Match List I with List II List I List II A. If 4 th 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, the last term is 45 and the sum of the terms is 400. The number of term 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 comm

A – IV; B – III; C – I; D – II Explanation: A. GP ka Common Ratio Maan lijiye pehla term hai aur common ratio hai. Condition di gayi hai: . Formula lagane par: Dono taraf se divide karne par: Matching: A IV B. AP mein Number of Terms ( ) Pehla term , aakhri term , aur sum hai. Sum ka formula: . Isliye, . Matching: B III C. AP ka Common Difference ( ) Teen numbers ko maan lijiye. Sum diya hai : Sum of squares diya hai : . Matching: C I D. AP ka Common Difference ( ) Diya gaya hai: aur . Formulas: (Eq 2) mein se (Eq 1) ko ghatane (subtract) par: Isse simplify karne par: . Matching: D II Final Match Table: List I List II Result A IV 3 B III 16 C I 5 D II -5/2 Correct Option: A-IV, B-III, C-I, D-II

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CUET PG 2022 Mathematics PYQ — Match List I with List II List I List II A. If 4 th term of a G.P… | Mathem Solvex

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CUET PG 2022 Mathematics PYQ — Match List I with List II List I List II A. If 4 th term of a G.P… | Mathem Solvex | Mathem Solvex

Explanation

A. GP ka Common Ratio

Maan lijiye pehla term $a = 3$ hai aur common ratio $r$ hai.
Condition di gayi hai: $a_4 = (a_2)^2$ .
Formula lagane par:

$ar^3 = (ar)^2$

$3 \cdot r^3 = (3 \cdot r)^2 \implies 3r^3 = 9r^2$
Dono taraf $3r^2$ se divide karne par:

$r = 3$

Matching: A $\rightarrow$ IV

B. AP mein Number of Terms ( $n$ )

Pehla term $a = 5$ , aakhri term $l = 45$ , aur sum $S_n = 400$ hai.
Sum ka formula: $S_n = \frac{n}{2}(a + l)$ .

$400 = \frac{n}{2}(5 + 45)$

$400 = \frac{n}{2}(50) \implies 400 = 25n$
Isliye, $n = \frac{400}{25} = 16$ .

Matching: B $\rightarrow$ III

C. AP ka Common Difference ( $d$ )

Teen numbers ko $a-d, a, a+d$ maan lijiye.
Sum diya hai $27$ :

$(a-d) + a + (a+d) = 27 \implies 3a = 27 \implies a = 9$
Sum of squares diya hai $293$ :

$(9-d)^2 + 9^2 + (9+d)^2 = 293$

$(81 + d^2 - 18d) + 81 + (81 + d^2 + 18d) = 293$

$243 + 2d^2 = 293 \implies 2d^2 = 50$
$d^2 = 25 \implies d = 5$ .

Matching: C $\rightarrow$ I

D. AP ka Common Difference ( $d$ )

Diya gaya hai: $a_4 = 64$ aur $a_{54} = -61$ .
Formulas:

$a + 3d = 64 \quad \text{---(Eq 1)}$

$a + 53d = -61 \quad \text{---(Eq 2)}$
(Eq 2) mein se (Eq 1) ko ghatane (subtract) par:

$(a + 53d) - (a + 3d) = -61 - 64$

$50d = -125 \implies d = \frac{-125}{50}$
Isse simplify karne par: $d = -5/2$ .

Matching: D $\rightarrow$ II

Final Match Table:

List I	List II	Result
A	IV	3
B	III	16
C	I	5
D	II	-5/2

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

CUET PG 2022 — Mathematics PYQ

Choose the correct answer:

Explanation

A. GP ka Common Ratio

B. AP mein Number of Terms ( $n$ )

C. AP ka Common Difference ( $d$ )

D. AP ka Common Difference ( $d$ )

Final Match Table:

Explanation

A. GP ka Common Ratio

B. AP mein Number of Terms ( $n$ )

C. AP ka Common Difference ( $d$ )

D. AP ka Common Difference ( $d$ )

Final Match Table:

	List I		List II
A.	If 4^th 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, the last term is 45 and the sum of the terms is 400. The number of term 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