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The shape of a garden is rectangular in the middle and semi-circular at the ends as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is 20 – (3.5 + 3.5 meters]

Given Total length = 20 m Diameter of semi circle = 7 m Therefore, Radius of semi circle = 7/2 = 3.5 m Length of rectangular field = 20... View Article

Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the triangle ABC. Give the justification of the construction

To construct a triangle from given conditions 1. Let us draw a ΔABC with base side BC = 6 cm, and AB = 5 cm and ∠ABC = 60°. 2. Draw... View Article

If the sum of the first n terms of an AP is 4n − n², what is the first term (that is S₁) ? What is the sum of first two terms? What is the second term? Similarly find the 3rd, the10th and the nth terms.

Given that Sn = 4n−n2 Find out We have to find (i) first term (ii) Sum of first two terms (iii) Second term (iv) 3rd, the 10th and the... View Article

Check whether the following are quadratic equations: (i) (x + 1) ² = 2(x – 3) (ii) x² – 2x = (-2) (3 – x) (iii) (x – 2) (x + 1) = (x – 1) (x + 3) (iv) (x – 3) (2x + 1) = x(x + 5) (v) (2x – 1) (x – 3) = (x + 5) (x – 1) (vi) x² + 3x + 1 = (x – 2) ² (vii) (x + 2) ² = 2x (x² – 1) (viii) x³ – 4x² – x + 1 = (x – 2) ³

i)(x + 1)2 = 2(x – 3) By using the identity (a+b)2 = a2+2ab+b2 ⇒ x2 + 2x + 1 = 2x – 6 ⇒ x2 + 7 = 0 Since the above equation is in the form of... View Article

Which of the following are in inverse proportion? (i) The number of workers on a job and the time to complete the job. (ii) The time taken for a journey and the distance travelled in a uniform speed. (iii) Area of cultivated land and the crop harvested. (iv) The time taken for a fixed journey and the speed of the vehicle. (v) The population of a country and the area of land per person.

Solution (i) The number of workers on a job and the time to complete the job. Inversly proportional Since more number of workers can... View Article

An aeroplane leaves an airport and flies due north at a speed of 1,000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1,200 km per hour. How far apart will be the two planes after 1(1/2) hours?

Distance covered by place left towards north = 1000 * 1.1/2 Distance covered by place left towards west = 1200 * 1.1/2 = 1800km On applying... View Article

A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

Let the boy initially stand at point Y with inclination 30° and then he approaches the building to the point X with inclination 60°. To... View Article

The coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later, she buys another bat and 3 more balls of the same kind for Rs.1300. Represent this situation algebraically and geometrically.

Let us assume The cost of a bat be ‘Rs x’ The cost of a ball be ‘Rs y’ According to the given condition, the algebraic... View Article

A conical tent is 10 m high and the radius of its base is 24 m. Find (i) slant height of the tent. (ii) cost of the canvas required to make the tent, if the cost of 1 m2 canvas is Rs 70. (Assume π = 22/7)

Given Height of conical tent (h) = 10m Radius of conical base (r) = 24m Find out We have to find (i) slant height of the tent.(ii) cost of... View Article

Solve the following pairs of equations by reducing them to a pair of linear equations: (i) (7x-2y) / xy = 5 (8x + 7y) /xy = 15 (ii) 6x + 3y = 6xy 2x + 4y = 5xy (iii) 10/(x + y) + 2/(x-y) = 4 (iv) 1/(3x + y) + 1/(3x-y) = 3/4 1/2(3x + y) – 1/2(3x-y) = -1/8

(i) (7x-2y)/ xy = 5 (8x + 7y)/xy = 15 Solution: (7x-2y)/ xy = 5 7/y – 2/x =... View Article

The students of Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition? (Assume π = 22/7)

Given Radius of penholder=3 cm Height of penholder=10.5 cm Find out We have to find how much cardboard was required for 35 competitors... View Article

The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions. (i) In which subject did the student score 105 marks? (Hint: for 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle?) (ii) How many more marks were obtained by the student in Mathematics than in Hindi? (iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.

Solution: Total marks obtained by the students were 540, For 540 marks, the central angle = 360° For 1 mark, the central angle = (360... View Article

Given figure depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.

Given The diameter of the region representing the Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find out We have to find out... View Article

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.

Let AB and CD be the poles of equal height. O is the point between them from where the height of elevation taken. BD is the distance between the... View Article

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

From right ΔBCD, tan 60° = CD/BC √3 = 50/BC BC = 50/√3 …(1) Again From right ΔABC, tan 30° = AB/BC... View Article

Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case: (i) 2x³ + x²-5x + 2; -1/2, 1, -2 (ii) x³-4x² + 5x-2 ;2, 1, 1

(i) 2x3+x2-5x+2; -1/2, 1, -2 Given, p(x) = 2x3+x2-5x+2 and zeroes for p(x) are = 1/2, 1, -2 ∴ p(1/2) = 2(1/2)3+(1/2)2-5(1/2)+2 =... View Article

A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?

Given Side of the signal board = a Perimeter of the signal board = 3a = 180 cm ∴ a = 60 cm Find out We have to determine the Area of the... View Article

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.

Given r = 1 cm h = 1 cm. Find out We have to find out the volume of the solid in terms of π Solution Total Volume = Volume of cone +... View Article

Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle. Give the justification of the construction

To construct a triangle from given conditions 1. Let us draw a line segment AB which measures 4 cm, i.e., AB = 4 cm. 2. On considering... View Article

The inner diameter of a cylindrical wooden pipe is 24cm and its outer diameter is 28 cm. The length of the pipe is 35cm.Find the mass of the pipe, if 1cm3 of wood has a mass of 0.6g. (Assume π = 22/7)

Given Inner radius of cylindrical pipe, say r1 = diameter1/ 2 = 24/2 cm = 12cm Outer radius of cylindrical pipe, say r2 = diameter2/... View Article