Math Chapter Wise

EnglishPGT 2009

Q121.If sec–1 x = cosec–1 y, then the value of 1 1 cos cos x y − − + + is

A4/π B4 − π C2 − π D2/π

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EnglishPGT 2009

Q122.Value of sec2 (tan–1 2) + cosec2 (cot–1 3) is

A5 B6 C15 D13

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EnglishPGT 2005

Q123.The value of cos 200 cos 400 cos 600 cos 800 is:

A1/16 B1/8 C1/2 DNone of these

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EnglishPGT 2005

Q124.If in a triangle ABC, cosA+2cosB+cosC = 2, then a, b, c are in

AA.P. BH.P. CG.P. DNone of these

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EnglishPGT 2005

Q125.Let the angle A, B, C of ∆ ∆ ∆ABC be in A.P. and let b:c = 3: 2 then angle A is

A450 B600 C750 D900

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EnglishPGT 2004

Q126.If r1, r2, r3 be the radii of the described circles of ∆ ∆ ∆ ABC and r be the radius of the inscribed circle then the value of 1 2 3 1 1 1 1 r r r r + + − + + − + + − + + − is

A0 B1 C-1 DNone of the above

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EnglishPGT 2004

Q127.If in a triangle ABC, A 5 tan 2 6 =, C 2 tan 2 5 =, then

Aa, c, b are in G.P. Ba, b, c are in A.P. Cb, a, c are in A.P. Da, b, c are in G.P.

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EnglishPGT 2004

Q128.If f(x) = cos2 x + sec2 x, its value always will be

A() 1 < f x B() 1 = f x C2 () 1 > > f x D() 2 ≥ f x

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EnglishPGT 2004

Q129.The minimum value of sin cos 6 6 x x π + + + + + + + + + + + + in the interval 0, 2 π is attained at the following value of x

A12/π B6/π C3/π D2/π

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EnglishPGT 2004

Q130.If cosecθ p q + = −, then the value of cot 4 2 π θ + will be

Ap/q Bq/p Cpq Dpq

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EnglishPGT 2004

Q131.The sides of a triangle are 3x + 4y, 4x + 3y and 5x + 5y, where x, y < 0, then the triangle is

Aobtuse angled Bright angled Cequilateral DNone of the above

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EnglishPGT 2004

Q132.If in a triangle ABC, cos A = cos B cos C then the value of cot B cot C will be

A2 B3 C4 D1/2

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EnglishPGT 2003

Q133.3 5 2 4 5tan 10tan tan 1 10tan 5tan θ − + is equal to

Atan θ Btan 5θ Csin 5θ Dsin θ

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EnglishPGT 2002

Q134.The sides of a ∆ ∆ ∆ are a, b and (((()))) 2 2 a ab b + + + +, then the greatest angle is:

A600 B900 C1200 DNone of these

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EnglishPGT 2002

Q135.In an equilateral triangle, the in-radius, circum- radius and one of the ex-radii are in the ratio:

A2:3:5 B1:2:3 C1:3:7 D3:7:9

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EnglishRajasthan TGT 2016

Q136.If 2 cos 3cos 2 1, sin θ − θ + θ − θ + θ − θ + θ − θ + = θ where 0, 2 π < θ < < θ < < θ < < θ < then which of the following statements is/are correct? a. There are two value of θ satisfying the above equation. b. only θ = 600 is satisfied by the above equation. Select the correct answer.

A'a' only B'b' only CBoth 'a' and 'b' DNeither 'a' nor 'b'

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EnglishRajasthan TGT 2016

Q137.If 4 tan cot, 3 θ + θ = θ + θ = θ + θ = θ + θ = where 0, 2 π < θ < < θ < < θ < < θ < then sinθ+cosθ is equal to

A1 B−3 1/2 C3 1 2 + D2

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EnglishRajasthan TGT 2016

Q138.(1–sinA+ cosA)2 is equal to

A2(1–cosA)(1+sinA) B2(1+sinA)(1+cosA) C2(1–cosA)(1–sinA) DNone of these /

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EnglishRajasthan TGT 2016

Q139.For a triangle ABC, with sides a, b, c the ratio of sin(A–B) to sin (A+B) is

A2 2 2 b c a + B2 2 b c bc − C2 2 2 a b c − D2 2 a b ab −

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EnglishRajasthan TGT 2016

Q140.For a triangle ABC with side a,b,c the product of tan A/2 and tan B/2 is

Ab c a a b c + − + + Bc a b a b c + − + + Ca b c a b c + − + + D2c (a b c) + +

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