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CBSE Questions for Class 12 Commerce Maths Inverse Trigonometric Functions Quiz 8 - MCQExams.com

If sin1x+sin1y+sin1z=3π2 and f(1)=2,f(x+y)=f(x)f(y)  for all  x,yR. Then xf(1)+yf(2)+zf(3)x+y+zxf(1)+yf(2)+zf(3) is equal to
  • 0
  • 1
  • 2
  • 3
If cot1x+cot1y+cot1z=π2,x,y,z>0 and xy<1, then x+y+z is also equal to
  • 1x+1y+1z
  • xyz
  • xy+yz+zx
  • none of these
Exhaustive set of values of parameter a so that sin1xtan1x=a has a solution is
  • [π6,π6]
  • [π4,π4]
  • [π2,π2]
  • none of these
The value of a for which ax2+sin1(x22x+2)+cos1(x22x+2)=0 has a real solution is 
  • π2
  • π2
  • 2π
  • 2π
The number of solution of the equation 1+x2+2xsin(cos1y)=0 is :
  • 1
  • 2
  • 3
  • 4
The set of values of parameter a so that the equation (sin1x)3+(cos1x)3=aπ3 has a solution. 
  • [132,78]
  • [132,,98]
  • [0,78]
  • [132,78]
If sin1x+sin1y+sin1z=π, then x4+y4+z4+4x2y2z2=k(x2y2+y2z2+z2x2), where k is equal to
  • 1
  • 2
  • 4
  • noneofthese
The value of p for which system has a solution is
  • 1
  • 2
  • 0
  • 1
If the equation sin1(x2+x+1)+cos1(ax+1)=π2 has exactly two distinct solutions then value of a could not be
  • -1
  • 0
  • 1
  • 2
If sin1a+sin1b+sin1c=3π2  and  f(2)=2,f(x+y)=f(x)f(y)x,yϵR then af(2)+bf(4)+cf(6)3(af(2).bf(4).cf(6))af(2)+bf(4)+cf(6)  equals
  • 2
  • 4
  • 6
  • 8
Indicate the relation which can hold in their respective domain for infinite values of x.
  • tan|tan1x|=|x|
  • cot|cot1x|=|x|
  • tan1|tanx|=|x|
  • sin|sin1x|=|x|
If sin1x+sin1y+sin1z=3π2 and f(2)=2,f(a+b)=f(a)f(b),a,bϵR, then xf(2),yf(4),zf(6) are in
  • A.P.
  • G.P
  • H.P
  • None
Let f:AB be a function defined by y=f(x) where f is a bijective function, means f is injective (one-one) as well as surjective (onto), then there exist a unique mapping g:BA such that f(x)=y if and only if g(y)=xxϵA,yϵB Then function g is said to be inverse of f and vice versa so we write g=f1:BA[{f(x),x}:{x,f(x)}ϵf1]when branch of an inverse function is not given (define) then we consider its principal value branch.

