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If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true? (a) BC · EF = AC · FD (b) AB · EF = AC · DE (c) BC · DE = AB · EF (d) BC · DE = AB · FD

Answer The correct answer is (c) BC · DE = AB · EF Solution We know that if sides of one triangle are proportional to the side... View Article

If the lengths of the diagonals of rhombus are 16 cm and 12 cm. Then, the length of the sides of the rhombus is (a) 9 cm (b) 10 cm (c) 8 cm (d) 20 cm

Answer The correct answer is (b) 10 cm Solution As per the definition, a rhombus is a quadrilateral whose four sides are of the same length... View Article

In figure, if ∠BAC =90° and AD⊥BC. Then, (a) BD.CD = BZC² (b) AB.AC = BC² (c) BD.CD=AD² (d) AB.AC =AD²

Answer: (c) BD.CD=AD² Solution Let us consider ∆ADB and ∆ADC, According to the given data we know that ∠D = ∠D = 90° (∵ AD ⊥ BC) ∠DBA... View Article

Find the sum of the integers between 100 and 200 that are (i) divisible by 9 (ii) not divisible by 9

Solution: (i) divisible by 9The number between 100 and 200 which is divisible by 9 = 108, 117, 126, …198 Let the number of terms between... View Article

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.

Given n = 37 the sum of the three middlemost terms is 225 the sum of the last three is 429 Find out We have to determine the AP... View Article

The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1. Find the 15th term.

Given a8 = ½ a2 a11 = 1/3 a4 + 1 Find out We have to determine the fifteenth term Solution We know that the nth term... View Article

Find the (i) Sum of those integers between 1 and 500 which are multiples of 2 as well as of 5. (ii) Sum of those integers from 1 to 500 which are multiples of 2 as well as of 5 . (iii) Sum of those integers from 1 to 500 which are multiples of 2 or 5. [Hint (iii): These numbers will be: multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]

Solution: (i) Sum of those integers between 1 and 500 which are multiples of 2 as well as of 5. Multiples of 2 as well as of 5 = LCM of (2, 5) =... View Article

The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.

Given S5 + S7 = 167 S10 = 235 Find out We have to determine the sum of its first twenty terms Solution We know that... View Article

Determine the AP whose fifth term is 19 and the difference of the eighth term from the thirteenth term is 20.

Given a5 = 19 13th term – 8th term = 20 Find out We have to determine the AP Solution We know that the nth term... View Article

Find a, b and c such that the following numbers are in AP: a, 7, b, 23, c.

Solution To determine a, b and c in the AP a, 7, b, 23, c… the necessary condition is, a5 – a4 = a4 –... View Article

Write the first three terms of the APs when a and d are as given below: 1) a =1/2, d = -1/6 2) a = -5, d = -3 3) a = 2 , d = 1/√2

Solution: (i) a =1/2, d = -1/6 We know that, The first three terms of AP can be expressed as : a, a + d, a + 2d ½,... View Article

Verify that each of the following is an AP, and then write its next three terms. (i) 0, 1/4, 1/2, 3/4,… (ii) 5, 14/3, 13/3, 4… (iii) √3 , 2√3, 3√3,… (iv) a + b, (a + 1) + b, (a + 1) + (b + 1), … (v) a, 2a + 1, 3a + 2, 4a + 3,…

(i) 0, 1/4, 1/2, 3/4,… Answer Here, a1 = 0 a2 = ¼ a3 = ½ a4 = ¾ a2 – a1 =... View Article

Match the APs given in column A with suitable common differences given in column B.

1. Match the APs given in column A with suitable common differences given in column B. Column A Column B (A1) 2, – 2, – 6,... View Article

Two APs have the same common difference. The first term of one AP is 2 and that of the other is 7. The difference between their 10th terms is the same as the difference between their 21st terms, which is the same as the difference between any two corresponding terms. Why?

Let us there are two AP’s with first terms a and A Let their common differences be d and D respectively Suppose n be any... View Article

For the AP: -3, -7, -11, …, can we find directly a₃₀ – a₂₀ without actually finding a₃₀ and a₂₀? Give reasons for your answer.

Solution The given statement is True As per the given details First term, a = – 3 Common difference, d = a2 – a1 = –... View Article

Justify whether it is true to say that -1, -3/2, -2, 5/2,… forms an AP as a₂ – a₁ = a₃ – a₂

Solution The given statement is False Given that a1 = -1 a2 = -3/2 a3 = -2 a4 = 5/2 Common difference can be calculated... View Article

Which of the following form an AP? Justify your answer. (i) -1, -1, -1, -1,… (ii) 0, 2, 0, 2,… (iii) 1, 1, 2, 2, 3, 3… (iv) 11, 22, 33… (v) 1/2,1/3,1/4, … (vi) 2, 22, 23, 24, … (vii) √3, √12, √27, √48, …

Solution (i) –1, –1, –1, –1,… Answer According to the given data we get to know that a a1 = – 1... View Article