Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

If $x y equals c to the power of 2 end exponent$ , then minimum value of $a x plus b y$ is

$c \sqrt{a b}$
$2 c \sqrt{a b}$
$- c \sqrt{a b}$
$- 2 c \sqrt{a b}$

The correct answer is: $2 c square root of a b end root$

Given curve is
$x y equals c to the power of 2 end exponent blank rightwards double arrow y equals fraction numerator c to the power of 2 end exponent over denominator x to the power of 2 end exponent end fraction$

Let $f open parentheses x close parentheses equals a x plus b y equals a x plus fraction numerator b c to the power of 2 end exponent over denominator x to the power of 2 end exponent end fraction$

On differentiating w.r.t. $x$ , we get

$f to the power of ´ end exponent open parentheses x close parentheses equals a minus fraction numerator b c to the power of 2 end exponent over denominator x to the power of 2 end exponent end fraction$

For a maximum or minima, put $f to the power of ´ end exponent open parentheses x close parentheses equals 0$

$rightwards double arrow blank a x to the power of 2 end exponent minus b c to the power of 2 end exponent equals 0$

$rightwards double arrow blank x to the power of 2 end exponent equals fraction numerator b c to the power of 2 end exponent over denominator a end fraction blank rightwards double arrow blank x equals plus-or-minus c square root of fraction numerator b over denominator a end fraction end root$

Again on differentiating, we get $f to the power of ´ ´ end exponent open parentheses x close parentheses equals fraction numerator 2 b c to the power of 2 end exponent over denominator x to the power of 3 end exponent end fraction$

At6 $x equals c square root of fraction numerator b over denominator a end fraction end root comma blank f to the power of ´ ´ end exponent open parentheses x close parentheses greater than 0$

$therefore blank f open parentheses x close parentheses$ is minimum at $x equals c square root of fraction numerator b over denominator a end fraction end root$

The minimum value at $x equals c square root of fraction numerator b over denominator a end fraction end root$ is

$therefore blank f open parentheses c square root of fraction numerator b over denominator a end fraction end root close parentheses equals a. c square root of fraction numerator b over denominator a end fraction end root plus fraction numerator b c to the power of 2 end exponent over denominator c end fraction. blank square root of fraction numerator a over denominator b end fraction end root$

$equals fraction numerator a b c plus a b c over denominator square root of a b end root end fraction equals fraction numerator 2 a b c over denominator square root of a b end root end fraction equals 2 c square root of a b end root$

Related Questions to study

A function $f$ is defined by $f open parentheses x close parentheses equals e to the power of x end exponent sin invisible function application x$ in $left square bracket 0 comma blank pi right square bracket$ . Which of the following is not correct?

A function $f$ is defined by $f open parentheses x close parentheses equals e to the power of x end exponent sin invisible function application x$ in $left square bracket 0 comma blank pi right square bracket$ . Which of the following is not correct?

On the interval [0, 1] the function $x to the power of 25 end exponent open parentheses 1 minus x close parentheses to the power of 75 end exponent$ takes its maximum value at the point

On the interval [0, 1] the function $x to the power of 25 end exponent open parentheses 1 minus x close parentheses to the power of 75 end exponent$ takes its maximum value at the point

The function which is neither decreasing nor increasing in $open parentheses fraction numerator pi over denominator 2 end fraction comma fraction numerator 3 pi over denominator 2 end fraction close parentheses$ , is

The function which is neither decreasing nor increasing in $open parentheses fraction numerator pi over denominator 2 end fraction comma fraction numerator 3 pi over denominator 2 end fraction close parentheses$ , is

parallel

The angle between the curves $y equals a to the power of x end exponent$ and $y equals b to the power of x end exponent$ is equal to

The angle between the curves $y equals a to the power of x end exponent$ and $y equals b to the power of x end exponent$ is equal to

If $g open parentheses x close parentheses equals min invisible function application left parenthesis x comma blank x to the power of 2 end exponent right parenthesis$ where $x$ is real number, then

