Question
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
- 4
- 6
- 8
- none of these
Hint:
Here, equation f(x)−g(x)=0 or f(x)=g(x)=y says, then draw the graphs of y=f(x) and y=g(x). if graphs 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 correct answer is: 6
Here, we have to find out number of solutions.
Firstly, we have given
Sinx = ,
We know that,
-1 ≤ sinx ≤ 1 so,
0 ≤ |x|/10 ≤ 1,
The, the curve on graph, X belongs to [ 0, 10]
From fig, f(x) = sinx and g(x) =, so it intersects 6 points
The number of solutions is 6.
The correct answer is 6.
In this question, we have drawn the graph. The number of intersections of both function fx and gx are the number solutions. Draw the graph carefully and find the intersection points.
Related Questions to study
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 
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, Start solving first Statement and try to prove it. Then solve the Statement-II.
Statement-I : If and then
Statement-II : If sinA = sinB and cosA = cosB, then
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, Start solving first Statement and try to prove it. Then solve the Statement-II.
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 
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, it has 5 solutions, but tanθ &tan3θ are not defined at 
, 
, 
. respectively so it remains only 2.
Statement-I : In (0, ), the number of solutions of the equation is two
Statement-II : is not defined at
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, it has 5 solutions, but tanθ &tan3θ are not defined at , , . respectively so it remains only 2.
Statement-I : If sin x + cos x = 
then 
Statement-II : AM ≥ GM
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, Start solving first Statement and try to prove it. Then solve the Statement-II. Always, the AM–GM inequality states that AM ≥ GM.
Statement-I : If sin x + cos x = then
Statement-II : AM ≥ GM
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, Start solving first Statement and try to prove it. Then solve the Statement-II. Always, the AM–GM inequality states that 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
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, -1 ≤ sinx ≤ 1 for all value, remember that.
Statement-I : The number of real solutions of the equation sin x = 2x + 2–x is zero
Statement-II : Since |sin x| ≤ 1
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason. Here, -1 ≤ sinx ≤ 1 for all value, remember that.
if
if
if
if
if
if
if
if
if
In this question, we have to find the general solution of x. Here more than one option will correct. Remember the rules for finding the general solution.
if
In this question, we have to find the general solution of x. Here more than one option will correct. Remember the rules for finding the general solution.
is
