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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

A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows: 2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5 3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7 2.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8 3.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4 4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6 Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2 – 2.5.

Solution Grouped frequency distribution table with class intervals of size 0.5 starting from the interval 2 – 2.5: The data is represented in... View Article

In an AP (i) Given a = 5, d = 3, an = 50, find n and Sn. (ii) Given a = 7, a13 = 35, find d and S₁₃. (iii) Given a₁₂ = 37, d = 3, find a and S₁₂. (iv) Given a₃ = 15, S₁₀ = 125, find d and a₁₀. (v) Given d = 5, S₉ = 75, find a and a₉. (vi) Given a = 2, d = 8, S_n = 90, find n and a_n. (vii) Given a = 8, a_n = 62, S_n = 210, find n and d. (viii) Given an = 4, d = 2, S_n = − 14, find n and a. (ix) Given a = 3, n = 8, S = 192, find d. (x) Given l = 28, S = 144 and there are total 9 terms. Find a.

(i) Given that, a = 5, d = 3, an = 50 We know that an = a +(n −1)d, Therefore,... View Article

(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective? (ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?

(i) Numbers of defective bulbs = 4 The total numbers of bulbs = 20 P(E) = (Number of favourable outcomes/ Total number of outcomes) ∴... View Article

ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig.) . If AD is extended to intersect BC at P, show that (i) ΔABD ΔACD (ii) ΔABP ΔACP (iii) AP bisects A as well as D. (iv) AP is the perpendicular bisector of BC.

An Isosceles triangle is a triangle that has two equal sides. Also, the two angles opposite to the two equal sides are equal. In other words, we... View Article

12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

Given that 12 defective pens are accidentally mixed with 132 good ones. One pen is taken out at random. Find out The probability that the pen is... View Article

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q Give the justification of the construction

To construct a tangent from given conditions 1. Let us draw a circle with a radius of 3cm with centre “O”. 2. Draw a diameter of... View Article

During the medical check-up of 35 students of a class, their weights were recorded as follows: Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

Weight in kg Number of students Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less... View Article

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Probability is a branch of mathematics that deals with the occurrence of a random event. The probability formula is defined as the possibility of... View Article

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.

The distances of potatoes from the bucket are 5, 8, 11, 14…, which is in the form of arithmetic progression (AP). Given, the distance run by the... View Article

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be Rs. x and that of a pen to be Rs. y)

Given The cost of a notebook is twice the cost of a pen Find out We have to write a linear equation to represent the given statement Solution... View Article

What happens to the force between two objects, if (i) The mass of one object is doubled? (ii) The distance between the objects is doubled and tripled? (iii) The masses of both objects are doubled?

As per the universal law of gravitation, every object in the universe attracts every other object by the force of attraction which is directly... View Article

The inner diameter of a circular well is 3.5m. It is 10m deep. Find (i) its inner curved surface area, (ii) the cost of plastering this curved surface at the rate of Rs. 40 per m2. (Assume π = 22/7)

Given Inner radius of circular well, r = 3.5/2m = 1.75m Depth of circular well, say h = 10m Find out We have to find (i) its inner curved surface... View Article

The distance (in km) of 40 engineers from their residence to their place of work were found as follows: 5 3 10 20 25 11 13 7 12 31 19 10 12 17 18 11 32 17 16 2 7 9 7 8 3 5 12 15 18 3 12 14 2 9 6 15 15 7 6 12 Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included) . What main features do you observe from this tabular representation?

Solution Grouped frequency distribution table of class size 5. The class interval will be 0-5, 5-10, 10-15, 15-20 and so on. The data is... View Article

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x

Total number of black balls = x Total number of balls = 12 Total number of outcomes = 12 p(x)= x/12 When 6 more black balls are put in the box,... View Article

It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10m deep. If the cost of painting is at the rate of Rs 20 per m², find (i) inner curved surface area of the vessel (ii) radius of the base (iii) capacity of the vessel (Assume π = 22/7)

Height of cylinder (h) = 10 m Cost of painting rate = ₹20 per m2 (i) For 1 m2 = ₹20 For lateral surface = ₹2200 So the lateral surface... View Article

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows. Find the mean heart beats per minute for these women, choosing a suitable method.

Number of heart beats per minute 65-68 68-71 71-74 74-77 77-80 80-83 83-86 Number of women 2 4 3 8 7 4 2 Solution Let us assume the mean... View Article

Diagram of the adjacent picture frame has outer dimensions = 24 cm×28 cm and inner dimensions 16 cm×20 cm. Find the area of each section of the frame, if the width of each section is same.

Solution: Divide the given figure into 4 parts, as shown below: Now two of given figures (I) and (II) are similar in dimensions.... View Article