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CBSE Questions for Class 12 Commerce Maths Inverse Trigonometric Functions Quiz 2 - MCQExams.com

Range of sin1xcos1x is
  • [3π2,π2]
  • [5π3,π3]
  • [3π2,π]
  • [0,π]
ABC is a triangular park with AB=AC=100 cm. A clock tower is situated at the midpoint of BC. The angles of elevation of the top of the tower from A and B are cot13.2 and cosec12.6. The height of the tower is
  • 25 mt
  • 50 mt
  • 100 mt
  • 502 mt
A vertical pole more than 100ft high consists of two portions, the lower being 1/3 of the whole. lf the upper portion subtends an angle tan1(1/2) at a point distant 40 ft. from the foot of the pole, the height of the pole is
  • 105
  • 120
  • 135
  • 150
If θsin1x+cos1xtan1x, 0x1, then the smallest interval in which θ lies is given by ?
  • π4θπ2
  • π4θ0
  • 0θπ4
  • π2θ3π4
The value of sin sin{tan1(tan7π6)+cos1(cos7π3)} is
  • 0
  • 1
  • -1
  • None of these
If αϵ(0,π2), then the value of tan1(cotα)cot1(tanα)+sin1(sinα)cos1(cosα) is equal to
  • 2α
  • π+α
  • 0
  • π2α
If tan11+x21x=4,then
  • x=tan2
  • x=tan4
  • x=tan(1/4)
  • x=tan8
If cot1x+cot1y+cot1z=π2  then x+y+z equals
  • xyz
  • xy+yz+zx
  • 2xyz
  • None of these
f(x)=tan1(sinx+cosx) is an increasing function in
  • (0,π4)
  • (0,π2)
  • (π4,π4)
  • None of these
If sin{sin115+cos1x}=1, then x is equal to
  • 1
  • 0
  • 45
  • 15
If 0x1, then tan{12sin12x1+x2+12cos12x1+x2}
  • 1
  • 0
  • 2x1+x2
  • x
tan(cot1x) is equal to

  • π2x
  • cot(tan1x)
  • tanx
  • none of these
If x takes negative permissible value, then sin1x is equal to
  • cos11x2
  • cos11x2
  • cos1x21
  • πcos11x2
sec2(tan12)+cosec2(cot13)=
  • 5
  • 10
  • 15
  • 20
The range of the function, f(x)=(1+sec1x)(1+cos1x) is
  • (,)
  • (,0][4,)
  • {0,(1+π)2}
  • [1,(1+π)2]
Number of real value of x satisfying the equation, arctanx(x+1)+arcsinx(x+1)+1=π2 is
  • 0
  • 1
  • 2
  • more than 2
Range of f(x)=sin1x+tan1x+cos1x is
  • [0,π]
  • [π4,3π4]
  • [π,2π]
  • None of these
If f(x)=sin1x+sec1x is defined, then which of the following value/values is/are in its range?
  • π2
  • π2
  • π
  • 3π2
α=sin1(cos(sin1x)) and β=cos1(sin(cos1x)) then:
  • tanα=cotβ
  • tanα=cotβ
  • tanα=tanβ
  • tanα=tanβ
The value of sin1(cos(cos1(cosx)+sin1(sinx))), where xϵ(π2,π), is equal to 
  • π2
  • π
  • π
  • π2
There exists a positive real number x satisfying cos(tan1x)=x. The value of cos1(x22) is
  • π10
  • π5
  • 2π5
  • 4π5
If α,β(α<β) are the roots of the equation 6x2+11x+3=0 then which of the following are real?
  • cos1α
  • sin1β
  • cosec1α
  • Both cot1α and cot1β
The value of sin1(sin10) is

