∫0π2secxnsecxn +cscxndx is equal to from Mathem

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

21.

The acute angle between the line r = i^ + 2j^ + k^ + λi^ + j^ + k^ and the plane 2i^ - j^ + k^ = 5

  • cos-123

  • sin-123

  • tan-123

  • sin-123


22.

The area of the region bounded by the curve y = 2x - x2 and X - axis is

  • 23 sq units

  • 43 sq units

  • 53 sq units

  • 83 sq units


23.

If fxlogsinxdx = loglogsinx + c, then f(x) is equal to

  • cot(x)

  • tan(x)

  • sec(x)

  • csc(x)


24.

If A and B are foot of perpendicular drawn from point Q(a, b, c) to the planes yz and zx, then equation of plane through the points A, B and O is

  • xa + yb - zc = 0

  • xa - yb + zc = 0

  • xa - yb - zc = 0

  • xa + yb + zc = 0


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25.

If a = i^ + j^ - 2k^, b = 2i^ - j^ + k^ and c = 3i^ - k^ and c = ma + nb, then m + n is equal to

  • 0

  • 1

  • 2

  • - 1


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26.

0π2secxnsecxn +cscxndx is equal to

  • π2

  • π3

  • π4

  • π6


C.

π4

0π2secxnsecxn +cscxndx           ...i   = 0π2secπ2 - xnsecπ2 - xn +cscπ2 - xndx   = 0π2cscxncscxn +secxndx    ...iiOn adding Eq. (i) and (ii), we get2I = 0π2secxn + cscxnsecxn +cscxndx    = 0π2dx = x0π2 2I = π2   I = π4


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27.

If the probability density function of a random variable X is given as
xi - 2 - 1 0 1 2
P(X = xi) 0.2 0.3 0.15 0.25 0.1

then F(0) is equal to

  • P(X < 0)

  • P(X > 0)

  • 1 - P(X > 0)

  • 1 - P(X < 0)


28.

The particular solution of the differential equation

y1 + logxdxdy - xlogx = 0, when, x = e, y = e2 is

  • y = exlog(x)

  • ey = xlog(x)

  • xy = elog(x)

  • ylog(x) = ex


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29.

M and N are the mid-points of the diagonals AC and BO respectively of quadrilateral ABCD, then AB + AD + CB + CD is equal to

  • 2MN

  • 2NM

  • 4MN

  • 4NM


30.

If sinx  is the integrating factor (IF) of the linear differential equation dydx + Py = Q, then P is

  • logsinx

  • cosx

  • tanx

  • cotx


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