Question
Total number of solutions of the equation 3x + 2 tan x =
in x 
[0, 2
] is equal to
- 1
- 2
- 3
- 4
Hint:
Here, we have given is 3x + 2 tanx = . We have to find how many solutions it has. Firstly, separate the tanx. And draw the graph for tanx and find the intersection point this equation. The intersection point is solution It given region to [ 0, 2π].
The correct answer is: 1
Here we have to find the how many solutions it has.
Firstly, the equation is
3x + 2 tanx =
2tanx = – 3x
tanx =
– 
3/2 x
let y = tanx ; y = – x
Now using graph,
At x = 0, y =
And at y = 0, x = 
Given region of graph is [ 0, 2π ] .
Hence, according to graph it intersects = 3 so it has 3 number of solutions
Therefore, the correct answer is 3
In this question, we use the graph of tanx . The intersection is the total number of solutions of this equation. The graph region is [ 0, 2π ].
Related Questions to study
The number of sigma bonds in 
is:
The number of sigma bonds in is:
Statement 1:Oxidation number of Ni in is zero.
Statement 2:Nickel is bonded to neutral ligand carbonyl.
Statement 1:Oxidation number of Ni in is zero.
Statement 2:Nickel is bonded to neutral ligand carbonyl.
Suppose equation is f(x) – g(x) = 0 of f(x) = g(x) = y say, then draw the graphs of y = f(x) and y = g(x). If graph of y = f(x) and y = g(x) cuts at one, two, three, ...., no points, then number of solutions are one, two, three, ...., zero respectively.
The number of solutions of sin x = 
is
Suppose equation is f(x) – g(x) = 0 of f(x) = g(x) = y say, then draw the graphs of y = f(x) and y = g(x). If graph of y = f(x) and y = g(x) cuts at one, two, three, ...., no points, then number of solutions are one, two, three, ...., zero respectively.
The number of solutions of sin x = is
The first noble gas compound obtained was:
The first noble gas compound obtained was:
Statement 1:The redox titrations in which liberated 
is used as oxidant are called as iodometric titrations
Statement 2:Addition of KI of 
liberates which is estimated against hypo solution.
Statement 1:The redox titrations in which liberated is used as oxidant are called as iodometric titrations
Statement 2:Addition of KI of liberates which is estimated against hypo solution.
molecule is completely changed into 
molecules at:
molecule is completely changed into molecules at:
Statement-I : If 
and 
then 
Statement-II : If sinA = sinB and cosA = cosB, then 
Statement-I : If and then
Statement-II : If sinA = sinB and cosA = cosB, then
Arsine is:
Arsine is:
Statement-I : The equation sin(cos x) = cos(sin x) does not possess real roots.
Statement-II : If sin x > 0, then 
Statement-I : The equation sin(cos x) = cos(sin x) does not possess real roots.
Statement-II : If sin x > 0, then
Statement-I : In (0, ), the number of solutions of the equation 
is two
Statement-II : 
is not defined at 
Statement-I : In (0, ), the number of solutions of the equation is two
Statement-II : is not defined at
Statement-I : If sin x + cos x = 
then 
Statement-II : AM ≥ GM
Statement-I : If sin x + cos x = then
Statement-II : AM ≥ GM
Statement-I : The number of real solutions of the equation sin x = 2x + 2–x is zero
Statement-II : Since |sin x| ≤ 1
Statement-I : The number of real solutions of the equation sin x = 2x + 2–x is zero
Statement-II : Since |sin x| ≤ 1
if
if
