Sequences Questions for MAH – CET 2022 – Download PDF

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Question 1: find the area of an equilateral triangle if the height of the triangle is 24 cm.

a) $192\sqrt{3} cm^2$

b) $175\sqrt{3} cm^2$

c) $178\sqrt{3} cm^2$

d) $164\sqrt{3} cm^2$

Question 2: ​If a metallic cone of radius 30 cm and height 40 cm is melted and recast into metallic spheres of radius 10 cm, find the number of spheres formed.

a) 5

b) 9

c) 6

d) 12

Question 3: If every alternate character, starting from the first character from the right end of the line is removed, what will be the fourth character to the left of the third character from the right?

a) 7560

b) 6860

c) 7960

d) 7860

Question 4: In the given series below, certain trend is being followed in each term. Find the next term in the series which follows the same trend.
DDDDCCCBBA ,DDDCCB ,DDC, ?

a) none

b) DC

c) C

d) D

Question 5: How many digits in the number ‘83657294’ will be as far away from ‘4’ as when the digits are rearranged in descending order from left to right within the number? Ignore the digit 4 for counting the final tally.

a) 1

b) 3

c) 4

d) 2

e) 0

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Question 6: The position of how many digits in the number ‘725683’ will be unchanged when the digits are rearranged in ascending order from left to right within the number?

a) None

b) One

c) Four

d) Three

e) Two

Question 7: If in the word FLOURISH ,all the vowels are first arranged alphabetically and then all the consonants are arranged and then all the vowels are replaced by previous letters and all consonants are replaced by the next letter from the English alphabets ,which of the following will be the third from the right end?

a) I

b) S

c) M

d) V

e) None of these

Question 8: How many such 6s are there in the following number series, each of which is immediately preceded by 1 or 5 and immediately by 3 or 9?
2 6 3 7 5 6 4 2 9 6 1 3 4 1 63 9 1 5 6 9 2 3 1 6 5 4 3 2 1 9 6 7 1 6 3

a) None

b) One

c) Two

d) Three

e) None of these

Question 9: How many such 7s are there in the following number sequence each of which is immediately preceded by 5 and not immediately followed by 8?
2  3   5   7   8   9   3   4   5   7    6    1   9   3   5   7   4   8   3   2   5   7   8   8  9   2  5

a) None

b) One

c) Two

d) Three

e) More than three

Question 10: Which of the following symbols should be placed in the blank spaces respectively (it the same order from left to right) in order to complete the given expression in such a manner that both
‘A > I’ as well as ‘V ≥ T’ definitely hold true?
A_V_I_C_T

a) >, =, ≤, >

b) ≥, ≤, >, =

c) >, ≥, ≥, =

d) ≤, =, >, ≥

e) ≥, <, ≤, =

Question 11: Which of the given expression is definitely true if the expression` Q > U < I ≤ E = T ≥ S ‘is definitely true?

a) Q ≥ T

b) U < T

c) E ≥ S

d) E ≥ Q

e) I > S

Question 12: The following series is based on the English alphabet. Which one of the following will come in place of the question mark (?) in the given alphabetical series?
XBF UDK RFO OHR ?

a) LKU

b) MKS

c) LJT

d) MJS

e) LJV

Question 13: If the letters of the word ‘PRINCE’ are rearranged as they appear in the English alphabet, the position of how many letters will remain unchanged after the rearrangement ?

a) None

b) One

c) Two

d) Three

e) None of these

Question 14: The positions of the first and the second digits in the number 7986032451 are interchanged. Similarly the positions of the third and fourth digits are interchanged and so on. Which of the following will be the fifth digit from the right end after the rearrangement ?

a) 3

b) 6

c) 4

d) 0

e) None of these

Question 15: If it is possible to make a meaningful word with the third, the fifth, the seventh and the tenth letters of the word ‘OUTRAGEOUS’, which of the following will be the second letter of that word? If more than one such word can be formed, give ‘X as the answer and if no such word can be formed, give ‘Y’ as the answer.

a) E

b) A

c) S

d) Y

e) X

Question 16: How many such pairs of letters are there in the word `CHILDREN’ each of which has as many letters between them in the word as there are between them in the English alphabet ?

a) 3

b) 5

c) 4

d) 2

e) None of these

Question 17: J, D, L, H and F each travelling to station, each one reaches at a different time. L reaches only after J and D reaches only before F. Who amongst them is third to reach ?

a) F

b) L

c) D

d) Cannot be determined

e) None of these

Question 18: How many meaningful English words can be made with the letters EPRY using each letter only once in each word ?

a) None

b) One

c) Two

d) Three

e) More than three

Question 19: What should come next in the letter series given below ?
ABABCABCDABCDEABCDEFABCDEFGABC

a) D

b) E

c) F

d) H

e) None of these

Question 20: How many such digits are there in the number 764528 each of which is as far away from the beginning of the number as when the digits are arranged in descending order within the number ?

a) None

b) One

c) Two

d) Three

e) More than three

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Answers & Solutions:

1) Answer (A)

Given,
AD = 15 cm and ABC is an equilateral triangle

2) Answer (B)

Given, a metallic cone of radius 30 cm and height 40 cm
Volume of metallic cone = $\frac{1}{3} \pi r^2 h$

3) Answer (A)

Given the sides of triangle are 28 m, 45 m and 53 m

4) Answer (D)

In the first term we have DDDDCCCBBA and in the nest step 1 A,1 B,1 D,1 C are deleted and the trend goes on and so we have DDC in the third term and we should delete ! d and 1 C and so we get the required answer as D.

