Math Chapter Wise

EnglishTGT 2003

Q41.The straight roads intersect at an angle of 60° ° °. A bus on one road is 2km away from the intersection and a car on the other road is 3 km away from the intersection. Then the direct distance between the two vehicles is:

A1 km B2 km C4km D7 km

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EnglishTGT 2003

Q42.In a triangle ABC, B, C 3 4 π ∠ = ∠ = ∠ = ∠ = ∠ = ∠ = ∠ = ∠ =, Let D divides BC internally in the ratio 1:3 then sin BAD sin CAD ∠ =

A1/6 B1/3 C1/3 D2/3

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EnglishTGT 2003

Q43.If in a triangle PQR, sin P, sin Q, sin R are in A.P. then

Athe altitudes are in A.P. Bthe altitudes are in H.P. Cthe medians are in G.P. Dthe medians are in A.P.

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EnglishTGT 2003

Q44.If the data given to construct a triangle ∆ ∆ ∆ABC are a = 5, b = 7, sin 3 A 4 =, then it is possible to construct

AOnly one triangle Btwo triangles Cinfinitely many triangles Dno triangle

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EnglishTGT 2001

Q45.In a triangle ABC, If a=3, b=4 and 3 sinA = 4 then ∠ ∠ ∠ B =?

A600 B900 C450 D300

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EnglishTGT 2001

Q46.If A + B + C = π Then sin2A + sin2B =

AcosA cos (B – C) Bcin A cos (A – B) C2 sin C cos (A – B) DNone of these

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EnglishTGT 2001

Q47.If α + β − γ = π α + β − γ = π α + β − γ = π α + β − γ = π then ((()) sin α + β α + β α + β α + β will be equal

Asin γ B– sin γ Ccos γ D– cos γ

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EnglishTGT 2001

Q48.In triangle ABC, side AD is perpendicular to side BC and DB = 3CD then what is the reaction between sides AB, BC, CA?

A(AB)2 = (AC)2 + (BC)2 B2(AB)2 = 2(AC)2 + (BC)2 C2(AC)2 = 2(AB)2 + (BC)2 D2(AB)2 = (AC)2 + (BC)2

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EnglishTGT 1999

Q49.If in a triangle ABC, (a – b) (s – c) = (b – c) (s – a) then F1, F2, F3 in AP will be.

Aand BImage/formula option B (see source) CBoth DNone of these

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EnglishTGT 1999

Q50.In a triangle A, B and C are in A.P. then.

Ac2 = a2 +b2 -ab Bb2 = a2 +c2 –ac Cc2 = a2 +b2 DNone of these

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EnglishPGT 2011

Q51.If 1 2 2x y sin 1 x − = + where 0<x<1 and 0 y 2 π < < then dy dx is equal to:

A2/1+ x B2 2x 1+ x C2 1 1+ x D2 x 1+ x −

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EnglishPGT 2011

Q52.tan (cos–1 x) is equal to:

A2 1 x x − Bx 1 x2 + C2 1 x x + D−2/1 x

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EnglishPGT 2011

Q53.The value of 1 1 1 1 tan tan 2 3 − − + + is

A0 B3/π C6/π D4/π

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EnglishPGT 2011

Q54.If A= tan–1 x, then the value of sin2A is:

A2 2x 1 x − B2 2x 1 x − C2 2x 1 x + DNone of these

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EnglishPGT 2013

Q55.If sin–1 x = y then

A0 y π/≤ B2 2 y π − ≤ C0 y π/< < D2 2 y π − < <

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EnglishPGT 2010

Q56.The value of 1 1 4 2 tan cos tan 5 3 − − + is

A6/17 B7/16 C17/6 DNone of these

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EnglishPGT 2010

Q57.If the angle of a triangle ABC △ are in A.P. and ratio of the sides b and c is 3: 2 then the angle A will be

A450 B300 C650 D750

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EnglishPGT 2010

Q58.If ∆ ∆ ∆ABC is a triangle and sides, a 3 1, = + b 3 1 = − = − and the angle C, 3 π = then angle B will be equal to

A300 B450 C600 DNone of these

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EnglishPGT 2009

Q59.If R is the radius of the circumcircle of a ∆ ∆ ∆ABC and ∆ ∆ ∆ is its area, then

AR = a b c + + ∆ Ba b c R 4 + + = ∆ Cabc R 4 = ∆ Dabc R = ∆

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EnglishPGT 2009

Q60.In a ∆ ∆ ∆ABC, a = 1, b = 2 c = 3. Then cos 2 A is

A0 B1 C2 D−1/2

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