If $g open parentheses x close parentheses equals min invisible function application left parenthesis x comma blank x to the power of 2 end exponent right parenthesis$ where $x$ is real number, then

The coefficient of mutual inductance of two coils is $6 blank m H$ . If the current flowing in one is $2 blank a m p e r e$ , then the induced e.m.f. in the second coil will be

The coefficient of mutual inductance of two coils is $6 blank m H$ . If the current flowing in one is $2 blank a m p e r e$ , then the induced e.m.f. in the second coil will be

Physics-General

parallel

The resistance and inductance of series circuit are $5 capital omega$ and $20 H$ respectively. At the instant of closing the switch, the current is increasing at the rate $4 A divided by s$ . The supply voltage is

The resistance and inductance of series circuit are $5 capital omega$ and $20 H$ respectively. At the instant of closing the switch, the current is increasing at the rate $4 A divided by s$ . The supply voltage is

Physics-General

In the circuit shown below, the key $K$ is closed at $t equals 0$ . The current through the battery is

In the circuit shown below, the key $K$ is closed at $t equals 0$ . The current through the battery is

Physics-General

A coil of $N$ turns and mean cross-sectional area $A$ is rotating with uniform angular velocity $omega$ about an axis at right angle to uniform magnetic field $B$ . The induced e.m.f. $E$ in the coil will be

A coil of $N$ turns and mean cross-sectional area $A$ is rotating with uniform angular velocity $omega$ about an axis at right angle to uniform magnetic field $B$ . The induced e.m.f. $E$ in the coil will be

Physics-General

parallel

An aluminium ring $B$ faces an electromagnet $A$ . The current $I$ through $A$ can be altered

An aluminium ring $B$ faces an electromagnet $A$ . The current $I$ through $A$ can be altered

Physics-General

The adjoining figure shows two bulbs $B subscript 1 end subscript$ and $B subscript 2 end subscript$ , resistor $R$ and an inductor $L$ . When the switch $S$ is turned off

The adjoining figure shows two bulbs $B subscript 1 end subscript$ and $B subscript 2 end subscript$ , resistor $R$ and an inductor $L$ . When the switch $S$ is turned off

Physics-General

A step-down transformer is connected to $2400 blank v o l t s$ line and 80 amperes of current is found to flow in output load. The ratio of the turns in primary and secondary coil is 20:1. If transformer efficiency is 100%, then the current flowing in primary coil will be

A step-down transformer is connected to $2400 blank v o l t s$ line and 80 amperes of current is found to flow in output load. The ratio of the turns in primary and secondary coil is 20:1. If transformer efficiency is 100%, then the current flowing in primary coil will be

Physics-General

parallel

When a magnet is pushed in and out of a circular coil $C$ connected to a very senstitive galvanometer $G$ as shown in the adjoining diagram with a frequency $v$ , then

When a magnet is pushed in and out of a circular coil $C$ connected to a very senstitive galvanometer $G$ as shown in the adjoining diagram with a frequency $v$ , then

Physics-General

The mutual inductance between a primary and secondary circuits is $0.5 blank H$ . The resistances of the primary and the secondary circuits are $20 blank o h m s$ and $5 blank o h m s$ respectively. To generate a current of $0.4 blank A$ in the secondary, current in the primary must be changed at the rate of

The mutual inductance between a primary and secondary circuits is $0.5 blank H$ . The resistances of the primary and the secondary circuits are $20 blank o h m s$ and $5 blank o h m s$ respectively. To generate a current of $0.4 blank A$ in the secondary, current in the primary must be changed at the rate of

Physics-General

A metallic ring is dropped down, keeping its plane perpendicular to a constant and horizontal magnetic field. The ring enters the region of magnetic field at $t equals 0$ and completely emerges out at $t equals T s e c.$ The current in the ring varies as

A metallic ring is dropped down, keeping its plane perpendicular to a constant and horizontal magnetic field. The ring enters the region of magnetic field at $t equals 0$ and completely emerges out at $t equals T s e c.$ The current in the ring varies as

Physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.