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Given here are some figures. Classify each of them on the basis of the following. Simple curve (b) Simple closed curve (c) Polygon (d) Convex polygon (e) Concave polygon

Solution a) Simple curve: Figures: 1, 2, 5, 6 and 7 b) Simple closed curve: Figures 1, 2, 5, 6 and 7 c) Polygon: Figures 1 and 2 d)... View Article

The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs.10 per m2 is Rs.15000, find the height of the hall.

Given Perimeter of the rectangular hall = 250m The cost of painting the four walls at the rate of Rs.10 per m2 is =Rs.15000 Find out We have to... View Article

When a die is thrown, list the outcomes of an event of getting (i) (a) a prime number (b) not a prime number. (ii) (a) a number greater than 5 (b) a number not greater than 5.

Solution (i) (a) Outcomes of event of getting a event with prime number are 2, 3 and 5. (b) Outcomes of event of not getting a event with prime... View Article

The relative humidity (in %) of a certain city for a month of 30 days was as follows: 98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1 89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3 96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89 (i) Construct a grouped frequency distribution table with classes 84 – 86, 86 – 88, etc. (ii) Which month or season do you think this data is about? (iii) What is the range of this data?

Solution Grouped frequency distribution table of class size 2. The class interval will be 84-86, 86-88, 88-90, 90-92 and so on. The data is... View Article

A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, ……… as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take π = 22/7)

We have to find out the total length of such a spiral made up of thirteen consecutive semicircle. Solution We have learnt that The... View Article

A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length 1 m.

Given Diameter of road roller, d = 84 cm Radius of road roller, r = d/2 = 84/2 = 42 cm Length of road roller, h = 1 m = 100 cm Find... View Article

Find the area of the shaded region in Fig. where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

Solution Given OAB is an equilateral triangle having each angle as 60° Area of the sector is common in both. The radius of the... View Article

A contractor estimates that 3 persons could rewire Jasminder’s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?

Solution Let time taken to complete the job be x. The number of persons and the number of days are in inversely proportional. Therefore,... View Article

A survey conducted by an organisation for the cause of illness and death among the women between the ages 15 – 44 (in years) worldwide, found the following figures (in %) :(i) Represent the information given above graphically. (ii) Which condition is the major cause of women’s ill health and death worldwide? (iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.

S.No. Causes Female fatality rate (%) 1. Reproductive health conditions 31.8 2. Neuropsychiatric conditions 25.4 3. Injuries 12.4 4.... View Article

A cistern, internally measuring 150 cm × 120 cm × 100 cm, has 129600 cm3 of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each being 22.5 cm × 7.5 cm × 6.5 cm?

Given Length of Cistern (L) = 150 cm Breadth of Cistern (W) = 120 cm Height of Cistern (H) = 110 cm Length of Brick (l) = 22.5 cm Breadth of... View Article

If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.

Solution Given (i) AB and CD are 2 chords which are intersecting at point E. (ii) PQ is the diameter of the circle. (iii) AB = CD. To... View Article

The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

Let us assume, the shorter side of the rectangle be x m. Then, larger side of the rectangle = (x + 30) m As per the given data The length of the... View Article

A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

Solution Let one of the positive number be x Then other number will be 5x. According to the given details the equation becomes 5x + 21 =... View Article

State whether the following statements are true or false: Every point on the number line is of the form √m where m is a natural number. Give reasons for your answers.

FalseWe can represent both negative and positive numbers on a number line.Positive numbers can be written as √16=4 that is a natural... View Article

Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages?

Solution Let the present age of Shobo be x Let the age of her mother will be 6x. Shobo’s age after 5 years = x + 5 According to... View Article

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is : (A) 12 cm (B) 13 cm (C) 8.5 cm (D) √119 cm

Option D=√119 From the above figure, the line that is drawn from the centre of the given circle to the tangent PQ is perpendicular to... View Article

In Fig. P is a point in the interior of a parallelogram ABCD. Show that (i) ar(APB) + ar(PCD) = 1/2 ar(ABCD) (ii) ar(APD) + ar(PBC) = ar(APB) + ar(PCD) [Hint : Through P, draw a line parallel to AB.]

(i) Construction Draw a line segment EF, passing through point P and parallel to line segment AB. In parallelogram ABCD, AB || EF (By... View Article

Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (i) 2x² – 7x + 3 = 0 (ii) 2x² + x – 4 = 0 (iii) 4x² + 4√3x + 3 = 0 (iv) 2x² + x + 4 = 0

(i) 2x2 – 7x + 3 = 0 ⇒ 2x2 – 7x = – 3 On dividing by 2 on both sides, we get ⇒... View Article

Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method.

Daily wages (in Rs.) 100-120 120-140 140-160 160-180 180-200 Number of workers 12 14 8 6 10 Solution To determinet the Class Mark... View Article

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

the radius of the cone and the hemisphere (r) = 3.5 cm or 7/2 cm The total height of the toy is given as 15.5 cm. So, the height of the cone (h)... View Article