The two curves y = 3 and y = 5 intersect at an angle from Mathem

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 Multiple Choice QuestionsMultiple Choice Questions

121.

If x = secθ - cosθ, y = secnθ - cosnθ, then x2 + 4dydx2 is equal to

  • n2(y2 - 4)

  • n2(4 - y2)

  • n2(y2 + 4)

  • None of these


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122.

The two curves y = 3 and y = 5 intersect at an angle

  • tan-1log3 - log51 + log3log5

  • tan-1log3 + log51 - log3log5

  • tan-1log3 + log51 + log3log5

  • tan-1log3 - log51 - log3log5


A.

tan-1log3 - log51 + log3log5

Given curves y = 3x      ...(i)

and              y = 5x      ...(ii)

Intersect at the point (0, 1).

Now, differentiating Eqs. (i) and (ii) w.r.t. x, we get

dydx = 3xlog3 and dydx = 5xlog5 dydx0, 1 = log3 and dydx0, 1 = log5 m1 = log3 and m2 = log5Angle between these curves is given by     tanθ = m1 - m21 + m1m2 tanθ = log3 - log51 + log3 . log5       θ = tan-1log3 - log51 + log3 . log5


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123.

The period of sin4x + cos4x is

  • π42

  • π22

  • π4

  • π2


124.

If 3 cos x 2 sin x, then the general solution of sin2x - cos2x = 2 - sin2x is

  •  + - 1nπ2, n  Z

  • 2, n  Z

  • 4n ± 1π2, n  Z

  • (2n - 1)π, n  Z


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125.

If cosx + cos2x = 1, then the value of sin12x + 3sin10x + 3sin8x + sin6x - 1, is equal to :

  • 2

  • 1

  • - 1

  • 0


126.

The product of all values of cosα + isinα3/5 is :

  • 1

  • cosα + isinα

  • cos3α + isin3α

  • cos5α + isin5α


127.

1 + cosπ81 + cos3π81 + cos5π81 + cos7π8 is equal to

  • 12

  • 18

  • cosπ8

  • 14


128.

If 3cosθ + sinθ = 2, then the value of θ is

  •  + - 1nπ4

  • - 1nπ4 - π3

  •  + π4 - π3

  •  + - 1nπ4 - π3


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129.

If in a AABC, (s - a)(s - b) = s(s - c) then angle C is equal to

  • 90°

  • 45°

  • 30°

  • 60°


130.

The length of the shadows of a vertical pole of height h, thrown by the sun's rays at three different moments are h, 2h and 3h. The sum of the angles of elevation of the rays at these three moments is equal to

  • π2

  • π3

  • π4

  • π6


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