NIMCET 2012 — Mathematics PYQ

Q: How do I solve NIMCET 2012 Mathematics questions?

Practice NIMCET 2012 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 NIMCET Mathematics questions?

NIMCET 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 NIMCET previous year papers available for free?

Yes. Mathem Solvex provides free access to NIMCET 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

NIMCET 2012 — Mathematics PYQ

NIMCET | Mathematics | 2012

If $\vec{a} + \vec{b} + \vec{c} = 0, |\vec{a}| = 3, |\vec{b}| = 5, |\vec{c}| = 7$ , then the angle between the vectors $\vec{a}$ and $\vec{b}$ is:

Choose the correct answer:

Explanation

1. Isolate $\vec{a}$ and $\vec{b}$

Given:

\vec{a} + \vec{b} + \vec{c} = 0

\vec{a} + \vec{b} = -\vec{c}

2. Square both sides

To involve the magnitudes and the angle, we take the dot product of each side with itself (squaring):

(\vec{a} + \vec{b}) \cdot (\vec{a} + \vec{b}) = (-\vec{c}) \cdot (-\vec{c})

|\vec{a}|^2 + |\vec{b}|^2 + 2(\vec{a} \cdot \vec{b}) = |\vec{c}|^2

3. Substitute the dot product formula

We know that $\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta$ , where $\theta$ is the angle between $\vec{a}$ and $\vec{b}$ :

|\vec{a}|^2 + |\vec{b}|^2 + 2|\vec{a}| |\vec{b}| \cos \theta = |\vec{c}|^2

4. Plug in the given values

Given $|\vec{a}| = 3, |\vec{b}| = 5,$ and $|\vec{c}| = 7$ :

(3)^2 + (5)^2 + 2(3)(5) \cos \theta = (7)^2

9 + 25 + 30 \cos \theta = 49

34 + 30 \cos \theta = 49

5. Solve for $\cos \theta$

30 \cos \theta = 49 - 34

30 \cos \theta = 15

\cos \theta = \frac{15}{30}

\cos \theta = \frac{1}{2}

6. Find the angle $\theta$

Since $\cos \theta = \frac{1}{2}$ , we know:

\theta = \cos^{-1}\left(\frac{1}{2}\right) = 60^\circ

In radians:

\theta = \frac{\pi}{3}

Correct Option:

(b) $\frac{\pi}{3}$

Choose the correct answer:

Explore More