Maths-

General

Easy

Question

If f(x) is a polynomial of degree five with leading coefficient one such that f(1)=1²,f(2)=2²,f(3)=3²,f(4)=4²,f(5)=5² then

f(6)= 156
$\lim_{x \to \infty} (\frac{f (x)}{x^{5}})$
f(0) $<$ 0
f(0) $>$ 0

The correct answer is: f(6)= 156

$f left parenthesis x right parenthesis minus x to the power of 2 end exponent equals left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis left parenthesis x minus 4 right parenthesis left parenthesis x minus 5$

If f(x) = ax²+ bx + c such that f(p) + f(q) = 0 where a $not equal to$ 0 ; p , q $element of$ R then number of real roots of equation f(x) = 0in interval [p, q] is

f(p)=–f(q)

rightwards double arrow

eitherf(p)f(q)<0 or f(p) =0=f(q)

rightwards double arrow

exactlyonerootin(p,q) orrootsarepandq

If f(x) = ax²+ bx + c such that f(p) + f(q) = 0 where a $not equal to$ 0 ; p , q $element of$ R then number of real roots of equation f(x) = 0in interval [p, q] is

maths-General

f(p)=–f(q)

rightwards double arrow

eitherf(p)f(q)<0 or f(p) =0=f(q)

rightwards double arrow

exactlyonerootin(p,q) orrootsarepandq

General

maths-

If f(x) is a differentiable function satisfying f(x+ y)= f(x)f(y) $straight for all$ x, y $element of$ R and f'(0)=2 then f(x)=

table row cell f left parenthesis x plus y right parenthesis equals f left parenthesis x right parenthesis f left parenthesis y right parenthesis         rightwards double arrow         f left parenthesis x right parenthesis equals k e to the power of x f left parenthesis 0 right parenthesis end exponent text end text text w end text text h end text text e end text text r end text text e end text text end text k text end text text i end text text s end text text end text text a end text text end text text c end text text o end text text n end text text s end text text t end text text a end text text n end text text t end text text end text end cell row cell text end text text A end text text s end text text end text f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 2         rightwards double arrow         k equals 1 rightwards double arrow f left parenthesis x right parenthesis equals e to the power of 2 x end exponent end cell end table rightwards double arrow f left parenthesis x right parenthesis equals k e to the power of 2 x end exponent

If f(x) is a differentiable function satisfying f(x+ y)= f(x)f(y) $straight for all$ x, y $element of$ R and f'(0)=2 then f(x)=

maths-General

table row cell f left parenthesis x plus y right parenthesis equals f left parenthesis x right parenthesis f left parenthesis y right parenthesis         rightwards double arrow         f left parenthesis x right parenthesis equals k e to the power of x f left parenthesis 0 right parenthesis end exponent text end text text w end text text h end text text e end text text r end text text e end text text end text k text end text text i end text text s end text text end text text a end text text end text text c end text text o end text text n end text text s end text text t end text text a end text text n end text text t end text text end text end cell row cell text end text text A end text text s end text text end text f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 2         rightwards double arrow         k equals 1 rightwards double arrow f left parenthesis x right parenthesis equals e to the power of 2 x end exponent end cell end table rightwards double arrow f left parenthesis x right parenthesis equals k e to the power of 2 x end exponent

General

physics-

Maximum kinetic energy (E_k ) of a photoelectron varies with the frequency ( v ) of the incident radiation as

physics-General

General

maths-

The degree of the differential equation satisfying $square root of 1 plus x squared end root plus square root of 1 plus y squared end root equals A open parentheses x square root of 1 plus y squared end root minus y square root of 1 plus x squared end root close parentheses$ is

maths-General

General

Maths-

If $x fraction numerator d y over denominator d x end fraction equals y left parenthesis log space y minus log space x plus 1 right parenthesis$ then the solution of the equation is :

Maths-General

General

physics-

A simple magnifying lens is used in such a way that an image is formed at 25 cm away from the eye. In order to have 10 times magnification, the focal length of the lens should be

fraction numerator D over denominator F end fraction

fraction numerator 25 over denominator F end fraction

A simple magnifying lens is used in such a way that an image is formed at 25 cm away from the eye. In order to have 10 times magnification, the focal length of the lens should be

physics-General

fraction numerator D over denominator F end fraction

fraction numerator 25 over denominator F end fraction

General

Maths-

The differential equation of all circles which pass through the origin and whose centres lie on y-axis is

Maths-General

General

maths-

Let p, q $element of$ {1,2,3,4}.Then number of equation of the form px²+qx+1=0,having real roots ,is

q2–4p

greater or equal than

0
q=2

rightwards double arrow

p=1
q=3

rightwards double arrow

p=1,2
q=4

rightwards double arrow

p=1,2,3,4
Hence 7 values of (p, q)7equationsarepossible.