If 1<x<0,then tan1x equals?
  • πcos1(1x2)
  • sin1(x1+x2)
  • cos1(1x2x)
  •  cosec1x
The number of solutions of sin1(1+b+b2+)+cos1(aa23+a29)=π2 is
  • 1
  • 2
  • 3
Express in terms of an inverse function the angle formed at the intesection of the diagonals of a cube.
  • sin12/3
  • cos11/3
  • tan11/3
  • sin11/3
If tan1(tan5π4)=α and tan1(tan2π3)=β then.
  • αβ=7π12
  • α+β=7π12
  • 2α+3β=7π12
  • 4α+3β=7π12
sin135+sin145 is equal to
  • π2
  • π3
  • π4
  • π6
If 0<x1<x2 which of following is true for y=sec1x.
  • sec1x1+sec1x2>sec1(x1+x22)
  • sec1x1+sec1x2<2sec1(x1+x22)
  • sec1x1>sec1x2
  • sec1x1=sec1x2
If 3cos1x+sin1x=π, then x=.....
  • 32
  • 12
  • 12
  • 12
The domain of the function sin12x is:
  • [0,1]
  • [1,1]
  • [2,2]
  • [12,12]
Domain of f(x)=cot1x+cos1x+cosec1x is
  • [1,1]
  • R
  • (,1][1,)
  • {1,1}
Let E1={xϵR:x1 and xx1>0}
and E2={xϵE1:sin1(loge(xx1))is a real number}.
(Here, the inverse trigonometric function sin1x assumes values in [π2,π2])
Let f:E1R be the function define by f(x)=loge(xx1) and g:E2R be the function defined by g(x)=sin1(loge(xx1)).
LIST - ILIST - II
P. The range of f is(,11e][ee1,)
Q. The range of g contins(0,1)
R. The domain of f contains[12,12]
S. The domain of g is(,0)(0,)
(,ee1]
(,0)(12,ee1]
The correct option is
  • P4;Q2;R1;S1
  • P3;Q3;R6;S5
  • P4;Q2;R1;S6
  • P4;Q3;R6;S5
The value of sin1x+cos1x(|x|1) is
  • 1
  • π
  • π/2
  • π/2
Match the entries of Column - I and Column - II.
Column - IColumn - II
aIf 4 sin1x+cos1x=π, then x equals1ab
bIf C=900, then the value of tan1 ab+c + tan1 bc+a is 2π
ctan1 1 + tan1 2 + tan1 3 is3π/4
dIf sec1 xa - sec1 xb = sec1 b - sec1 a, then x equals41/2
  • a-4, b-3, c-2, d-1
  • a-1, b-3, c-2, d-4
  • a-4, b-3, c-1, d-2
  • a-3, b-4, c-2, d-1
Let a=(sin1x)sin1x,b=(sin1x)cos1x,c=(cos1x)sin1x,d=(cos1x)cos1x and if x(0,1)then 
  • a>b>d>c
  • b>a>d>c
  • d>c>a>b
  • none of these
If 0<x<1 , then tan1(1x21+x) is equal to
  • 12cos1x
  • cos11+x2
  • sin11x2
  • 121+x1x
Let a,b,c be a positive real numbers θ=tan1a(a+b+c)bc+tan1b(a+b+c)ca+tan1c(a+b+c)ab, then tanθ
  • 0
  • 3π
  • 1
  • 4π
 cos1[1+x+1x2]=π212cos1x
  • True
  • False
If cos1x2+cos1y3=θ, then 9x212xycosθ+4y2 is equal to
  • 36sin2θ
  • 36cos2θ
  • 36tan2θ
  • None of these
The range of the function f(x)=sin1(x22x+2)
  • ϕ
  • [π2,π2]
  • π2
  • none of these
2tan1[aba+btanθ2]=
  • cos1(acosθ+ba+bcosθ)
  • cos1(a+bcosθacosθ+b)
  • cos1(acosθa+bcosθ)
  • cos1(bcosθacosθ+b)
sin135+tan117=π2
  • True
  • False
cos[tan1{sin(cot1x)}] is equal to:
  • x2+2x2+3
  • x2+2x2+1
  • x2+1x2+2
  • none of these
sin1(aa23+a39+...)+cos1(1+b+b2+...)=π2 when?
  • a=3 and b=1
  • a=1 and b=13
  • a=16 and b=12
  • None of these
The range of f(x)=sin=1x+cos=1x+tan1x is ?
  • (0,π)
  • [π4,3π4]
  • [π4,π4]
  • [0,3π4]
If x1,x2,x3 are positive roots of x36x2+3px2p=0(pR), then the value of sin1(1x1+1x2)+cos1(1x2+1x3)tan1(1x3+1x1) is equal to
  • π8
  • π6
  • π4
  • π
The value of sin1[cot(sin1234+cos124+sec12)] is equal to
  • 1
  • 0
  • 2
  • 3
cos(cos1cos(8π7)+tan1tan(8π7)) has the value equal to -
  • 1
  • 1
  • cosπ7
  • 0
If (tan1x)2+(cot1x)2=5π28, then x equals to
  • 1
  • 1
  • 0
  • None Of These
The exhaustive set of values of a such that x2+ax+sing1 (x24x+5)+ cos1(x24x+5)=0 has at least one solution is
  • {2π4}
  • (,2π4)
  • (,2π4]
  • (2π4,+]
If |cos1(1x21+x2)|<π3,then: 
  • x[13,13]
  • x[13,13]
  • x[0,13]
  • none of these
tanh1(13)+coth1(3)=..... 
  • log2
  • log3
  • log3
  • log2
If y=12csc h1(12x1+x2) then x=
  • coshy
  • sinhy
  • tanhy
  • cothy
3cot1(12+3)cot1(1x)=cot1(13)+π2 then x=?
  • 1
  • 2
  • 3
  • 3
Sinh(cosh1x)=
  • x2+1
  • 1x2+1
  • x21
  • 1x21
The value of esinh1(tanθ) is equal to
  • cosecθ+cotθ
  • secθ+tanθ
  • cosecθ+secθ
  • tanθ+cotθ
If f(x)=sin1(32x121x2)12x1, then f(x) is equal to :
  • sin1(12)sin1(x)
  • sin1xπ6
  • sin1x+π6
  • None of these
The value of tan{π4+12cos1(xy)}+tan{π412cos1(xy)}
  • xy
  • yx
  • 2yx
  • 2xy
For which value of x, sin[cot1(x+1)]=cos(tan1x).
  • 12
  • 0
  • 1
  • 12
If cot1xcot1(x+2)=150 then x is equal to 
  • 3
  • 3
  • 3+2
  • 3+2
0:0:12


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Practice Class 12 Commerce Maths Quiz Questions and Answers