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If the moon attracts the earth, why does the earth not move towards the moon?

As per the universal law of gravitation and Newton’s third law, we all know that the force of attraction between two objects is the same,... View Article

Find the square of the following numbers. i) 32 ii) 35 iii) 86 iv) 93 v) 71 vi) 46

Solution (i) 32 (32)2 can be expressed as = (30 + 2)2 [From the identity, (a + b)2 = a2 + b2 + 2ab] =(30)2 + (2)2 + 2 × 30 × 2 = 900 + 4 +... View Article

Find the volume of a sphere whose radius is (i) 7 cm (ii) 0.63 m (Assume π = 22/7)

(i) Radius of sphere, r = 7 cm We know that Volume of sphere = (4/3) πr3 = (4/3)×(22/7)×73 = 4312/3 Hence, the volume... View Article

In a triangle ABC, E is the mid-point of median AD. Show that ar(BED) = 1/4 ar(ABC) .

ar(BED) = (1/2)×BD×DE Thus, E is the mid-point of AD, AE = DE Thus, AD is the median on side BC of triangle ABC,... View Article

For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal?

Given data Two APs as; 63, 65, 67,… and 3, 10, 17,… Find out We need to find the value of n, for which nth term for both the given AP's are... View Article

If 17th term of an A.P. exceeds its 10th term by 7. Find the common difference.

Given that 17th term of an A.P. exceeds its 10th term by 7 Find out We need to find out the common difference Solution We know that for an A.P... View Article

In Fig. PQR = 100°, where P, Q and R are points on a circle with centre O. Find OPR.

Given ∠PQR=100°To find: ∠OPR=? SolutionReflex ∠POR=2∠PQR ——–[ The angle subtended by an arc at... View Article

In the above figure both RISK and CLUE are parallelograms. Find the value of x.

∠K + ∠R = 180° {adjacent angles of a parallelogram are supplementary} ⇒ 120° + ∠R = 180° ⇒ ∠R =... View Article

If the areas of two similar triangles are equal, prove that they are congruent.

Given: ΔABC and ΔPQR are two similar triangles and equal in area. ar(ΔABC) = ar(ΔPQR) To prove: ΔABC and ΔPQR are congruent. Proof: Similar... View Article

Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm3?

Given the base area of the cuboid is 180 cm2 Th volume of cuboid is 900 cm3 Find out We have to find out the height of a... View Article

S and T are point on sides PR and QR of ΔPQR such that ∠P = ∠RTS. Show that ΔRPQ ~ ΔRTS.

Given S and T are point on sides PR and QR of ΔPQR And ∠P = ∠RTS. To Prove ΔRPQ ~ ΔRTS Proof In ΔRPQ and... View Article

Find the relation between x and y if the points (x, y) , (1, 2) and (7, 0) are collinear.

If given points are collinear then area of triangle formed by them must be zero. Let (x, y), (1, 2) and (7, 0) are vertices of a triangle, Area... View Article

Find the area of the triangle whose vertices are: (i) (2, 3) , (-1, 0) , (2, -4) (ii) (-5, -1) , (3, -5) , (5, 2)

Area of a triangle formula = (i) (2, 3), (-1, 0), (2, -4) Substitute all the values in the above formula, we get Area of triangle = 1/2 [2 {0-... View Article

Write three numbers whose decimal expansions are non-terminating non-recurring.

Non-terminating decimals are the one that does not have an end term. It has an infinite number of terms. Example: 0.5444444…..,... View Article

In what direction does the buoyant force on an object immersed in a liquid act?

The buoyant force on an object that is immersed in a liquid will be in a vertically upward direction. When an object is immersed in a liquid it... View Article

If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Given: AC = BD To Prove: ABCD is a rectangle if the diagonals of a parallelogram are equal Solution: As mentioned parallelogram, so... View Article

If the median of a distribution given below is 28.5 then, find the value of x & y.

Class Interval Frequency 0-10 5 10-20 x 20-30 20 30-40 15 40-50 Y 50-60 5 Total 60 Solution: Given Parameters, n = 60 Median... View Article

If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.

Answer: Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is... View Article

Give two different examples of pair of (i) Similar figures (ii) Non-similar figures

Similar figures are two figures having the same shape. The objects which are of exactly the same shape and size are known as congruent objects.... View Article

Classify the following numbers as rational or irrational according to their type:

Solution: √23 = 4.79583152…… As the number is non-terminating non-recurring. It is an irrational number.... View Article