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Q:

The sum of two numbers is . If one of the numbers is , find the other.

A:
Q:

Name the regular polygon with 8 sides.

A:
Octagon.
Q:

Find the square root of 729.

A:

Q:

Show that 189 is not a perfect cube.

A:
Prime factors of 189 = 3 3 3 7

Making triplets, one triplet is formed 3 3 3 leaving one more factor 7.

189 cannot be expressed as a product of triplets, hence 189 is not a perfect cube.

Q:

Using identity (x - a) (x + a) = x2 – a2, find 62 – 52.

A:

62 – 52 = (6 + 5) (6 – 5) = 11

Q:

How many edges are there in a triangular pyramid?

A:
There are 6 edges in a triangular pyramid.
Q:

Verify .

A:
Q:

Solve the equation:

A:
Q:

Find x in the following figure.

A:
Sum of the angles of a quadrilateral is 360.

130 + 120 + 60 + x = 360

310 + x = 360

x = 360 – 310

x = 50

Q:

The adjacent sides SP and PQ of a parallelogram PQRS are 4 cm each. State the measure of all the sides. What is another name of this figure?

A:
Since opposite sides of a parallelogram are equal, so in the parallelogram PQRS,
PQ=RS=4cm and QR=SP=4 cm
Since all sides of a parallelogram are equal, therefore, it is a rhombus.
Q:

The following pie chart shows the times spent by a child during a day.


Answer the following questions based on the given pie chart.

1. What proportion of the sector for hours is spent in sleeping?
2. What proportion of the sector for hours is spent in school?

A:



Q:

Find the value of x that makes the following statement correct.

A:

Q:

Find the smallest number by which 12500 must be multiplied so that the product is a perfect cube.

A:

12500= 5552255
The prime factors 2 and 5 do not appear in a group of three. So, 12500 is not a perfect cube.
To make it a perfect cube, multiply it by 25.
Thus, 1250025 = 555222555
= 12500,
which is a perfect cube.

Q:

On selling a fan for INR 810, Sunil gains 8%. For how much did he purchase it?

A:

Q:

Find the product of (x2 – y2)(2x + y).

A:
(x2 – y2)(2x + y)

= x2(2x + y) – y2(2x + y)

= 2x3 + x2y – 2xy2 - y3

= 2x3 - y3 + x2y – 2xy2

Q:

Can a polyhedron have 20 faces, 40 edges and 30 vertices?

A:
Given, F = 20, V = 30 and E = 40

For any polyhedron, by Euler’s formula, we have

F + V = E + 2

F + V = 20 + 30 = 50

E + 2 = 40 + 2 = 42

F + V E + 2

Therefore, a polyhedron can not be formed.
Q:

A:

Convert the given rational numbers to rational numbers with the same denominators.

Q:

The perimeter of a triangle is 49 cm. The one side is 7 cm longer than the other and 5 cm shorter than the third. Find the length of each side of the triangle.

A:
Let the third side of the triangle be x cm

First side of the triangle = (x – 5) cm

Second side of the triangle = (x – 5 – 7) = (x – 12) cm

Perimeter = 49 cm

Third side of the triangle = 22 cm

First side of the triangle = (22 – 5) = 17 cm

Second side of the triangle = (22 – 12) = 10 cm

Thus, the sides of the triangle are 17 cm, 10 cm and 22 cm.

Q:

Two adjacent angles of a parallelogram are (3x – 4) and (3x + 10). Find the angles of the parallelogram.

A:
Sum of the adjacent angles of a parallelogram = 180

(3x – 4) + (3x + 10) = 180

6x + 6 = 180

6x = 174

x = 29

(3 29) – 4 = 87 – 4 = 83

and, 3 29 + 10 = 87 + 10 = 97

Hence, four angles of a parallelogram are 83, 97, 83, 97.

Q:

Construct the quadrilateral ABCD in which AB = 4.5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm and AC = 7 cm.

A:
The given quadrilateral can be drawn as follows:

Step 1: Construct ABC with BC = 5.5 cm, AB = 4.5 cm and AC = 7 cm.

Step 2: Vertex D is 6 cm away from vertex A. Therefore, while taking A as centre, draw an arc of radius 6 cm.

