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Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. Give the justification of the construction

To construct a tangent from given conditions 1. Let us draw a line segment AB = 8 cm. 2. Considering A as... View Article

A dome of a building is in the form of a hemi sphere. From inside, it was white-washed at the cost of Rs. 4989.60. If the cost of white-washing isRs20 per square meter, find the (i) inside surface area of the dome (ii) volume of the air inside the dome (Assume π = 22/7)

(i) Given Cost of white-washing the dome from inside = Rs 4989.60 The Cost of white-washing 1m2 area = Rs 20 Therefore,... View Article

Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg) : 4.97 5.05 5.08 5.03 5.00 5.06 5.08 4.98 5.04 5.07 5.00 Find the probability that any of these bags chosen at random contains more than 5 kg of flour.

Given As per the given paramaters Total number of bags present = 11 Find out We have to find out the... View Article

A metallic right circular cone 20 cm high and whose vertical angle is 60° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained is drawn into a wire of diameter 1/16 cm, find the length of the wire.

Solution From ΔAEG \(\begin{array}{l}\frac{EG}{AG}=\tan 30\end{array} \) \(\begin{array}{l}\frac{10}{\sqrt{3}}=EG\Rightarrow EG=\frac{10\sqrt{3}}{3}\end{array} \) From ΔAEG \(\begin{array}{l}\frac{BD}{AD}=\tan 30\end{array} \) \(\begin{array}{l}BD=\frac{20}{\sqrt{3}}=\frac{20\sqrt{3}}{3}\end{array} \) Radius (r1) of upper end of... View Article

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Given Radius of cylinder (r) = 18 cm Height of cylinder (h) = 32 cm Height of cone (H) =... View Article

A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7cm. If the bowl is filled with soup to a height of 4cm, how much soup the hospital has to prepare daily to serve 250 patients? (Assume π = 22/7)

Given Height of cylinder (h) = 4 cm Radius of cylinder (r)= 7/2 cm=3.5 cm Bowl is filled with soup to a... View Article

Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see Fig. 15.4) . What is the probability that the fish taken out is a male fish?

Given that Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random... View Article

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Given The parallelogram and triangle have equal areas. The sides of the triangle are given as 26 cm, 28 cm... View Article

Two persons could fit new windows in a house in 3 days. (i) One of the persons fell ill before the work started. How long would the job take now? (ii) How many persons would be needed to fit the windows in one day?

Solution (i) Let the number of days be x. Here the number of persons and the number of days are... View Article

The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

Let the number of rows be R The number of students in a row be S. Total number of students =... View Article

A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

Given A guy wire attached to a vertical pole of height 18 m is 24 m long and has a... View Article

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

The capsule comprises two hemispheres and one cylinder is shown in the figure Given The diameter of the capsule =... View Article

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:

Expenditure Number of families 1000-1500 24 1500-2000 40 2000-2500 33 2500-3000 28 3000-3500 30 3500-4000 22 4000-4500 16 4500-5000 7... View Article

Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX) .

Given that A triangle with mid point To prove A line drawn through the mid-points of one side of a triangle... View Article

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (i) the length of the arc (ii) area of the sector formed by the arc (iii) area of the segment formed by the corresponding chord

Given A circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find out (i) the... View Article

Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. (i) 525 (ii) 1750 (iii) 252 (iv) 1825 (v) 6412

Solution (i) 525 We note that (22)2 < 525 < (23)2 484 < 525 < 529 ∴ If we add... View Article

The shoppers who come to a departmental store are marked as: man (M) , woman (W) , boy (B) or girl (G) . The following list gives the shoppers who came during the first hour in the morning. W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W W M W B W G M W W W W G W M M W M W G W M G W M M B G G W. Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.

Solution Frequency distribution table: Bar-graph:

An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below: Suppose a family is chosen. Find the probability that the family chosen is (i) earning Rs. 10000 – 13000 per month and owning exactly 2 vehicles. (ii) earning Rs. 16000 or more per month and owning exactly 1 vehicle. (iii) earning less than Rs. 7000 per month and does not own any vehicle. (iv) earning Rs. 13000 – 16000 per month and owning more than 2 vehicles. (v) owning not more than 1 vehicle.

Monthly income (in ₹) Vehicles per family 0 1 2 Above 2 Less than 7000 10 160 25 0 7000-10000... View Article

See Fig., and write the following: i. The coordinates of B. ii. The coordinates of C. iii. The point identified by the coordinates (-3, -5) . iv. The point identified by the coordinates (2, – 4) . v. The abscissa of the point D. vi. The ordinate of the point H. vii. The coordinates of the point L. viii. The coordinates of the point M.

Solution (i) The coordinates of point B are (−5, 2). The coordinates of point B is the distance of point B... View Article

Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method. (i) x – 3y – 3 = 0 and 3x – 9y – 2 = 0 (ii) 2x + y = 5 and 3x + 2y = 8 (iii) 3x – 5y = 20 and 6x – 10y = 40 (iv) x – 3y – 7 = 0 and 3x – 3y – 15 = 0

(i) Given, x – 3y – 3 =0 and 3x – 9y -2 =0 a1/a2=1/3 , b1/b2= -3/-9 =1/3, c1/c2=-3/-2... View Article

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