CUET · MATHS · PYQ PAPER 2025

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) be vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0},|\vec{a}|=3,|\vec{b}|=5\) and \(|\vec{c}|=7\), then the angle between \(\vec{a}\) and \(\vec{b}\) is

A \(\frac{\pi}{2}\)
B \(\frac{\pi}{3}\)
C \(\frac{\pi}{4}\)
D \(\frac{\pi}{6}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{\pi}{3}\)

Step-by-step Solution

Detailed explanation

\(\vec{a}+\vec{b}=-\vec{c}\) \(|\vec{a}+\vec{b}|^2=|-\vec{c}|^2\) \(|\vec{a}|^2+|\vec{b}|^2+2\vec{a}\cdot\vec{b}=|\vec{c}|^2\) \(|\vec{a}|^2+|\vec{b}|^2+2|\vec{a}||\vec{b}|\cos\theta=|\vec{c}|^2\) \(3^2+5^2+2(3)(5)\cos\theta=7^2\) \(9+25+30\cos\theta=49\) \(34+30\cos\theta=49\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

If \(\left(t_1, y_1\right),\left(t_2, y_2\right)\),...,\(\left(t_n, y_n\right)\) denote the time series and \(y_t\) are the trend values of the variables \(y\), then

CUET 2025 Medium

Match List - I with List - II.

List - I	List - II
(A) The common region determined by all the constraints of LPP is called	(I) objective function
(B) Minimize \(z=c_1 x_1+c_2 x_2+\cdots+c_n x_n\) is	(II) convex set
(C) A solution that also satisfies the non-negative restrictions of a LPP is called	(III) feasible region
(D) The set of all feasible solutions of a LPP is a	(IV) feasible solution

Choose the correct answer from the options given below :

CUET 2023 Easy

Match List - I with List - II

List - I (terms)	List - II (Definitions)
(A) POPULATION	(I) Measurable characteristics of the population such as mean, variance, standard deviation etc. of population
(B) SAMPLE	(II) Measurable characteristics of the sample such as mean, variance, standard deviation etc. of a sample
(C) PARAMETER	(III) Finite set of statistical individuals drawn from a population for investigation
(D) STATISTIC	(IV) Collection of objects having the same characteristics

Choose the correct answer from the options given below:

CUET 2025 Medium

Explore more questions on app

From CUET

Explore more questions on app

X	0	1	2
P(X)	\(1-7 a^2\)	\(\frac{1}{2} a+\frac{1}{4}\)	\(a^2\)