Let p, q $element of$ {1,2,3,4}.Then number of equation of the form px²+qx+1=0,having real roots ,is

maths-General

q2–4p

greater or equal than

0
q=2

rightwards double arrow

p=1
q=3

rightwards double arrow

p=1,2
q=4

rightwards double arrow

p=1,2,3,4
Hence 7 values of (p, q)7equationsarepossible.

General

maths-

Number of values of 'p' for which the equation $open parentheses p squared minus 3 p plus 2 close parentheses x squared minus open parentheses p squared minus 5 p plus 4 close parentheses x plus p minus p squared equals 0$ possess more than two roots ,is:

For (p2– 3p+2)x2–(p2–5p+4)x+p–p2=0tobe anidentity
p2–3p+2 =0

rightwards double arrow

p = 1, 2...(i)
p2 – 5p + 4 = 0

rightwards double arrow

p = 1, 4...(ii)
p – p2 = 0

rightwards double arrow

p = 0, 1...(iii)
For (i), (ii) & (iii) to hold simultaneously p = 1.

Number of values of 'p' for which the equation $open parentheses p squared minus 3 p plus 2 close parentheses x squared minus open parentheses p squared minus 5 p plus 4 close parentheses x plus p minus p squared equals 0$ possess more than two roots ,is:

maths-General

For (p2– 3p+2)x2–(p2–5p+4)x+p–p2=0tobe anidentity
p2–3p+2 =0

rightwards double arrow

p = 1, 2...(i)
p2 – 5p + 4 = 0

rightwards double arrow

p = 1, 4...(ii)
p – p2 = 0

rightwards double arrow

p = 0, 1...(iii)
For (i), (ii) & (iii) to hold simultaneously p = 1.

General

maths-

Statement-1- The number $blank to the power of 1000 end exponent C subscript 500 end subscript$ is not divisible by 11.Because
Statement-2- If p is a prime, the exponent of p in n! is $open square brackets fraction numerator n over denominator p end fraction close square brackets$ + $open square brackets fraction numerator n over denominator p to the power of 2 end exponent end fraction close square brackets$ + $open square brackets fraction numerator n over denominator p to the power of 3 end exponent end fraction close square brackets$ +……Where [x] denotes the greatest integer $less or equal than$ x.

maths-General

General

physics-

According to Newton’s law of cooling, the rate of cooling is proportional to $open parentheses increment theta close parentheses to the power of n end exponent$ , where $increment theta$ is the temperature differences between the body and the surroundings and $n$ is equal to

According to Newton’s law of cooling the rate of loss of heat of a body is directly proportional to the difference in temperature of the body,

i e comma

negative fraction numerator d Q over denominator d t end fraction proportional to left parenthesis increment theta right parenthesis

(i)
Given,

negative fraction numerator d Q over denominator d t end fraction proportional to open parentheses increment theta close parentheses to the power of n end exponent

(ii)
Comparing Eqs. (i) and (ii), we get

n

According to Newton’s law of cooling, the rate of cooling is proportional to $open parentheses increment theta close parentheses to the power of n end exponent$ , where $increment theta$ is the temperature differences between the body and the surroundings and $n$ is equal to

physics-General

According to Newton’s law of cooling the rate of loss of heat of a body is directly proportional to the difference in temperature of the body,

i e comma

negative fraction numerator d Q over denominator d t end fraction proportional to left parenthesis increment theta right parenthesis

(i)
Given,

negative fraction numerator d Q over denominator d t end fraction proportional to open parentheses increment theta close parentheses to the power of n end exponent

(ii)
Comparing Eqs. (i) and (ii), we get

n

General

Maths-

$text If end text y equals e to the power of 4 x end exponent plus 2 e to the power of negative x end exponent$ satisfies the relation $fraction numerator d cubed y over denominator d x cubed end fraction plus A fraction numerator d y over denominator d x end fraction plus B y equals 0$ then value of A and B respectively are:

Maths-General

General

physics-

Radius of a conductor increases uniformly from left end to right end as shown in fig Material of the conductor is isotropic and its curved surface is thermally insulated from surrounding. Its ends are maintained at temperatures $T subscript 1 end subscript$ and $T subscript 2 end subscript left parenthesis T subscript 1 end subscript greater than T subscript 2 end subscript right parenthesis$ : If, in steady state, heat flow rate is equal to $H$ , then which of the following graphs is correct