5) Answer (D)

83657294 when arranged in descending order we get 98765432.
We see that in the new number the distance between ‘4 – 2’ and ‘4-7’ is same as in the original number.
Hence, D is the right answer.

6) Answer (E)

The number when arranged in ascending order -235678
5 and 6 are as far away from the beginning as they were in the original number.

7) Answer (C)

Arrange all the vowels and then consonants from left.

IOUFHLRS

Now all the vowels are replaced with previous letters and all the consonants are replaced by next letter.

HNTGIMST

Now third letter from right is M.

Hence, C is the correct answer.

8) Answer (D)

6’s which are immediately preceded by 1 or 5 and immediately by 3 or 9 = (1/5) (6) (3/9)

2 6 3 7 5 6 4 2 9 6 1 3 4 1 6 3 9 1 5 6 9 2 3 1 6 5 4 3 2 1 9 6 7 1 6 3

Thus, there are three such 6’s.

=> Ans – (D)

9) Answer (C)

7’s which are immediately preceded by 5 and not immediately followed by 8 : (5) (7) (not 8)

2  3   5   7   8   9   3   4   5   7    6    1   9   3   5   7   4   8   3   2   5   7   8   8  9   2  5

Thus, there are two such 7’s.

=> Ans – (C)

10) Answer (C)

For, A > I in A _ V _ I, the two blank spaces must have at least one ‘greater than (>)’ symbol.

Thus,options (b),(d),(e) are ruled out.

For, V $\geq$ T in V _ I _ C _ T, we need to have at least one ‘greater than equal to ($\geq$)’ and rest by ‘equal (=)’ symbol.

Thus, (a) is also ruled out.

Now, to check the third option, => A > V ≥ I ≥ C = T

Here, A > I and V ≥ T

=> Ans – (C)

11) Answer (B)

Expression : Q > U < I ≤ E = T ≥ S

(A) : Q ≥ T     (False)

(B) : U < T     (True)

(C) : E ≥ S     (False, not definitely true)

(D) : E ≥ Q     (False)

(E) : I > S      (False)

=> Ans – (B)

12) Answer (C)

Series : XBF UDK RFO OHR ?

The first letters of the above series are decreasing by a factor of 3. Thus the first letter = O – 3 = L

The second letters are increasing by a factor of 2, => Second letter = H + 2 = J

The third letters are increasing by a factor of (+5,+4,+3), => Third letter = R + 2 = T

$\therefore$ LJT is next in the series.

=> Ans – (C)

13) Answer (C)

Word – PRINCE

If the letters are rearranged as they appear in the English alphabet

=> PRINCE = CEINPR

Thus, position of ‘I’ and ‘N’ remain unchanged after the rearrangement.

=> Ans – (C)

14) Answer (D)

Number = 7986032451

If the positions of 1st and 2nd , 3rd and 4th , 5th and 6th and so on are interchanged, new number will be

= 97 68 30 42 15

5th digit from right end = 0

=> Ans – (D)

15) Answer (E)

Word = ‘OUTRAGEOUS’

3rd, 5th, 7th and 10th letters = T, A, E, S

Words that can be formed using these four letters : Seat , Eats

Since, more than 1 word is formed, thus answer is ‘X’

=> Ans – (E)

16) Answer (C)

Word – CHILDREN

Pairs of letters each of which has as many letters between them in the word as there are between them in the English alphabet

= (H,I), (H,N), (I,N) and (E,I)

Thus, there are 4 such pairs.

=> Ans – (C)

17) Answer (E)

L reaches only after J, => J was the first one to reach the station and L was the second one.

D reaches only before F, => F reached last and D reaches at the 4th position.

Thus, the order of them reaching the station : J , L , H , D , F

Thus, H was the third one to reach the station.

=> Ans – (E)

18) Answer (C)

Meaningful English words that can be made with the letters EPRY

= PYRE , PREY

Thus, only 2 words can be formed.

=> Ans – (C)

19) Answer (A)

Series : ABABCABCDABCDEABCDEFABCDEFGABC

If we partition the above series, we can see it is an alphabetical series in increasing order

= AB , ABC , ABCD , ABCDE , ABCDEF , ABCDEFG , ABC

Thus, the next word is ‘D’

=> Ans – (A)

20) Answer (B)

Number = 764528

When digits are arranged in descending order,

New Number = 876542

Only 1 digit, i.e. ‘5’ remained at the same place after rearrangement.

=> Ans – (B)

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