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Phrases Previous Year Questions (PYQs)

Phrases Progressions PYQ


Phrases PYQ
List I List II
A. Dog : Rabies :: Mosquito : I. Bacteria
B. Amnesia : Memory :: Paralysis : II. Liver
C. Meningitis : Brain :: Cirrhosis : III. Movement
D. Influenza : Virus :: Typhoid : IV. Malaria






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Phrases Previous Year PYQPhrases CUET 2023 PYQ

Solution

Dog causes Rabies, Mosquito causes Malaria → A-IV
Amnesia affects Memory, Paralysis affects Movement → B-III
Meningitis affects Brain, Cirrhosis affects Liver → C-II
Influenza is caused by Virus, Typhoid is caused by Bacteria → D-I

Correct matching: A-IV, B-III, C-II, D-I

Phrases PYQ
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A:
If the A.M. and G.M. between two numbers are in the ratio $m:n$, then the numbers are in the ratio
$m+\sqrt{m^2-n^2} : m-\sqrt{m^2-n^2}$

Reason R:
If each term of a G.P. is raised to the same power, the resulting sequence also forms a G.P.

Choose the correct answer from the options given below:





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

Assertion A is true (standard result from A.M.–G.M. relations). Reason R is also true, but it does not explain Assertion A.

Phrases PYQ
The a, b, c and d are in GP and are in ascending order such that a+d = 112 and b+c 48. If the GP is continued with a as the first term, then the sum of the first six terms is:





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Phrases Previous Year PYQ Phrases CUET 2022 PYQ

Solution


Phrases PYQ
Match the list
LIST 1 LIST 2
A. If 4th term of a G.P. is square of its second term, and its first term is 3, then common ratio is _______ I. 5
B. The first term of an AP is 5 and the last term is 45 and the sum of the terms is 400. The number of terms is_____ II. -5/2
 C. The sum of three numbers which are in AP is 27 and sum of their squares is 293. Then the common difference is ______ III. 16
D. The fourth and 54th terms of an AP are, respectively, 64 and -61. The common difference is ______ IV. 3
choose the correct answer from the options given below:





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Phrases Previous Year PYQ Phrases CUET 2022 PYQ

Solution


Phrases PYQ
The H.P. of two numbers is $4$ and the arithmetic mean $A$ and geometric mean $G$ satisfy $2A+G^2=27$. The numbers are





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

If numbers are $a,b$:

H.P. $=\dfrac{2ab}{a+b}=4 \Rightarrow ab=2(a+b)$

$A=\dfrac{a+b}{2},\quad G^2=ab$

Given:
$2A+G^2=(a+b)+ab=27$

Substitute $ab=2(a+b)$:
$3(a+b)=27 \Rightarrow a+b=9$
$ab=18$

So numbers are roots of
$x^2-9x+18=0 \Rightarrow x=6,3$

Phrases PYQ
If $A_1,A_2$ be two A.M.’s and $G_1,G_2$ be two G.M.’s between $a$ and $b$, then $\dfrac{A_1+A_2}{G_1G_2}$ is equal to





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

For A.M.’s between $a$ and $b$: $A_1=\dfrac{2a+b}{3},\quad A_2=\dfrac{a+2b}{3}$ So, $A_1+A_2=\dfrac{2a+b+a+2b}{3}=a+b$ For G.M.’s between $a$ and $b$: $G_1=\sqrt[3]{a^2b},\quad G_2=\sqrt[3]{ab^2}$ So, $G_1G_2=\sqrt[3]{a^3b^3}=ab$ Hence, $\dfrac{A_1+A_2}{G_1G_2}=\dfrac{a+b}{ab}$

Phrases PYQ
If a, b and c are in Geometric Progression and $a^{\frac{1}{x}}=b^{\frac{1}{y}}=c^{\frac{1}{z}}$ then, x, y, z are in
1. Arithmetic Progression
2. Geometric Progression
3. $\frac{2}{y}=\frac{1}{x}+\frac{1}{z}$
4. $x=y+z$