Since the curved surface of the conductor is thermally insulated, therefore, in steady state, the rate of flow of heat at every section will be the same. Hence the curve between

H

and

x

will be straight line parallel to

x

-axis

Radius of a conductor increases uniformly from left end to right end as shown in fig Material of the conductor is isotropic and its curved surface is thermally insulated from surrounding. Its ends are maintained at temperatures $T subscript 1 end subscript$ and $T subscript 2 end subscript left parenthesis T subscript 1 end subscript greater than T subscript 2 end subscript right parenthesis$ : If, in steady state, heat flow rate is equal to $H$ , then which of the following graphs is correct

physics-General

Since the curved surface of the conductor is thermally insulated, therefore, in steady state, the rate of flow of heat at every section will be the same. Hence the curve between

H

and

x

will be straight line parallel to

x

-axis

General

physics-

Water and turpentine oil (specific heat less than that of water) are both heated to same temperature. Equal amounts of these placed in identical calorimeters are then left in air

As we know, Rate of cooling

proportional to fraction numerator 1 over denominator s p e c i f i c blank h e a t left square bracket c right square bracket end fraction

because c subscript o i l end subscript less than c subscript W a t e r end subscript

rightwards double arrow open parentheses R a t e blank o f blank c o o l i n g close parentheses subscript o i l end subscript greater than open parentheses R a t e blank o f blank c o o l i n g close parentheses subscript W a t e r end subscript

It is clear that, at a particular time after start cooling, temperature of oil will be less than that of water
So graph

B

represents the cooling curve of oil and

A

represents the cooling curve of water

Water and turpentine oil (specific heat less than that of water) are both heated to same temperature. Equal amounts of these placed in identical calorimeters are then left in air

physics-General

As we know, Rate of cooling

proportional to fraction numerator 1 over denominator s p e c i f i c blank h e a t left square bracket c right square bracket end fraction

because c subscript o i l end subscript less than c subscript W a t e r end subscript

rightwards double arrow open parentheses R a t e blank o f blank c o o l i n g close parentheses subscript o i l end subscript greater than open parentheses R a t e blank o f blank c o o l i n g close parentheses subscript W a t e r end subscript

It is clear that, at a particular time after start cooling, temperature of oil will be less than that of water
So graph

B

represents the cooling curve of oil and

A

represents the cooling curve of water

General

physics-

Variation of radiant energy emitted by sun, filament of tungsten lamp and welding are as a function of its wavelength is shown in figure. Which of the following option is the correct match?

lambda subscript m end subscript T equals c o n s t a n t

From the graph

T subscript 3 end subscript greater than T subscript 2 end subscript greater than T subscript 1 end subscript

Temperature of sun will be maximum

Variation of radiant energy emitted by sun, filament of tungsten lamp and welding are as a function of its wavelength is shown in figure. Which of the following option is the correct match?

physics-General

lambda subscript m end subscript T equals c o n s t a n t

From the graph

T subscript 3 end subscript greater than T subscript 2 end subscript greater than T subscript 1 end subscript

Temperature of sun will be maximum

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If f(x) is a polynomial of degree five with leading coefficient one such that f(1)=12,f(2)=22,f(3)=32,f(4)=42,f(5)=52 then

f(6)= 156 f(0)0 f(0)0

The correct answer is: f(6)= 156

Related Questions to study

If f(x) = ax2+ bx + c such that f(p) + f(q) = 0 where a0 ; p , qR then number of real roots of equation f(x) = 0in interval [p, q] is

If f(x) = ax2+ bx + c such that f(p) + f(q) = 0 where a0 ; p , qR then number of real roots of equation f(x) = 0in interval [p, q] is

If f(x) is a differentiable function satisfying f(x+ y)= f(x)f(y) x, y R and f'(0)=2 then f(x)=

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Maximum kinetic energy (Ek ) of a photoelectron varies with the frequency ( v ) of the incident radiation as

Maximum kinetic energy (Ek ) of a photoelectron varies with the frequency ( v ) of the incident radiation as

The degree of the differential equation satisfying is

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If then the solution of the equation is :

If then the solution of the equation is :

A simple magnifying lens is used in such a way that an image is formed at 25 cm away from the eye. In order to have 10 times magnification, the focal length of the lens should be

A simple magnifying lens is used in such a way that an image is formed at 25 cm away from the eye. In order to have 10 times magnification, the focal length of the lens should be

The differential equation of all circles which pass through the origin and whose centres lie on y-axis is

The differential equation of all circles which pass through the origin and whose centres lie on y-axis is

Let p, q{1,2,3,4}.Then number of equation of the form px2+qx+1=0,having real roots ,is

Let p, q{1,2,3,4}.Then number of equation of the form px2+qx+1=0,having real roots ,is

Number of values of 'p' for which the equation possess more than two roots ,is:

Number of values of 'p' for which the equation possess more than two roots ,is:

Statement-1- The number is not divisible by 11.BecauseStatement-2- If p is a prime, the exponent of p in n! is + + +……Where [x] denotes the greatest integer x.