Step 3: Taking C as centre, draw an arc of radius 4 cm, cutting the previous arc at point D. Join D to A and C.

ABCD is the required quadrilateral.

Q:

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a black king.

A:
Total cards in a pack are 52.

Number of black kings is 2.

Probability of getting a black king =

Q:

Find the least number that must be added to 893304 to obtain a perfect square.

A:

The remainder is 279. This shows that 893304 is greater then 9452. The next perfect square is 9462 (i.e.) 894916.

Hence the number to be added is 894916 – 893304 = 1612.

Q:

Find the smallest number by which 1600 must be divided so that the quotient is a perfect cube, further find its cube root.

A:
Q:

A shopkeeper offers his customers 10% discount and still makes a profit of 26%. What is the actual cost of an article marked INR 280?

A:

Q:

Using identity a2 - b2 = (a + b) (a – b),
find (1.02)2 – (0.98)2.

A:
(1.02)2 – (0.98)2
= (1.02 + 0.98) (1.02 – 0.98)
= (2.00) (.04)
= 0.08
Q:

Draw the three views of a brick.

A:

Q:

A:




Q:

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.

A:
Q:

Find the measure of angle x in the following figure:
(i)

(ii)

A:
(i)



(ii)

Q:

The number of apples collected from 50 trees is recorded below:
35, 67, 24, 111, 78, 45, 38, 52,15, 25, 73, 84, 65, 18, 82, 63, 78, 142, 23, 69, 32, 56, 12, 15, 55, 98, 71, 12, 9, 62, 6, 138, 102, 123, 46, 89, 110, 128, 48, 19, 53, 85, 70, 112, 148, 133, 63, 80, 98, 96.
Make a group frequency table and represent the data by using a histogram.

A:


Histogram of following data is given below:

Q:

Find the square root of 3 correct up to two places of decimal.

A:
Q:

In how much time will the simple interest on INR 3,500 at the rate of 6% per annum be the same as simple interest on INR 4,000 at 10.5% per annum for 4 years?

A:

Q:

The sum of two numbers is . If one of the numbers is , find the other.

A:
Q:

Name the regular polygon with 8 sides.

A:
Octagon.
Q:

Find the square root of 729.

A:

Q:

Show that 189 is not a perfect cube.

A:
Prime factors of 189 = 3 3 3 7

Making triplets, one triplet is formed 3 3 3 leaving one more factor 7.

189 cannot be expressed as a product of triplets, hence 189 is not a perfect cube.

Q:

Using identity (x - a) (x + a) = x2 – a2, find 62 – 52.

A:

62 – 52 = (6 + 5) (6 – 5) = 11

Q:

How many edges are there in a triangular pyramid?

A:
There are 6 edges in a triangular pyramid.
Q:

Verify .

A:
Q:

Solve the equation:

A:
Q:

Find x in the following figure.

A:
Sum of the angles of a quadrilateral is 360.

130 + 120 + 60 + x = 360

310 + x = 360

x = 360 – 310

x = 50

Q:

The adjacent sides SP and PQ of a parallelogram PQRS are 4 cm each. State the measure of all the sides. What is another name of this figure?

A:
Since opposite sides of a parallelogram are equal, so in the parallelogram PQRS,
PQ=RS=4cm and QR=SP=4 cm
Since all sides of a parallelogram are equal, therefore, it is a rhombus.
Q:

The following pie chart shows the times spent by a child during a day.


Answer the following questions based on the given pie chart.

1. What proportion of the sector for hours is spent in sleeping?
2. What proportion of the sector for hours is spent in school?

A:



Q:

Find the value of x that makes the following statement correct.

A:

Q:

Find the smallest number by which 12500 must be multiplied so that the product is a perfect cube.

A:

12500= 5552255
The prime factors 2 and 5 do not appear in a group of three. So, 12500 is not a perfect cube.
To make it a perfect cube, multiply it by 25.
Thus, 1250025 = 555222555
= 12500,
which is a perfect cube.

Q:

On selling a fan for INR 810, Sunil gains 8%. For how much did he purchase it?