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Phrases Previous Year PYQ Phrases CUET 2025 PYQ

Solution

We are given:

\(a^{\tfrac{1}{x}} = b^{\tfrac{1}{y}} = c^{\tfrac{1}{z}} = k\)

\(\Rightarrow a = k^x,\; b = k^y,\; c = k^z\)

Since \(a, b, c\) are in G.P.:

\(b^2 = ac\)

\(\Rightarrow (k^y)^2 = (k^x)(k^z)\)

\(\Rightarrow k^{2y} = k^{x+z}\)

\(\Rightarrow 2y = x+z\)

This implies \(y\) is the arithmetic mean of \(x\) and \(z\).

x, y, z are in Arithmetic Progression.

Correct Answer: (1) Arithmetic Progression


Phrases PYQ
Matching
Column A Column B
A. $(\sqrt{2}+1)+1+(\sqrt{2}-1)+\ldots \infty$ IV. $\frac{4+3\sqrt{2}}{2}$
B. $ \frac{1}{2}+\frac{1}{3^2}+\frac{1}{2^3}+\frac{1}{3^4}+\frac{1}{2^5}+\frac{1}{3^6}+\ldots \infty$ I. $\frac{19}{24}$
C. $6^{1/2}\times 6^{1/4}\times 6^{1/8}\ldots \infty$ II. $6$
D. $8+4\sqrt{2}+4+\ldots \infty$ III. $8(2+\sqrt{2})$

(a) (A)-I, (B)-II, (C)-III, (D)-IV 
(b) (A)-IV, (B)-I, (C)-II, (D)-III 
(c) (A)-IV, (B)-I, (C)-III, (D)-II 
(d) (A)-I, (B)-IV, (C)-III, (D)-II





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Phrases Previous Year PYQ Phrases CUET MCA 2026 PYQ

Solution


Phrases PYQ

Assertion: 1/3, −1/2, 3/4, −9/8 form an AP

Reason: The constant sequence is the only sequence which is both AP as well as GP.

Options:

(a) Assertion is true, Reason is true, and Reason is the correct explanation of the Assertion.

(b) Assertion is true, Reason is true, but Reason is not the correct explanation of the Assertion.

(c) Assertion is true, but Reason is false.

(d) Assertion is false, but Reason is true.






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Phrases Previous Year PYQ Phrases CUET MCA 2026 PYQ

Solution


Phrases PYQ
The arithmetic means of two observations is 125 and their geometric mean is 60. Find the harmonic mean of the two observations.





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Phrases Previous Year PYQ Phrases CUET 2022 PYQ

Solution


Phrases PYQ
The terms $1,\, \log _y(x),\, \log _z(y)\, and\, 15\log _x(z)$ are in AP.

Based on this information answer the following questions. 
The Common difference of AP is 





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Phrases Previous Year PYQ Phrases CUET 2022 PYQ

Solution


Phrases PYQ
The terms $1,\, \log _y(x),\, \log _z(y)\, and\, 15\log _x(z)$ are in AP.

Based on this information answer the following questions. 
The value of xy is:  





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Phrases Previous Year PYQ Phrases CUET 2022 PYQ

Solution


Phrases PYQ
The terms $1,\, \log _y(x),\, \log _z(y)\, and\, 15\log _x(z)$ are in AP.

Based on this information answer the following questions. 
yz is equal to : 





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Phrases Previous Year PYQ Phrases CUET 2022 PYQ

Solution


Phrases PYQ
Math List I with List II:
 LIST I LIST 2
 A. In a GP, the third term is 24 and 6th term is 192. The common ratio is _____ I. 78
 B. Let Sn denotes the sum of first n terms of an AP. If S2n=3Sn, then S3n/Sn equals to _______ II. 6
 C. The sum of 3 terms of a GP is 13/12 and their product is -1. The first term is ______ III. -1
 D. The least value of n for which the sum 3+6+9+...+n is greater than 1000 is  IV. 2
Choose the correct answer from the options given below :





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Phrases Previous Year PYQ Phrases CUET 2022 PYQ

Solution



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