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Test Level 2: Progressions, Sequences & Series - 1 - CAT MCQ


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10 Questions MCQ Test - Test Level 2: Progressions, Sequences & Series - 1

Test Level 2: Progressions, Sequences & Series - 1 for CAT 2024 is part of CAT preparation. The Test Level 2: Progressions, Sequences & Series - 1 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 2: Progressions, Sequences & Series - 1 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 2: Progressions, Sequences & Series - 1 below.
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Test Level 2: Progressions, Sequences & Series - 1 - Question 1

The interior angles of a polygon are in A.P. If the least angle is 42° and common difference is 33°, the number of sides is  

Detailed Solution for Test Level 2: Progressions, Sequences & Series - 1 - Question 1

Given: a = 42°, d = 33°
Sum of all the interior angles of an n-sided polygon is (n - 2)180°.


(n - 2) × 180 = (n/2)(2 × 42 + (n - 1) × 33)
360n - 720 = 84n + 33n2 - 33n
11n2 - 103n + 240 = 0
(n - 5)(11n - 48) = 0
This implies, n = 5 as sides can't be fraction in number.

Test Level 2: Progressions, Sequences & Series - 1 - Question 2

If the sum of the series 1 + 3/x +9/x2 + 27/x3 + … to infinity exists, then which of the following must be true?
(Given that x is not less than or equal to zero)

Detailed Solution for Test Level 2: Progressions, Sequences & Series - 1 - Question 2

Since the sum to infinity of the given GP exists, so its common ratio should be 0 < |3/x| < 1.
0 < 3/x is always true because x > 0.
3/x < 1
or

or
x > 3
According to question, x is not negative.
So, x > 3

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Test Level 2: Progressions, Sequences & Series - 1 - Question 3

If x, y, z are in A.P, then (x + 2y - z)(2y + z - x)(z + x - y) equals  

Detailed Solution for Test Level 2: Progressions, Sequences & Series - 1 - Question 3

x, y, z are in A.P.
Therefore, 2y = x + z
Given equation: (x + 2y - z)(2y + z - x)(z + x - y)
= (x + x + z - z)(x + z + z - x)(2y - y)
= 2x(2z)(y) = 4xyz

Test Level 2: Progressions, Sequences & Series - 1 - Question 4

In a GP, the third term is 10 more than the second term and the second term is 6 more than the first term. What is the fifth term?

Detailed Solution for Test Level 2: Progressions, Sequences & Series - 1 - Question 4

T3 - T2 = ar2 - ar = 10
⇒ ar(r - 1) = 10
and T2 - T1 = 6, or ar - a = 6
⇒ a(r - 1) = 6
r = 10/6 = 5/3 and a = 9

Test Level 2: Progressions, Sequences & Series - 1 - Question 5

If the sum of the first 8 terms of an AP is exactly half of the sum of the next 8 terms, what is the ratio of the 16th term to the 8th term of the AP?  

Detailed Solution for Test Level 2: Progressions, Sequences & Series - 1 - Question 5


4a + 14d = 2a + 23d

Test Level 2: Progressions, Sequences & Series - 1 - Question 6

Sweety purchased a box of chocolates. She ate 1 chocolate on the first day, 3 on the second day, 6 on the third day, 10 on the fourth day and so on. Finally, she finished all the chocolates in exactly 20 days. How many chocolates were there in the box?  

Detailed Solution for Test Level 2: Progressions, Sequences & Series - 1 - Question 6



Total number of chocolates 

Test Level 2: Progressions, Sequences & Series - 1 - Question 7

The sums of odd and even numbered terms of an infinite GP are in the ratio of 3 : 2. What is the common ratio (r)?

Detailed Solution for Test Level 2: Progressions, Sequences & Series - 1 - Question 7

Let the GP be a, ar, ar2, ar3, ………….

Test Level 2: Progressions, Sequences & Series - 1 - Question 8

If log3 2, log3 (2x - 5) and log3 (2x - 7/2) are in arithmetic progression, then the value of x is equal to  

Detailed Solution for Test Level 2: Progressions, Sequences & Series - 1 - Question 8

Since log3 (2), log3 (2x - 5) and log3  are in AP, therefore we can write:

∴ log3 (2x - 5)2 = log3 (2x + 1 - 7)
∴ (2x - 5)2 = 2x + 1 - 7
Let, 2x = y.
Then, (y - 5)2 = 2y - 7
⇒ y2 + 25 - 10y = 2y - 7
⇒ y2 - 12y + 32 = 0
⇒ (y - 8)(y - 4) = 0
We get, 2x = 8 and 2x = 4
⇒ x = 3 and 2
If x = 2, then 2x - 5 = 4 - 5 = -1< 0, not possible
So x = 3

Test Level 2: Progressions, Sequences & Series - 1 - Question 9

 up to 50 terms is equal to

Detailed Solution for Test Level 2: Progressions, Sequences & Series - 1 - Question 9




= 50/51

Test Level 2: Progressions, Sequences & Series - 1 - Question 10

Detailed Solution for Test Level 2: Progressions, Sequences & Series - 1 - Question 10

The nth term of the given series is tn 

The sum of the series is

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