Consider the function f(x) = g(x) + h(x)Where gx = 

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71.

Consider the function f(x) = g(x) + h(x)

Where gx = sinx4 and hx = cos4x5

What is the period of the function f(x) ?

  • 10π

  • 20π

  • 40π

  • 80π


C.

40π

f(x) = g(x) + h(x)

period of f(x) = L.C.M of {period of g(x), period of h(x)}

L.C.M of {8π, 5π2}

L.C.M = {LCM of numerator/HCF of denominator}

i.e,  T = 40π1 = 40π

hence, option C is correct.


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72.

Consider the function f(x) = g(x) + h(x)

Where gx = sinx4 and hx = cos4x5

What is the period of the function h(x) ?

  • π

  • 4π5

  • 5π2

  • 3π2


73.

Consider the function f(x) = g(x) + h(x)

Where gx = sinx4 and hx = cos4x5

What is the period of the function g(x) ?

  • π

  • 2π

  • 4π

  • 8π


74.

Let f(x) = x2, g(x) = tan(x) and h(x) = ln(x). What is [fo(fof)](2) equal to ?

  • 2

  • 8

  • 16

  • 256


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75.

Let f(x) = x2, g(x) = tan(x) and h(x) = ln(x). For x = π2, What isvalue of  [ho(gof)](x) equal to ?

  • 0

  • 1

  • π4

  • π2


76.

Let S = {1, 2, 3, ...}. A relation R on S × S is defined by x Ry if loga(x) > loga(y) when a = 12Then the relation is

  • reflexive only

  • symmetric only

  • transitive only

  • both symmetric and transitive


77.

If 1.5 ≤ x ≤ 4.5, then which one of the following is correct ?

  • (2x – 3) (2x – 9) > 0

  • (2x – 3) (2x – 9) < 0

  • (2x – 3) (2x – 9) ≥ 0

  • (2x – 3) (2x – 9) ≤ 0


78.

If, x = logc (ab), y = loga(bc), z = logb(ca), then which of the following is correct ?

  • xyz = 1

  • x + y + z = 1

  • (1 + x)-1 + (1 + y)-1 + (1 + z)-1 = 1

  • (1 + x)-2 + (1 + y)-2 + (1 + z)-2 = 1


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79.

What is the value of 110log51024 - log510 + 15log53125 ?

  • 0

  • 1

  • 2

  • 3


80.

The number (1101101 + 1011011)2 can be written in decimal system as

  • (198)10

  • (199)10

  • (200)10

  • (201)10


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