiples of 5 are 5, 10, 15, 20, 25.

Mean =
Mean = 15

Q:

Two-third of a number is 3 more than one-third of the number. Find the number.

A:


Thus, the number is 9.

Q:

In the given figure, decide whether l is parallel to m:

A:
(i) l is parallel to m.
(ii) l is not parallel to m.
(iii) l is parallel to m.
Q:

Find angles x and y in the following figure:

A:

In triangle PQR,

P = x ( vertically opposite angles)

Q = x

R = y = x (vertically opposite angles)

Therefore, P + Q + R = 1800

3x = 1800

x = 600.

Since, x = y (Verically opposide triangle)

Hence, y = 600.

Q:

In Fig, BD and CE are altitudes of ABC such that BD = CE.
(i) State the three pairs of equal parts in CBD and BCE.
(ii) Is CBD BCE? Why or why not?
(iii) Is DCB = EBC? Why or why not?

A:
(i) In CBD and BCE,
the three pairs of equal parts are as given below:

BEC = CDB (=90)

BD = CE (Given)

and BC= BC (Common in both)

(ii) From (i) above, CBD BCE (By RHS congruence rule)

(iii) Yes, DCB = EBC (Corresponding parts of congruent triangles)

Q:

A man buys 3 oranges for Rs. 4 and sells 4 oranges for Rs. 6. Find his Gain or loss per cent.

A:
C.P of one orange = Rs.
S.P of one orange = Rs. 3/2x3/3 = 9/6 and 4/3x2/2 = 8/6

S.P > C.P


Q:

Simplify .

A:

Q:

In a class test containing 15 questions, 3 marks are given for every correct answer and (–1) marks given for every incorrect answer.
(i) Gurpreet attempts all the questions but only 9 of her answers are correct. What is her total score?
(ii) One of her friends gets only 5 answers correct. What will be her score?

A:

Marks given for correct answer = 3
Marks given for wrong answer = - 1

Total number of questions = 15
(i) Number of correct answers of
Gurpreet = 9
Number of incorrect answers of
Gurpreet = 15 – 9
= 6
Total score of Gurpreet = 9 (3) + 6(-1)
= 27 – 6
= 21
(ii) Number of correct answers of
her friend = 5
Number of incorrect answers of
her friend = 15 – 5 = 10

Total score of Gurpreet’s friend = 5(3) + 10(-1)
=15 – 10 = 5

Q:

The following table shows the weight of 12 students in a class.

Weight (in Kg )

48

50

52

54

58

No. of students

4

3

2

2

1

Find the Median of the weights.

A:

Weight(x)

No. of students (f)

Cummalative frequency

48

4

4

50

3

7

52

2

9

54

2

11

58

1

12

N =f = 12 (even number)

Median

Q:

Solve the following equations:
(i)2y+5/2=37/2 (ii)(5x)/2=25/2,
(iii)6z+10=-2, (iv)(a/4)+7=5.

A:
(i)


(ii)


(iii)


(iv)


Q:

If 35 shirts of equal size can be stitched from 49/2 metres of cloth, what is the length of the cloth required for each shirt? Find the length of cloth required for 4 shirts of equal size.

A:
Length of cloth used in 35 equal shirts = 49/2 m
Length of cloth used in 1 shirts = (49/2)/35 m
= 49/70
= 0.7 m
Length of cloth used for 4 equal shirts = 4×0.7 m
= 2.8 m
Thus, cloth required for 4 equal shirts is 2.8 m.
Q:

The diagonals of a rhombus measure 10 cm and 24 cm. Find its perimeter.

A:
ABCD is a rhombus and its diagonals bisect at O.
AC = 12 cm and BD = 10 cm
So, OA = 24/2 = 12 cm, OB = 10/2 = 5 cm
In AOB, AOB = 90°
Using Pythagoras Theorem,

 AB2 = AO2 + OB2
 AB2 = (12)2 + (5)2
 = 144 + 25
= 169
AB = 13 cm.
So, the perimeter of rhombus = 4× 13 cm
= 52 cm
Q:

In triangle ABC, AB = AC and ADBC. Prove that B = C.

A:


AB = AC and ADBC
To Prove: B = C
Proof: In ABD and ACD,
AB = AC [Given]
ADB = ADC [Each 90°]
AD = AD [Common]
ABD ACD [By RHS]
So, B = C [By CPCT]

Q:

If INR 1250 is to be divided amongst Raj, Pallavi and Ronit such that Raj gets two parts, Pallavi three parts and Ronit five parts. How much money will each get? What will it be in percentage?

A:

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