NIMCET 2018 — Mathematics PYQ

Q: How do I solve NIMCET 2018 Mathematics questions?

Practice NIMCET 2018 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 2018 — Mathematics PYQ

NIMCET | Mathematics | 2018

The vector $a = α \hat{i} + 2 \hat{j} + β \hat{k}$ lies in the plane of the vector $b = \hat{i} + \hat{j}$ and $c = \hat{j} + \hat{k}$ and bisects the angle between $b$ and $c$ . Then, which one of the following gives possible values of $α$ and $β$ ?

Choose the correct answer:

Explanation

Concept:
If two or more vectors lie on the same plane than they are called coplanar vector and satisfies the conditions
$< / s p an >< s p an s t y l e = " f o n t - s i z e : 14 pt; f o n t - f ami l y : a r ia l, h e l v e t i c a, s an s - ser i f; " > a am p; b am p; c < / s p an >< s p an s t y l e = " f o n t - s i z e : 14 pt; f o n t - f ami l y : a r ia l, h e l v e t i c a, s an s - ser i f; " > = 0$
$< / s p an >< s p an s t y l e = " f o n t - s i z e : 14 pt; f o n t - f ami l y : a r ia l, h e l v e t i c a, s an s - ser i f; " > a_{x} < / s p an >< s p an s t y l e = " f o n t - s i z e : 14 pt; f o n t - f ami l y : a r ia l, h e l v e t i c a, s an s - ser i f; " > b_{x} < / s p an >< s p an s t y l e = " f o n t - s i z e : 14 pt; f o n t - f ami l y : a r ia l, h e l v e t i c a, s an s - ser i f; " > c_{x} am p; a_{y} am p; b_{y} am p; c_{y} am p; a_{z} am p; b_{z} am p; c_{z} < / s p an >< s p an s t y l e = " f o n t - s i z e : 14 pt; f o n t - f ami l y : a r ia l, h e l v e t i c a, s an s - ser i f; " > = 0$

Calculation:
$a am p; b am p; c = 0$
$ α 10 am p; 2 am p; 1 am p; 1 am p; β am p; 0 am p; 1 = 0$
$α + β = 2$
Also, $a$ bisects the angle between $b$ and $c$ .
$ a = \frac{λ}{2} (\hat{b} + \overset{c}{^})$
$= \frac{λ}{2} (\hat{i} + 2 \hat{j} + \hat{k})$
On comparing with $a = α \hat{i} + 2 \hat{j} + β \hat{k}$ ,
We get, $λ = 2$ , $α = 1$ , and $β = 1$