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Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (i) 2, 4, 8, 16 … (ii) 2, 5/2, 3, 7/2 …. (iii) -1.2, -3.2, -5.2, -7.2 … (iv) -10, – 6, – 2, 2 … (v) 3, 3 + √2, 3 + 2√2, 3 + 3√2 (vi) 0.2, 0.22, 0.222, 0.2222 …. (vii) 0, – 4, – 8, – 12 … (viii) -1/2, -1/2, -1/2, -1/2 …. (ix) 1, 3, 9, 27 … (x) a, 2a, 3a, 4a … (xi) a, a2, a3, a4 … (xii) √2, √8, √18, √32 … (xiii) √3, √6, √9, √12 … (xiv) 12, 32, 52, 72 … (xv) 12, 52, 72, 73 …

(i) Given that ,2, 4, 8, 16 … The common difference is a2 – a1 = 4 – 2 = 2 a3 – a2 = 8... View Article

Which of the following experiments have equally likely outcomes? Explain. (i) A driver attempts to start a car. The car starts or does not start. (ii) A player attempts to shoot a basketball. She/he shoots or misses the shot. (iii) A trial is made to Solution: a true-false question. The Solution: is right or wrong. (iv) A baby is born. It is a boy or a girl.

(i)The car may not start. It does not have equally likely outcomes as the probability of it depends on many different technical factors like... View Article

A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.

From the given data, the figure is Let BC = Height of the kite from the ground, BC = 60 m AC = Inclined length of the string from the ground and... View Article

The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below. (i) Represent the information above by a bar graph. (ii) In the classroom discuss what conclusions can be arrived at from the graph.

S.No. Section Number of girls per thousand boys 1. Scheduled Caste (SC) 940 2. Scheduled Tribe (ST) 970 3. Non SC/ST 920... View Article

Find (i) the lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5m high. (ii) How much steel was actually used, if 1/12 of the steel actually used was wasted in making the tank. (Assume π = 22/7)

Given Diameter of cylindrical tank=4.2 m Hence, radius of cylindrical tank (r)=4.2/2=2.1 m Height of cylindrical tank (h)=4.5 m Find out We have... View Article

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5.

Given that A box contains 90 discs which are numbered from 1 to 90, one disc is drawn at random from the box, Find out The probability that it... View Article

A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.

Let the number of rows and columns be x. Total number of plants = x2 x2 = 1000 x = √1000 We note that (31)2 < 1000 >... View Article

If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non-blue sector?

Solution A total of 5 sectors are present 3 green + 1 blue + 1 red Out of the 5 sectors, 3 sectors are green Thus, the probability of getting... View Article

In fig, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade. (Assume π = 22/7)

Given Base diameter = 20 cm Height =30 cm. Find out We have to find how much cloth is required for covering the lampshade. Solution: Base... View Article

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig.. Find: (i) the total length of the silver wire required. (ii) the area of each sector of the brooch.

(i) Total length of silver wire required=circumference of broach+5diameter =5*35*mm*πd =175+22/7*35 =175+110 =185mm (ii) Area of... View Article

There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see Fig) . If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Given AB = a = 11 m BC = b = 6 m AC = c = 15 m Find out We have to determine the area painted in colour. Formula By using Heron’s... View Article

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that (i) D is the mid-point of AC (ii) MD ⊥ AC (iii) CM = MA = 1/2 AB

(i) D is the mid-point of AC Considering ∆ABC We observe that M is the mid point of side AB and DM || BC [Given] This implies, DC= AD... View Article

A right circular cylinder just encloses a sphere of radius r (see fig.) . Find (i) surface area of the sphere, (ii) curved surface area of the cylinder, (iii) ratio of the areas obtained in(i) and (ii)

(i) Surface area of sphere = 4πr², where r is the radius of sphere (ii) As Height of cylinder, h = r+r =2r And Radius of... View Article

A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs. 20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs. 8 per 100 cm².

Given Height of frustum (h)= 16 cm Let radius of smaller circle end (r) = 8 cm Let radius of larger circle end (R) = 20 cm Find out We have... View Article

100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:(i) Draw a histogram to depict the given information. (ii) Write the class interval in which the maximum number of surnames lie.

Solution (i) The width of the class intervals in the given data is varying in nature. Also, The area of a rectangle is proportional to the... View Article

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

Given Radius of cylinder (r) = 6 cm Height of cylinder (h) = 15 cm Radius of each cone (R) = 3 cm Height of each cone (H) = 12 cm Find out We... View Article

Numbers 1 to 10 are written on ten separate slips (one number on one slip) , kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of . (i) getting a number 6? (ii) getting a number less than 6? (iii) getting a number greater than 6? (iv) getting a 1-digit number?

Solution There are 10 separate slips in the box. (i) Number 6 is written only on 1 slip. Therefore, probability of getting a number 6 is =... View Article

A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm3.

Given Radius of copper wire (r) = 3/2 mm = 3/20 cm Height of cylinder (H) = 12 cm Radius of Cylinder (R) = 10/2 = 5... View Article

The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m2? (Assume π = 22/7)

Given Diameter of a roller(d)=84 cm, Height of cylinder(h)=Length of roller=120cm=1.2 m Revolutions done by roller=500 Find out We have to... View Article

ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see Fig.) . Show that F is the mid-point of BC.

Given that ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. To prove F is the mid-point of BC. Proof BD... View Article