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Maths-

General

Easy

Question

If $f left parenthesis x right parenthesis equals open vertical bar table row cell s i n invisible function application x end cell cell s i n invisible function application a end cell cell s i n invisible function application b end cell row cell c o s invisible function application x end cell cell c o s invisible function application a end cell cell c o s invisible function application b end cell row cell t a n invisible function application x end cell cell t a n invisible function application a end cell cell t a n invisible function application b end cell end table close vertical bar$ where $0 less than a less than b less than fraction numerator pi over denominator 2 end fraction$ hen the equation f(x) = 0 has, in the interval (a, b)

atleast one root
atmost one root
no root
exactly one root

The correct answer is: atleast one root

Related Questions to study

The velocity-time graph of a particle moving along a straight line is shown in figure. The displacement of the body in 5s is

Displacement (in magnitude)

equals fraction numerator 1 over denominator 2 end fraction open parentheses 3 cross times 2 minus fraction numerator 1 over denominator 2 end fraction cross times 1 cross times 2 plus 1 cross times 1 close parentheses

The velocity-time graph of a particle moving along a straight line is shown in figure. The displacement of the body in 5s is

physics-General

Displacement (in magnitude)

equals fraction numerator 1 over denominator 2 end fraction open parentheses 3 cross times 2 minus fraction numerator 1 over denominator 2 end fraction cross times 1 cross times 2 plus 1 cross times 1 close parentheses

Let f x( ) and g x( ) are defined and differentiable for $x greater or equal than x subscript 0 end subscript$ and $f open parentheses x subscript 0 close parentheses equals g open parentheses x subscript 0 close parentheses comma f to the power of ´ left parenthesis x right parenthesis greater than straight g to the power of straight prime left parenthesis x right parenthesis text for end text x greater than x subscript 0$ then

ϕ left parenthesis x right parenthesis equals f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis text  where  end text x element of open square brackets x subscript 0 end subscript comma b close square brackets

c element of open parentheses x subscript 0 end subscript comma b close parentheses contains as member

ϕ to the power of ´ end exponent left parenthesis c right parenthesis equals fraction numerator ϕ left parenthesis b right parenthesis minus ϕ open parentheses x subscript 0 end subscript close parentheses over denominator b minus x subscript 0 end subscript end fraction greater than 0

therefore f left parenthesis x right parenthesis greater than g left parenthesis x right parenthesis text  for  end text x equals b

Let f x( ) and g x( ) are defined and differentiable for $x greater or equal than x subscript 0 end subscript$ and $f open parentheses x subscript 0 close parentheses equals g open parentheses x subscript 0 close parentheses comma f to the power of ´ left parenthesis x right parenthesis greater than straight g to the power of straight prime left parenthesis x right parenthesis text for end text x greater than x subscript 0$ then

ϕ left parenthesis x right parenthesis equals f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis text  where  end text x element of open square brackets x subscript 0 end subscript comma b close square brackets

c element of open parentheses x subscript 0 end subscript comma b close parentheses contains as member

ϕ to the power of ´ end exponent left parenthesis c right parenthesis equals fraction numerator ϕ left parenthesis b right parenthesis minus ϕ open parentheses x subscript 0 end subscript close parentheses over denominator b minus x subscript 0 end subscript end fraction greater than 0

therefore f left parenthesis x right parenthesis greater than g left parenthesis x right parenthesis text  for  end text x equals b

In the given figure, if POQ is a diameter of the circle and PR = QR, then RPQ is

In the given figure, if POQ is a diameter of the circle and PR = QR, then RPQ is

parallel

In the given figure, find the values of ‘x’ and ‘y’

In the given figure, find the values of ‘x’ and ‘y’

PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If QPR= ° 35 , then the value of PSR is

PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If QPR= ° 35 , then the value of PSR is

Find the value of ‘x’ in the given figure

Find the value of ‘x’ in the given figure

parallel

In the given figure, find PR

In the given figure, find PR

In the given figure PA, PB, EC, FB, FD and ED are tangents to the circle. If PA=13cm,CE = 4.5cm and EF = 9cm then PF is

In the given figure PA, PB, EC, FB, FD and ED are tangents to the circle. If PA=13cm,CE = 4.5cm and EF = 9cm then PF is

If TP and TQ are the two tangents to a circle with centre ‘O’ such that then $text end text text PTO end text$ , is

If TP and TQ are the two tangents to a circle with centre ‘O’ such that then $text end text text PTO end text$ , is

parallel

Consider a rubber ball freely falling from a height $h equals 4.9 blank m$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time will be

h equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent comma blank

v equals negative g t

and after the collision,

v equals g t

(straight line)
Collision is perfectly elastic then ball reaches to same height again and again with same velocity

Consider a rubber ball freely falling from a height $h equals 4.9 blank m$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time will be

physics-General

h equals fraction numerator 1 over denominator 2 end fraction g t to the power of 2 end exponent comma blank

v equals negative g t

and after the collision,

v equals g t

(straight line)
Collision is perfectly elastic then ball reaches to same height again and again with same velocity

A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its flight if the air resistance is not ignored

For upward motion
Effective acceleration

equals negative open parentheses g plus a close parentheses

And for downward motion
Effective acceleration

equals left parenthesis g minus a right parenthesis

But both are constants. So the slope of speed-time graph will be constant

A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its flight if the air resistance is not ignored

physics-General

For upward motion
Effective acceleration

equals negative open parentheses g plus a close parentheses

And for downward motion
Effective acceleration

equals left parenthesis g minus a right parenthesis

But both are constants. So the slope of speed-time graph will be constant

The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point

Slope is negative at the point

E

The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point

physics-General

Slope is negative at the point

E

parallel

Figure shows the graphical variation of displacement with time for the case of a particle moving along a straight line. The accelerations of the particle during the intervals $O A comma A B comma B C$ and $C D$ are respectively

O A

of the graphs is convex upward. It represents negative acceleration. The portion

A B

represents negative acceleration. The portion

A B

represents that

x

is not changing with time. Clearly, it is a case of zero acceleration. The portion

B C

of the graph is concave upward. It represents positive acceleration. The portion

C D

is a straight line sloping upward to the right. It represents uniform velocity and hence acceleration is zero

Figure shows the graphical variation of displacement with time for the case of a particle moving along a straight line. The accelerations of the particle during the intervals $O A comma A B comma B C$ and $C D$ are respectively

physics-General

O A

of the graphs is convex upward. It represents negative acceleration. The portion

A B

represents negative acceleration. The portion

A B

represents that

x

is not changing with time. Clearly, it is a case of zero acceleration. The portion

B C

of the graph is concave upward. It represents positive acceleration. The portion

C D

is a straight line sloping upward to the right. It represents uniform velocity and hence acceleration is zero

In the following circle, ‘O’ is the centre .If $C A B equals 35 to the power of ring operator end exponent text then end text left floor A B C equals$

In the following circle, ‘O’ is the centre .If $C A B equals 35 to the power of ring operator end exponent text then end text left floor A B C equals$

The length of AC in the figure

The length of AC in the figure

parallel

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