In a ∆ABCa - b2cos2C2 + a +&t

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 Multiple Choice QuestionsMultiple Choice Questions

211.

For x IR, 3cos4x - 5 + 4 lies in the interval

  • [1, 7]

  • [4, 7]

  • [0, 7]

  • [2, 7]


212.

If x = logcotπ4 + θ, then the value of sinhx is

  • tan2θ

  • - tan2θ

  • cot2θ

  • - cot2θ


213.

If in a ABC, r3 = r1 + r2 + r, then A + B is equal to

  • 120°

  • 100°

  • 90°

  • 80°


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214.

In a ABCa - b2cos2C2 + a +b2sin2C2 is equal to

  • a2

  • c2

  • b2

  • a2 + b2


B.

c2

We have,a - b2cos2C2 + a + b2sin2C2 a2 + b2 - 2abcos2C2 +  a2 + b2 + 2absin2C2 a21 + b21 - 2abcos2C2 - sin2C2 a2 + b2 - 2abcosC      cosC = a2 + b2 - c22ab ora2 + b2 - 2abcosC = c2       = C2


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215.

In a ABC, the correct formulae among the following are

I. r = 4RsinA2sinB2sinC2II. r1 = s - atanA2III. r3 = s - c

  • only I, II

  • only II, III

  • only I, III

  • I, II, III


216.

An aeroplane flying with uniform speed horizontally one km above the ground is observed at an elevation of 60°. After 10 s if the elevation is observed to be 30°, then the speed of the plane (in km/h) is

  • 2403

  • 2003

  • 2403

  • 1203


217.

If the distance between the points (acosθ, asinθ) and  (acosϕ, asinϕ) is 2a, then θ is equal to

  • 2 ± π + ϕ, n  Z

  •  + π2 + ϕ, n  Z

  • nπ - ϕ, n  Z

  • 2 + ϕ, n  Z


218.

E1 : a + b + c = 0, if 1 is a root of ax2 + bx + c = 0, E2 : b2 - a2 = 2ac, if sinθ, cosθ are the roots of ax2 + bx + c = 0 Which of the following is true ?

  • E1 is true, E2 is true

  • E1 is true, E2 is false

  • E1 is false, E2 is true

  • E1 is false, E2 is false


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219.

If A + C = 2B, then cosC - cosAsinA - sinC is equal to

  • cotB

  • cot2B

  • tan2B

  • tanB


220.

A + B = C  cos2A + cos2B + cos2C - 2cosAcosBcosC is equal to

  • 1

  • 2

  • 0

  • 3


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