Math Chapter Wise

EnglishEMRS PGT-2023

Q01.In a ∆ ∆ ∆ABC, if a = 2, B = tan–1 1 2 and C = tan–1 1, 3 then (A, b) is equal to:

A2 2, 4 5 π B3 2 2, 4 5 π C2, 4 5 π D3 2, 4 5 π

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EnglishEMRS PGT-2023

Q02.If the area of an equilateral triangle inscribed in the circle x2 +y2 + 10x + 12y + c = 0 is 27 3 sq. units, then c is equal to:

A–25 B13 C25 D20

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EnglishKVS PGT 2023

Q03.If sin (sin-1 1 4 + cos-1 x) = 1, then the value of x is:

A1/2 B2/π C1/4 D4/π

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EnglishKVS PGT 2023

Q04.If tan-1 x + tan-1 y = 2 5 π, then cot-1 x + cot-1 y is:

A5/π B2 5 π C3 5 π Dπ

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EnglishKVS PGT 2023

Q05.The value of tan-1 cosx 1-sinx is:

Ax/2 Bx 4 2 π − Cx 4 2 π + Dx 4 2 π ±

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EnglishNVS PGT 2022

Q06.Which among the following is wrong?

A1 1 sin x cos x 2 − − π = − B1 1 2 2sin x sin 2x 1 x − − = − C() 1 1 3 3sin x sin 4x 3x − − = − D1 1 sec x cosec x 2 − − π = −

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EnglishNVS PGT 2022

Q07.Match the inverse trignometric functions with their ranges: Function Range 1. sin-1 x

A, 4− B, 3− CImage/formula option C (see source) D, 2−

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EnglishKVS PGT 2022

Q08.Solution of trigonometric equation 2 tan−1 (sinx) = tan−1 (2secx), is:

A0 B4/π C3/π D6/π

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EnglishKVS PGT 2022

Q09.The principal value of 1 1 sin cos is: 2 2 − − − + −

A2/π B3/π C6/π D0

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EnglishOAVS TGT 2021

Q10.A car is moving at uniform speed towards a tower. It takes 8 minutes for the angle of depression from the top of tower to the car to change from 300 to 450. How long after this will the car reach the base of the tower?

A2 (3 1) minutes B8 (3 1) minutes C2 (3 1) minutes D2 (3 1) minutes

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EnglishOAVS TGT 2017

Q11.The sides of a right angled triangle are in ratio 3:4:5 and 'θ' is adjacent to the smallest side then find the ratio of sin θ: cos θ: tan θ.

A4: 3: 5 B1: 2: 3 C3: 4: 5 D12: 9: 20

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EnglishKVS TGT 2017

Q12.If 1 sin x, 5 then 1 cos x equals–

A10 B3/10 C5/10 D7/4

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EnglishKVS TGT 2017

Q13.A solution of the equation 1 1 tan (1 x) tan (1 x) 2 is–

Ax = 1 Bx = –1 Cx = 0 Dx = π

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EnglishKVS TGT 2017

Q14.1 1 3 sin cot 2 4 is equal to–

A1/5 B2/5 C2/5 D1/5

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EnglishUPPSC GIC 2021

Q15.The value of cos-1 2 1 x − + is-

A2 cot-1/x B2 sec-1/x C2 tan-1/x D2 sin-1/x

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EnglishUPPSC GIC 2021

Q16.The principal value of cot-1 1 3 − is-

A3/π B2 3 π C6/π DNone of these

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EnglishUP TGT 2021 UP TGT 2016 (08-03-2019)

Q17.In the equation 2 2 –1 –1 –1 2 2 1 – a 1 – b cos – cos = 2tan x 1+ a 1+ b value of x is

Aa b 1 ab + Ba – b 1 ab + Ca – b/1– ab DNone of the above

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EnglishUP TGT 2021

Q18.What is the principal-value of –1 2π sin sin 3?

A4/π B2/π C3/π D2 3 π

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EnglishUP TGT 2021

Q19.–1 –1 3 12 sin – cos 5 13 equal to

A–1 56 sin 65 B–1 16 sin 65 C1 D0

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EnglishUPPSC Ashram Paddhati 2021

Q20.If sin–1 x – cos–1 x = π 6, then x is

A1/2 B1 – 2 C3 – 2 D3/2

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