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A river 3m deep and 40m wide is flowing at the rate of 2km per hour. How much water will fall into the sea in a minute?

Given Depth of river, h = 3 m Width of river, b = 40 m Rate of water flow = 2km per hour Find out We have to find out how much water... View Article

A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get -7/12. What is the number?

Solution Let the rational be ‘n’. According to the given details the equation becomes n × (5/2) + 2/3 = -7/12 5(n/2) +... View Article

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that AE2 + BD2 = AB2 + DE2.

To prove: (AE)2 + (BD)2 = (AB)2 + (DE)2 Construction: Join AE, BD and DE Proof: In ∆ACE, by Pythagoras theorem (AE)2 =... View Article

Find the volume of the right circular cone with (i) radius 6cm, height 7 cm (ii) radius 3.5 cm, height 12 cm (Assume π = 22/7)

Volume of cone (V) = (1/3) × πr2h (i) Given Radius of cone (r) = 6 cm Height of cone (h) = 7 cm On taking π=22/7... View Article

A point, whose distance from the centre of a circle is greater than its radius lies in __________ of the circle. (exterior/ interior)

(ii) A point, whose distance from the centre of a circle is greater than its radius lies in exterior of the circle. A circle is a... View Article

In Fig., A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find BAC.

Given: ∠BEC=130° ∠ECD=20°To find: ∠BAC?Solution: In ∆EDC∠E=180°-130° ———[linear... View Article

There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

Solution: To find which box requires the lesser amount of material to make we have to calculate the total surface area of both these boxes.... View Article

BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

Solution Given: Altitude BE and CF are equal To prove: ΔABC is an isosceles Δ In ΔBEC and ΔCEB ∠E=∠F —————-[each 90°] BC=BC —————–[common]... View Article

State whether the following statements are true or false: Every integer is a whole number. Give reasons for your answers.

False Explanation: Integers are the numbers that have both positive and negative numbers including 0 Example: …..-4, -3, -2, -1, 0,... View Article

The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Given that first term, a = 5 last term, l = 45 Find out We need to find the number of terms and the common difference Solution Sum of... View Article

Name the quadrilaterals whose diagonals. (i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal

(i) bisect each other Solution It is a rhombus, parallelogram, rectangle, or square as their diagonals bisect each other. (ii) are... View Article

Check which of the following are solutions of the equation x-2y = 4 and which are not: (i) (0, 2) (ii) (2, 0) (iii) (4, 0) (iv) (√2, 4√2) (v) (1, 1)

(i) (0, 2) Given: x – 2y = 4 As, x=0 and y=2 On substituting the values of x and y in the equation, we get, x – 2y = 4 0 –... View Article

Using the given pattern, find the missing numbers. 12 + 22 + 22 = 32 22 + 32 + 62 = 72 32 + 42 + 122 = 132 42 + 52 + _2 = 212 5 + _ 2 + 302 = 312 6 + 7 + _ 2 = _ 2

Solution 12 + 22 + 22 = 32 22 + 32 + 62 = 72 32 + 42 + 122 = 132 42 + 52 + _2 = 212 5... View Article

Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.

ABCD is a figure of quadrilateral which is not a parallelogram but has exactly two opposite angles that is ∠B = ∠D of equal... View Article

The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Given The diameter of the moon is approximately one-fourth of the diameter of the earth. Find out The ratio of the surface areas of earth and... View Article

The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.

Solution y = 40° {alternate interior angle} ∠P = 70° {alternate interior angle} ∠P = ∠H = 70° {opposite angles of a... View Article

Suppose 2 kg of sugar contains 9×106 crystals. How many sugar crystals are there in (i) 5 kg of sugar? (ii) 1.2 kg of sugar?

Solution (i) Let us assume that sugar crystals be = x. Since the weight of Sugar is directly proportional to the number of sugar... View Article

If A and B are (-2, -2) and (2, -4) , respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB.

The coordinates of point A and B are (-2,-2) and (2,-4) respectively. Since AP = 3/7 AB Therefore, AP: PB = 3:4 Point P divides the line... View Article

In Fig. PQRS and ABRS are parallelograms and X is any point on side BR. Show that (i) ar (PQRS) = ar (ABRS) (ii) ar (AXS) = 1/2 ar (PQRS)

From the diagram, we notice that parallelogram PQRS and ABRS lie on the same base SR and also, lie in between the same parallel lines SR and... View Article

A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?

Given The radius of a cylindrical tank, r = 7 m Height of cylindrical tank , h = 3 m Find out We have to find out the amount of metal... View Article

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