  • 10
  • 103π
  • 3π10
  • none of these
Which one of the following statement is meaningless?
  • cos1(ln(2e+43))
  • cosec1(π3)
  • cot1(π2)
  • sec1(π)
The value of tan(sin1(cos(sin1x)))tan(cos1(sin(cos1x))), where xϵ(0,1), is equal to 
  • 0
  • 1
  • 1
  • noneofthese
sec2(tan12)+cosec2(cot13) is equal to 
  • 5
  • 13
  • 15
  • 6
Which of the following is the solution set of the equation 2cos1x=cot1(2x212x1x2)
  • (0,1)
  • (1,1){0}
  • (1,0)
  • [1,1]
The value of sin1[x1xx1x2] is equal to
  • sin1x+sin1x
  • sin1xsin1x
  • sin1xsin1x
  • 0
The number of integer x satisfying sin1|x2|+cos1(1|3x|)=π2 is
  • 1
  • 2
  • 3
  • 4
If x1=2tan1(1+x1x),x2=sin1(1x21+x2), where x1,x2ϵ(0,1), then 2(x1+x2) is equal  to
  • 0
  • 2π
  • π
  • noneofthese
If f(x)=(sin1x)2+(cos1x)2, then
  • f(x) has the least value of π28
  • f(x) has the greatest value of 5π28
  • f(x) has the least value of π216
  • f(x) has the greatest value of 5π24
  • Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1
  • Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1
  • STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
  • STATEMENT 1 is FALSE and STATEMENT 2 is TRUE
tan1[cosx1+sinx] is equal to 
  • π4x2,forxϵ(π2,3π2)
  • π4x2,forxϵ(π2,π2)
  • π4x2,forxϵ(3π2,5π2)
  • π4x2,forxϵ(3π2,3π2)
The value of sin1(x24x+6)+cos1(x24x+6) for all xϵR is
  • π2
  • π
  • 0
  • none of these
Number of solutions of the equation sin(13cos1x)=1 are
  • only one
  • no solution
  • only three
  • at least two
The value of sin1(sin2) is?
  • 2+nπ
  • 2π
  • 2+π
  • 22nπ
The equation 3cos1xπxπ2=0 has
  • one negative solution
  • one positive solution
  • no solution
  • more than one solution
If sin1(x27x+12)=mπ,nI, then x=
  • -4
  • 4
  • 3
  • -3
The value of tan1(12tan2A)+tan1(cotA)+tan1(cot3A), for 0<A<π/4, is :
  • tan12
  • tan1(cotA)
  • 4tan1(1)
  • 2tan1(2)
There exists a positive real number x satisfying cos(tan1x)=x. Then the value of cos1(x22) is 
  • π10
  • π5
  • 2π5
  • 4π5
The number of real solution of the equation 1+cos2x=2sin1(sinx),π<xπ, is
  • 0
  • 1
  • 2
  • infinite
The equation sin1x=2sin1a , has a solution for
  • R
  • |a|<12
  • |a|12
  • 12a12
If sin1xsin1y=π2 ,then
  • x2+y2=1
  • y=1x2,0x1,1y0
  • y=1x2,|x|<1
  • None of these
Let f(x)=ecos1sin(x+π3), then f(8π9)  equals
  • e7π12
  • e13π18
  • e5π18
  • eπ12
If cot1[(cosα)1/2]+[tan1(cosα)1/2]=x , then sinx equals 
  • 1
  • cot2(α2)
  • tanα
  • cot(α2)
sin1(aa23+a39)+cos1(1+b+b2+b3+)=π2 , when
  • a=1,b=13
  • a=16,b=12
  • a=16,b=12
  • None of these
The domain of sin1[x], where [x] is greatest integer function, given by
  • [1,1]
  • [1,2)
  • {1,0,1}
  • None of these
If cos1x+cos1y+cos1z=3π, then value of xy equals
  • -3
  • 0
  • 3
  • -1
The domain of f(x)=sin1xx is
  • [1,1]
  • {0}
  • [1,0)
  • None of these
Number of triplets (x,y,z) satisfying sin1x+sin1y+cos1z=2π is
  • 1
  • 0
  • 2
0:0:1


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