Conditions on the Parameters of Logarithm Function
Trending Questions
Q. The domain of the function f(x)=sin−1(3x2+x−1(x−1)2)+cos−1(x−1x+1) is
- [0, 14]
- [0, 12]
- [14, 12]∪{0}
- [−2, 0]∪[14, 12]
Q.
When , what does equal?
Q. The number of real values of x, satisfying 32log3x−2x−3=0 is
- 0
- 1
- more than 2
- 2
Q. The domain of definition of the function f(x)=log10(√10⋅3x−2−9x−1−1)+√cos−1(1−x) is
- [0, 1]
- [1, 2]
- (0, 2)
- (0, 1)
Q. The domain of f(x)=log3{−log4(6x−46x+5)} is
- (23, ∞)
- (−56, ∞)
- (−∞, −56)
- R−{−56}
Q. Range of the function f(x)=4tan−1x+3sin−1x+sec−1x is
- {−3π2, 3π2}
- {−5π2, 5π2}
- {−5π2, 3π2}
- {−3π2, 5π2}
Q. The exhaustive domain of the function sin−1[log2(x2/2)] is
- [−2, 2]
- [1, 2]
- [−2, −1]∪[1, 2]
- [0, 2]
Q. For y=logax to be defined 'a' must be
- Any positive real number
- Any number
- ≥e
- Any positive real number ≠1
Q. The solution of the inequality log25−x216(24−2x−x214)>1 is
- (−3, 3)
- (−∞, 17)∪(−3, 4)∪(1, ∞)
- (−3, 1)∪(3, 4)
- (−17, 1)∪(3, 4)
Q. For y=logax to be defined 'a' must be
- Any positive real number
- Any number
- ≥e
- Any positive real number ≠1
Q. The domain of the function f(x)=
⎷cos−1(1−|x|2) is
- (−3, 3)
- [−3, 3]
- [0, 3]
- (−∞, −3)∪(3, ∞)
Q. Assertion (A): cos−1x and tan−1x are positive for all positive real values of x in their domain.
Reason (R): The domain of f(x)=cos−1x+tan−1x is [−1, 1].
Reason (R): The domain of f(x)=cos−1x+tan−1x is [−1, 1].
- Both A and R are true and R is the correct explanation of A
- Both A and R are true but R is not correct explanation of A
- A is true but R is false
- A is false but R is true
Q. The cubic equation whose roots are 2cosπ7, 2cos3π7, 2cos5π7, is
- x3−x2−x+1=0
- x3−x2+2x−1=0
- x3−2x2−2x+1=0
- x3−x2−2x+1=0
Q. If log1/5(3x−4) is defined, then
- x∈(−4, ∞)
- x∈(43, ∞)
- x∈(34, ∞)
- x∈(−43, ∞)
Q.
Solution of logx2+6x+8 logx2+2x+3 (x2−2x)=0 is
a natural number
a negative integer
-1
none of these
Q. Let D be the domain of the function f(x)=sin(log√9−x21−x). Then the number of integers in D is
Q. If the domain of the function f(x)=cos−1√x2−x+1√sin−1(2x−12) is the interval (α, β], then α+β is equal to:
- 1
- 32
- 12
- 2
Q. The solution set of the equation logx3log3x3=log9x3 is similar to which of the following options :
- logx3log3/x3=logx/93
- (log3x)2=2
- log2(12log2log3x2)=0
- √2logx3=1
Q. If log1/5(3x−4) is defined, then
- x∈(−4, ∞)
- x∈(43, ∞)
- x∈(34, ∞)
- x∈(−43, ∞)
Q.
Let A be the set of all 25 students of Class X in a school. Let : A → N be
function defined by () = roll number of the student . Then is:
one-one
onto but not one-one
one-one but not onto
many one
Q. If logx−7(x−4) is defined, then
- x∈(4, 7)
- x∈(4, ∞)−{8}
- x∈(7, ∞)−{8}
- x∈(8, ∞)
Q. log a base 2a=x, log 2a base 3a=y, log 3a base 4a=z; then xyz-2yz=
Q. For y=logax to be defined 'a' must be
- Any positive real number
- ≥e
- Any number
- Any positive real number ≠1
Q. The number of integral solutions of the inequation log2(x−1|≤1 is
- 4
- 3
- 2
- 5