Archives

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

The diameter of hemisphere = Edge of the cube = l So, the radius of hemisphere = l/2 ∴ The total surface area of solid = surface area of... View Article

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Given Diameter of cylinder = 3 m Radius of cylinder (r) = 3/2m Height of cylinder (h) = 14 m Width of embankment = 4 m Outer Radius of... View Article

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see Fig.12.16) , each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?

Solution Using Heron's formula, area of the triangle = Each ar(△)can be calculated by Heron’s Formula, where a = 50 cm b = 50 cm c = 20... View Article

Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: (i) x + y = 5, 2x + 2y = 10 (ii) x – y = 8, 3x – 3y = 16 (iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0 (iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0

(i)Given equations x + y = 5 and 2x + 2y = 10 (a1/a2) = 1/2 (b1/b2) = 1/2 (c1/c2) = 1/2 Since (a1/a2) = (b1/b2) = (c1/c2) ∴The equations... View Article

Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

Solution: Given Perpendicular distance (h) = 100 m Area of the trapezium-shaped field = 10500 m2 Find out We have to find... View Article

The following table gives the distribution of students of two sections according to the marks obtained by them: Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.

Solution The class-marks = (lower limit + upper limit)/2 For section A, Marks Class-marks Frequency 0-10 5 3 10-20 15 9 20-30 25 17... View Article

Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ∠ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.

Solution Given Vertex B of ∆ABC lie outside the circle, chord AD=CE To prove: ∠ABC=1/2(∠DOE-∠AOC) Construction: Join AE Solution:... View Article

A cubical box has each edge 10 cm and another cuboidal box is 12.5cm long, 10 cm wide and 8 cm high (i) Which box has the greater lateral surface area and by how much? (ii) Which box has the smaller total surface area and by how much?

Given Edge of a cube = 10cm Length, l = 12.5 cm Breadth, b = 10cm Height, h = 8 cm Find out We have to find i) Which box has the greater... View Article

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Let the current age of Aftab be ‘x’. And, the current age of his daughter be ‘y’. Now, we can write, seven years ago, Age... View Article

For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. i. 252 ii. 180 iii. 1008 iv. 2028 v. 1458 vi. 768

Solution (i) 252 252 = 2 × 2 × 3 × 3 × 7 = (2 × 2) × (3 × 3) × 7 7 cannot be paired.... View Article

The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

Given that The age difference between Ani and Biju is 3 yrs. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his... View Article

The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?

The earth attracts the moon with an equal force with which the moon attracts the earth but these forces are in opposite directions. By... View Article

Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 , find the radius of the circle.

Given: AB=5cm, CD =11cm Construction: Draw OM perpendicular AB and ON perpendicular CD. As OM perpendicular AB and ON perpendicular CD and... View Article

Archives

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see Fig.12.16) , each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?

Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: (i) x + y = 5, 2x + 2y = 10 (ii) x – y = 8, 3x – 3y = 16 (iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0 (iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0

Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

The following table gives the distribution of students of two sections according to the marks obtained by them: Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.

Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ∠ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.

A cubical box has each edge 10 cm and another cuboidal box is 12.5cm long, 10 cm wide and 8 cm high (i) Which box has the greater lateral surface area and by how much? (ii) Which box has the smaller total surface area and by how much?

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. i. 252 ii. 180 iii. 1008 iv. 2028 v. 1458 vi. 768

The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?

Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 , find the radius of the circle.

UN-OHRLLS [UPSC Notes]

Which Fruit Is Not Good For Diabetes?

What Fruit Has The Most Sugar?

Which Fruit Has Lactic Acid?

Which Fruit Contains Lactic Acid?

Is Fermented Fruit Alcohol?

What Is The Most Eaten Fruit In The World?

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