In ΔPQR and ΔMST, ∠P = 55°, ∠Q =25°, ∠M = 100° and ∠S = 25°. Is ΔQPR ~ ΔTSM? Why?
Solution We know that, The sum of the three angles of a triangle = 180°. From ∆PQR, ∠P + ∠Q + ∠R =... View Article
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In figure, BD and CE intersect each other at the point P. Is ΔPBC ~ ΔPDE? Why?
Answer The given statement is True. Solution From ∆PBC and ∆PDE, ∠BPC = ∠EPD [vertically opposite angles] PB/PD = 5/10 = 1/2 … (i)... View Article
A and B are respectively the points on the sides PQ and PR of a ΔPQR such that PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm. Is AB || QR? Give reason for your answer.
Answer The given statement is True. Solution PQ = 12.5 cm PA = 5 cm BR = 6 cm PB... View Article
It is given that ΔDEF ~ ΔRPQ. Is it true to say that ∠D = ∠R and ∠F = ∠P ? Why?
Answer The given statement is False. Solution We know that, The corresponding angles are equal in similar triangles. So, ∠D... View Article
Is the triangle with sides 25 cm, 5 cm and 24 cm a right triangle? Give reason for your answer.
Answer The given statement is False. Solution According to the given details, Let us consider A = 25 cm B =... View Article
In figure, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30°. Then, ∠PBA is equal to (a) 50° (b) 30° (c) 60° (d) 100°
Answer The correct answer is (d) 100° Solution From ∆APB and ∆CPD, ∠APB = ∠CPD = 50° (since they are vertically... View Article
If in two Δ PQR,AB/QR = BC/PR = CA/PQ, then (a)Δ PQR~Δ CAB (b) Δ PQR ~ Δ ABC (c)Δ CBA ~ Δ PQR (d) Δ BCA ~ Δ PQR
Answer The correct answer is (a)Δ PQR~Δ CAB Solution From ∆ABC and ∆PQR, we know that AB/QR = BC/PR = CA/PQ... View Article
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... 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... 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 = ∠DAC... 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... 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... 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... 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.... 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... 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... 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 –... 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 +... 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 = ¼ – 0... 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... View Article
