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NIMCET Previous Year Questions (PYQs)

NIMCET Trigonometry PYQ


NIMCET PYQ 2020
The expression  tanA1cotA+cotA1tanA can be written as 





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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NIMCET PYQ 2020
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



NIMCET PYQ 2020
If 3sinx+4cosx=5, then 6tanx29tan2x2 





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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NIMCET PYQ 2023
Largest value of cos2θ6sinθcosθ+3sin2θ+2 is





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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NIMCET PYQ 2023
Number of point of which f(x) is not differentiable f(x)=|cosx|+3 in [π,π]





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NIMCET PYQ 2019
If A > 0, B > 0 and A + B = π6 , 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)

NIMCET PYQ 2019
The sin2xtanx+cos2xcotxsin2x=1+tanx+cotx, x(0,π), then x





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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

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NIMCET PYQ 2022
If cosecθcotθ=2, then the value of cosecθ is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2022
The solution of the equation 4cos2x+6sin2x=5 are





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
The value of tan(π4+θ)tan(3π4+θ) is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2024
If sinx=siny and cosx=cosy, then the value of x-y is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
If a1,a2,a3,...an, are in Arithmetic Progression with common difference d, then the sum (sind)(coseca1.coseca2+coseca2.coseca2+...+cosecan1.cosecan) is equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution


NIMCET PYQ 2021
In a ΔABC, if tan2A2+tan2B2+tan2C2=k , then k is always





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2021
The general value of θ, satisfying the equation sinθ=12,tanθ=13





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2018
If  then the value of  is





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

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NIMCET PYQ 2017
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

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NIMCET PYQ 2021
The value of tan9tan27tan63+tan81 is equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2017
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

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NIMCET PYQ 2017
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


NIMCET PYQ 2021
If 32tan8θ=2cos2α3cosα and 3cos2θ=1, then the general value of α =





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2021
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



NIMCET PYQ 2021
If acosθ+bsinθ=2 and asinθbcosθ=3 , then a2+b2=





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2023
If ni=1tan(αi)=1αi[0,π2] where i=1,2,3,...,n. Then maximum value of ni=1sin(αi).





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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NIMCET PYQ 2020
Solve the equation sin2 x - sinx - 2 = 0 for for x on the interval 0 ≤ x < 2π





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution


NIMCET PYQ 2020
If tanx2=tanx3=tanx5 and x + y + z = π, then the value of tan2x + tan2y + tan2z is





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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NIMCET PYQ 2020
Find the value of sin 12°sin 48°sin 54°





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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NIMCET PYQ 2020
If cos x = tan y , cot y = tan z and cot z = tan x, then sinx =





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution


NIMCET PYQ 2020
The value of  is





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution









NIMCET PYQ 2020
The value of sin 10°sin 50°sin 70° is





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution

sin10° sin50° sin70°
= sin10° sin(60°−10°) sin(60°+10°)
= 1/4 sin3x10°
=1/4x1/2=1/8


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