Q:

A:

Q:

A:

Octagon.

Q:

A:

Q:

A:

Prime factors of 189 = 3 3 3 7

Making triplets, one triplet is formed 3 3 3 leaving one more factor 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) = x^{2 }– a^{2}, find 6^{2} – 5^{2}.

A:

6^{2} – 5^{2} = (6 + 5) (6 – 5) = 11

Q:

A:

There are 6 edges in a triangular pyramid.

Q:

A:

Q:

A:

Q:

A:

Sum of the angles of a quadrilateral is 360^{}.

130^{} + 120^{} + 60^{} + x = 360^{ }

310^{} + x = 360^{}

130

310

x = 360^{} – 310^{}

x = 50^{}

Q:

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.

PQ=RS=4cm and QR=SP=4 cm

Q:

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:

A:

Q:

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 810, Sunil gains 8%. For how much did he purchase it?

A:

Q:

A:

(x^{2} – y^{2})(2x + y)

= x^{2}(2x + y) – y^{2}(2x + y)

= x

= 2x^{3} + x^{2}y – 2xy^{2} - y^{3}

= 2x^{3} - y^{3} + x^{2}y – 2xy^{2}

Q:

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.

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:

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:

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:

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 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:

Total cards in a pack are 52.

Number of black kings is 2.

Probability of getting a black king =

Q:

A:

The remainder is 279. This shows that 893304 is greater then 945

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

Q:

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 280?

A:

Q:

find (1.02)

A:

(1.02)^{2} – (0.98)^{2}^{ }= (1.02 + 0.98) (1.02 – 0.98)

= (2.00) (.04)

= 0.08

= (2.00) (.04)

= 0.08

Q:

A:

Q:

A:

Q:

A:

Q:

(ii)

A:

(i)

(ii)

(ii)

Q:

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.

A:

Histogram of following data is given below:

Q:

A:

Q:

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

A:

Q:

A:

Q:

A:

Octagon.

Q:

A:

Q:

A:

Prime factors of 189 = 3 3 3 7

Making triplets, one triplet is formed 3 3 3 leaving one more factor 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) = x^{2 }– a^{2}, find 6^{2} – 5^{2}.

A:

6^{2} – 5^{2} = (6 + 5) (6 – 5) = 11

Q:

A:

There are 6 edges in a triangular pyramid.

Q:

A:

Q:

A:

Q:

A:

Sum of the angles of a quadrilateral is 360^{}.

130^{} + 120^{} + 60^{} + x = 360^{ }

310^{} + x = 360^{}

130

310

x = 360^{} – 310^{}

x = 50^{}

Q:

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.

PQ=RS=4cm and QR=SP=4 cm

Q:

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:

A:

Q:

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 810, Sunil gains 8%. For how much did he purchase it?

A:

Q:

A:

(x^{2} – y^{2})(2x + y)

= x^{2}(2x + y) – y^{2}(2x + y)

= x

= 2x^{3} + x^{2}y – 2xy^{2} - y^{3}

= 2x^{3} - y^{3} + x^{2}y – 2xy^{2}

Q:

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.

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:

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:

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:

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 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:

Total cards in a pack are 52.

Number of black kings is 2.

Probability of getting a black king =

Q:

A:

The remainder is 279. This shows that 893304 is greater then 945

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

Q:

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 280?

A:

Q:

find (1.02)

A:

(1.02)^{2} – (0.98)^{2}^{ }= (1.02 + 0.98) (1.02 – 0.98)

= (2.00) (.04)

= 0.08

= (2.00) (.04)

= 0.08

Q:

A:

Q:

A:

Q:

A:

Q:

(ii)

A:

(i)

(ii)

(ii)

Q:

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.

A:

Histogram of following data is given below:

Q:

A:

Q:

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

A:

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