A:

Q:

Find the product of (x2 – y2)(2x + y).

A:
(x2 – y2)(2x + y)

= x2(2x + y) – y2(2x + y)

= 2x3 + x2y – 2xy2 - y3

= 2x3 - y3 + x2y – 2xy2

Q:

Can a polyhedron have 20 faces, 40 edges and 30 vertices?

A:
Given, F = 20, V = 30 and E = 40

For any polyhedron, by Euler’s formula, we have

F + V = E + 2

F + V = 20 + 30 = 50

E + 2 = 40 + 2 = 42

F + V E + 2

Therefore, a polyhedron can not be formed.
Q:

A:

Convert the given rational numbers to rational numbers with the same denominators.

Q:

The perimeter of a triangle is 49 cm. The one side is 7 cm longer than the other and 5 cm shorter than the third. Find the length of each side of the triangle.

A:
Let the third side of the triangle be x cm

First side of the triangle = (x – 5) cm

Second side of the triangle = (x – 5 – 7) = (x – 12) cm

Perimeter = 49 cm

Third side of the triangle = 22 cm

First side of the triangle = (22 – 5) = 17 cm

Second side of the triangle = (22 – 12) = 10 cm

Thus, the sides of the triangle are 17 cm, 10 cm and 22 cm.

Q:

Two adjacent angles of a parallelogram are (3x – 4) and (3x + 10). Find the angles of the parallelogram.

A:
Sum of the adjacent angles of a parallelogram = 180

(3x – 4) + (3x + 10) = 180

6x + 6 = 180

6x = 174

x = 29

(3 29) – 4 = 87 – 4 = 83

and, 3 29 + 10 = 87 + 10 = 97

Hence, four angles of a parallelogram are 83, 97, 83, 97.

Q:

Construct the quadrilateral ABCD in which AB = 4.5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm and AC = 7 cm.

A:
The given quadrilateral can be drawn as follows:

Step 1: Construct ABC with BC = 5.5 cm, AB = 4.5 cm and AC = 7 cm.

Step 2: Vertex D is 6 cm away from vertex A. Therefore, while taking A as centre, draw an arc of radius 6 cm.

Step 3: Taking C as centre, draw an arc of radius 4 cm, cutting the previous arc at point D. Join D to A and C.

ABCD is the required quadrilateral.

Q:

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a black king.

A:
Total cards in a pack are 52.

Number of black kings is 2.

Probability of getting a black king =

Q:

Find the least number that must be added to 893304 to obtain a perfect square.

A:

The remainder is 279. This shows that 893304 is greater then 9452. The next perfect square is 9462 (i.e.) 894916.

Hence the number to be added is 894916 – 893304 = 1612.

Q:

Find the smallest number by which 1600 must be divided so that the quotient is a perfect cube, further find its cube root.

A:
Q:

A shopkeeper offers his customers 10% discount and still makes a profit of 26%. What is the actual cost of an article marked INR 280?

A:

Q:

Using identity a2 - b2 = (a + b) (a – b),
find (1.02)2 – (0.98)2.

A:
(1.02)2 – (0.98)2
= (1.02 + 0.98) (1.02 – 0.98)
= (2.00) (.04)
= 0.08
Q:

Draw the three views of a brick.

A:

Q:

A:




Q:

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.

A:
Q:

Find the measure of angle x in the following figure:
(i)

(ii)

A:
(i)



(ii)

Q:

The number of apples collected from 50 trees is recorded below:
35, 67, 24, 111, 78, 45, 38, 52,15, 25, 73, 84, 65, 18, 82, 63, 78, 142, 23, 69, 32, 56, 12, 15, 55, 98, 71, 12, 9, 62, 6, 138, 102, 123, 46, 89, 110, 128, 48, 19, 53, 85, 70, 112, 148, 133, 63, 80, 98, 96.
Make a group frequency table and represent the data by using a histogram.

A:


Histogram of following data is given below:

Q:

Find the square root of 3 correct up to two places of decimal.

A:
Q:

In how much time will the simple interest on INR 3,500 at the rate of 6% per annum be the same as simple interest on INR 4,000 at 10.5% per annum for 4 years?

A:

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