Statement-1- The number is not divisible by 11.BecauseStatement-2- If p is a prime, the exponent of p in n! is + + +……Where [x] denotes the greatest integer x.

According to Newton’s law of cooling, the rate of cooling is proportional to , where is the temperature differences between the body and the surroundings and is equal to

According to Newton’s law of cooling, the rate of cooling is proportional to , where is the temperature differences between the body and the surroundings and is equal to

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Water and turpentine oil (specific heat less than that of water) are both heated to same temperature. Equal amounts of these placed in identical calorimeters are then left in air

Water and turpentine oil (specific heat less than that of water) are both heated to same temperature. Equal amounts of these placed in identical calorimeters are then left in air

Variation of radiant energy emitted by sun, filament of tungsten lamp and welding are as a function of its wavelength is shown in figure. Which of the following option is the correct match?

Variation of radiant energy emitted by sun, filament of tungsten lamp and welding are as a function of its wavelength is shown in figure. Which of the following option is the correct match?

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If f(x) is a polynomial of degree five with leading coefficient one such that f(1)=1²,f(2)=2²,f(3)=3²,f(4)=4²,f(5)=5² then

f(6)= 156
$\lim_{x \to \infty} (\frac{f (x)}{x^{5}})$
f(0) $<$ 0
f(0) $>$ 0

If f(x) = ax²+ bx + c such that f(p) + f(q) = 0 where a $not equal to$ 0 ; p , q $element of$ R then number of real roots of equation f(x) = 0in interval [p, q] is

If f(x) = ax²+ bx + c such that f(p) + f(q) = 0 where a $not equal to$ 0 ; p , q $element of$ R then number of real roots of equation f(x) = 0in interval [p, q] is

If f(x) is a differentiable function satisfying f(x+ y)= f(x)f(y) $straight for all$ x, y $element of$ R and f'(0)=2 then f(x)=

If f(x) is a differentiable function satisfying f(x+ y)= f(x)f(y) $straight for all$ x, y $element of$ R and f'(0)=2 then f(x)=

Maximum kinetic energy (E_k ) of a photoelectron varies with the frequency ( v ) of the incident radiation as

Maximum kinetic energy (E_k ) of a photoelectron varies with the frequency ( v ) of the incident radiation as

The degree of the differential equation satisfying $square root of 1 plus x squared end root plus square root of 1 plus y squared end root equals A open parentheses x square root of 1 plus y squared end root minus y square root of 1 plus x squared end root close parentheses$ is

The degree of the differential equation satisfying $square root of 1 plus x squared end root plus square root of 1 plus y squared end root equals A open parentheses x square root of 1 plus y squared end root minus y square root of 1 plus x squared end root close parentheses$ is

If $x fraction numerator d y over denominator d x end fraction equals y left parenthesis log space y minus log space x plus 1 right parenthesis$ then the solution of the equation is :

If $x fraction numerator d y over denominator d x end fraction equals y left parenthesis log space y minus log space x plus 1 right parenthesis$ then the solution of the equation is :

Let p, q $element of$ {1,2,3,4}.Then number of equation of the form px²+qx+1=0,having real roots ,is

Let p, q $element of$ {1,2,3,4}.Then number of equation of the form px²+qx+1=0,having real roots ,is

Number of values of 'p' for which the equation $open parentheses p squared minus 3 p plus 2 close parentheses x squared minus open parentheses p squared minus 5 p plus 4 close parentheses x plus p minus p squared equals 0$ possess more than two roots ,is:

Number of values of 'p' for which the equation $open parentheses p squared minus 3 p plus 2 close parentheses x squared minus open parentheses p squared minus 5 p plus 4 close parentheses x plus p minus p squared equals 0$ possess more than two roots ,is:

According to Newton’s law of cooling, the rate of cooling is proportional to $open parentheses increment theta close parentheses to the power of n end exponent$ , where $increment theta$ is the temperature differences between the body and the surroundings and $n$ is equal to

According to Newton’s law of cooling, the rate of cooling is proportional to $open parentheses increment theta close parentheses to the power of n end exponent$ , where $increment theta$ is the temperature differences between the body and the surroundings and $n$ is equal to