NIMCET Trigonometry Previous Year Question Paper and Solution with PDF

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NIMCET Previous Year Questions (PYQs)

NIMCET Trigonometry PYQ

Qus : 1NIMCET PYQ

The expression $\frac{tanA}{1-cotA}+\frac{cotA}{1-tanA}$ can be written as

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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution

Qus : 2NIMCET PYQ

Angle of elevation of the top of the tower from 3 points (collinear) A, B and C on a road leading to the foot of the tower are 30°, 45° and 60°, respectively. The ratio of AB and BC is

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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution

According to the given information, the figure should be as follows.

Let the height of tower = h

Qus : 3NIMCET PYQ

If $3 sin x + 4 cos x = 5$, then $6tan\frac{x}{2}-9tan^2\frac{x}{2}$

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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution

Qus : 4NIMCET PYQ

Largest value of $cos^2\theta -6sin\theta cos\theta+3sin^2\theta+2 $ is

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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

Solution

Qus : 5NIMCET PYQ

Number of point of which f(x) is not differentiable $f(x)=|cosx|+3$ in $[-\pi, \pi]$

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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

Solution

Qus : 6NIMCET PYQ

If A > 0, B > 0 and A + B = $\frac{\pi}{6}$ , then the minimum value of $tanA + tanB$

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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution

On differentiating

x= tanA + tan(π/6-A)

we get :

dx/dA = sec²A-sec²(π/6-A)

now putting

dx/dA=0

we get

cos²(A) = cos²(π/6-A) so 0≤A≤π/6

therefore

A=π/6-A from here we get A = π/12 = B

so minimum value of that function is

2tanπ/12 which is equal to 2(2-√3)

Qus : 7NIMCET PYQ

The $sin^2 x tanx + cos^2 x cot x-sin2x=1+tanx+cotx $, $x \in (0 , \pi)$, then x

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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution

Qus : 8NIMCET PYQ

If $cosec\theta-\cot \theta=2$, then the value of $cosec\theta$ is

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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

Qus : 9NIMCET PYQ

The solution of the equation ${4\cos }^2x+6{\sin }^2x=5$ are

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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

Qus : 10NIMCET PYQ

The value of $\tan \Bigg{(}\frac{\pi}{4}+\theta\Bigg{)}\tan \Bigg{(}\frac{3\pi}{4}+\theta\Bigg{)}$ is

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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution

Qus : 11NIMCET PYQ

If $\sin x=\sin y$ and $\cos x=\cos y$, then the value of x-y is

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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

Solution

Qus : 12NIMCET PYQ

If $a_1, a_2, a_3,...a_n$, are in Arithmetic Progression with common difference d, then the sum $(sind) (cosec a_1 . cosec a_2+cosec a_2.cosec a_2+...+cosec a_{n-1}.cosec a_n)$ is equal to

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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

Qus : 13NIMCET PYQ

In a ΔABC, if $\tan ^2\frac{A}{2}+\tan ^2\frac{B}{2}+\tan ^2\frac{C}{2}=k$ , then k is always

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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution

Qus : 14NIMCET PYQ

The general value of $\theta$, satisfying the equation $\sin \theta=\frac{-1}{2},\, \tan \theta=\frac{1}{\sqrt[]{3}}$

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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution

Qus : 15NIMCET PYQ

then the value of

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 16NIMCET PYQ

If tan x = - 3/4 and 3π/2 < x < 2π, then the value of sin2x is

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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Qus : 17NIMCET PYQ

The value of $\tan 9{^{\circ}}-\tan 27{^{\circ}}-\tan 63{^{\circ}}+\tan 81{^{\circ}}$ is equal to

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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution

Qus : 18NIMCET PYQ

If cosθ = 4/5 and cosϕ = 12/13, θ and ϕ both in the fourth quadrant, the value of cos( θ + ϕ )is

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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Qus : 19NIMCET PYQ

The value of sin36^o is

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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Qus : 20NIMCET PYQ

Express (cos 5x – cos7x) as a product of sines or cosines or sines and cosines,

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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution

Qus : 21NIMCET PYQ

If $32\, \tan ^8\theta=2\cos ^2\alpha-3\cos \alpha$ and $3\, \cos \, 2\theta=1$, then the general value of $\alpha$ =

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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution

Qus : 22NIMCET PYQ

If |k|=5 and 0° ≤ θ ≤ 360°, then the number of distinct solutions of 3cos⁡θ + 4sin⁡θ = k is

NIMCET 2021

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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution

Qus : 23NIMCET PYQ

, then value of

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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution

Qus : 24NIMCET PYQ

If $a\, \cos \theta+b\, \sin \, \theta=2$ and $a\, \sin \, \theta-b\, \cos \, \theta=3$ , then ${a}^{2^{}}+{b}^2=$

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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution

Qus : 25NIMCET PYQ

If $\prod ^n_{i=1}\tan ({{\alpha}}_i)=1\, \forall{{\alpha}}_i\, \in\Bigg{[}0,\, \frac{\pi}{2}\Bigg{]}$ where i=1,2,3,...,n. Then maximum value of $\prod ^n_{i=1}\sin ({{\alpha}}_i)$.

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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