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The length of 40 leaves of a plant are measured correct to one millimeter, and the obtained data is represented in the following table: (i) Draw a histogram to represent the given data. [Hint: First make the class intervals continuous] (ii) Is there any other suitable graphical representation for the same data? (iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

S.No. Length (in mm) Number of leaves 1. 118 - 126 3 2. 127 - 135 5 3. 136 - 144 9 4. 145 - 153 12 5. 154 - 162 5 6. 163 - 171 4... View Article

(i) For which values of a and b does the following pair of linear equations have an infinite number of solutions? 2x + 3y = 7 (a – b) x + (a + b) y = 3a + b – 2 (ii) For which value of k will the following pair of linear equations have no solution? 3x + y = 1 (2k – 1) x + (k – 1) y = 2k + 1

(i) Givesn equation 3y + 2x -7 =0 (a + b)y + (a-b)y – (3a + b -2) = 0 We have to find for which values of a and b the pair of... View Article

The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Fig.) . Find the area of the shaded region. (Use π = 3.14 and √3 = 1.73205)

Given ABC is an equilateral triangle. ∴ ∠ A = ∠ B = ∠ C = 60° There are three sectors hence each makes an angle of... View Article

A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet.

(i) When the stone from the top of the tower is thrown, Initial velocity u = 0 Distance travelled = x Time taken = t Therefore, Height, h = (100... View Article

Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.

Solution Let the total number of deer be x. Deer grazing in the field = x/2 Deer playing nearby = x/2 × ¾ = 3x/8 Deer drinking water... View Article

A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?

Given ABCD is a rhombus having diagonal AC = 48 cm side AB=BC=CD=AD=30 cm The diagonal of the Rhombus divides the area into two equal parts.... View Article

It is required to make a closed cylindrical tank of height 1m and base diameter 140cm from a metal sheet. How many square meters of the sheet are required for the same? Assume π = 22/7

Given Height of cylindrical tank (h)=1 m Base diameter of cylinder (d)=140 cm Radius of cylinder (r)=d/2=140/2=70cm=0.7 m Find out We have to... View Article

The volume of a 500 g sealed packet is 350 cm3. Will the packet float or sink in water if the density of water is 1 g cm-3? What will be the mass of the water displaced by this packet?

Given that The volume of a 500 g sealed packet = 350 cm3 Find out The mass of the water displaced by this packet and also whether it will... View Article

Gravitational force on the surface of the moon is only 1/6 as strong as gravitational force on the earth. What is the weight in newton’s of a 10 kg object on the moon and on the earth?

Given that The gravitational force on the surface of the moon is only 1/6 as strong as the gravitational force on the earth. Acceleration due... View Article

If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance travelled by the body is (i) 2 units (ii) 0 unit

As per the given condition Work done = force × displacement Constant force = 5 units let's assume work done as y units and,... View Article

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations) . If the average speeds of the express train is 11 km/h more than that of the passenger train, find the average speed of the two trains.

Let us assume, The average speed of passenger train = x km/h. Average speed of express train = (x + 11) km/h As per given data, time... View Article

An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel (see Fig.) .

Given Larger radius of frustum (R) = 18/2 = 9 cm Smaller radius of frustum (r) = 8/2 = 4 cm Height of frustum (H) = 22-10 =... View Article

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

BC = 8 m To Find: Height of the tree, which is AB From diagram Total height of the tree is the sum of AB and AC i.e. AB+AC In rt ∆ABC, BC = 8m... View Article

In Fig. PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB is parallel to CD.

Solution: Draw two lines BE and CF such that BE ⊥ PQ and CF ⊥ RS. Now, since PQ RS, So, BE CF Since, PQ || RS => BE || CF [ So, BE || PQ... View Article

1500 families with 2 children were selected randomly, and the following data were recorded: Compute the probability of a family, chosen at random, having (i) 2 girls (ii) 1 girl (iii) No girl Also check whether the sum of these probabilities is 1.

Number of girls in a family 2 1 0 Number of families 475 814 211 Solution According to the given parametersTotal numbers of... View Article

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Give the justification of the construction

To construct a circle from given conditions 1. Let us draw a circle with radius = 6 cm with centre O. 2. Position a point P, which... View Article

Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?

Solution Let age of Baichung’s father be ‘n’. Then, age of Baichung’s grandfather = (n + 26) and, Age of Baichung... View Article

Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Given, the equations for graphs are x – y + 1 = 0 and 3x + 2y – 12 = 0. For, x – y + 1 = 0 or x = 1+y x 0 1 2 y 1 2 3... View Article

ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig) . AC is a diagonal. Show that: (i) SR || AC and SR = 1/2 AC (ii) PQ = SR (iii) PQRS is a parallelogram.

Given P, Q, R and S are the mid points of quadrilateral ABCD Solution Theorem :The line segment joining the mid-points of two sides... View Article

CD and GH are respectively the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC ~ ΔFEG, Show that: (i) CD/GH = AC/FG (ii) ΔDCB ~ ΔHGE (iii) ΔDCA ~ ΔHGF

Given CD and GH are respectively the bisectors of ∠ACB and ∠EGF such that D and H lie on sides AB and FE of ΔABC and ΔEFG... View Article