CUET PG 2023 — Mathematics PYQ

Q: How do I solve CUET PG 2023 Mathematics questions?

Practice CUET PG 2023 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

Q: What is the difficulty level of CUET PG Mathematics questions?

CUET PG Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Q: Are CUET PG previous year papers available for free?

Yes. Mathem Solvex provides free access to CUET PG previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

Question

CUET PG 2023 — Mathematics PYQ

CUET PG | Mathematics | 2023

The two adjacent sides of a cyclie QUADRILATERAL are 2 and 5 and the angle between them is 60°. If the third side is 3, the remaining fourth side is

Choose the correct answer:

Explanation

Step 1: Diagonal $AC$ ki length nikaalna

Pehle hum triangle $ABC$ mein Law of Cosines lagayenge:

AC^2 = AB^2 + BC^2 - 2(AB)(BC)\cos(60^\circ)

Values rakhne par:

AC^2 = 2^2 + 5^2 - 2(2)(5)(0.5)

AC^2 = 4 + 25 - 10

AC^2 = 19

Step 2: Fourth side $x$ nikaalna

Cyclic quadrilateral mein opposite angles supplementary hote hain, isliye $\angle D = 180^\circ - 60^\circ = 120^\circ$ .

Ab triangle $ADC$ mein Law of Cosines lagate hain:

AC^2 = AD^2 + CD^2 - 2(AD)(CD)\cos(120^\circ)

Humein pata hai ki $\cos(120^\circ) = -0.5$ aur $AC^2 = 19$ :

19 = x^2 + 3^2 - 2(x)(3)(-0.5)

19 = x^2 + 9 + 3x

Ab is quadratic equation ko solve karte hain:

x^2 + 3x - 10 = 0

Step 3: Factorization

(x + 5)(x - 2) = 0

Side ki length negative nahi ho sakti, isliye $x = 2$ .