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# Ask a Mathematics(Class XI-XII Tuition (PUC)) Question

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Chandramami 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Solve: y = x sin x?

Sarvajeet replied | 02/12/2016

dy/dx = sin x+x cos x.

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A

Ashwini 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Define differential equation?

Shiva replied | 04/12/2016

A differential equation is an equation which relates functions with their derivatives.

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J

Jayshree 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Solve: x / a + y / b = 1?

Sarvajeet replied | 02/12/2016

-b/a.

Sarvajeet replied | 02/12/2016

dy/dx= -b/a.

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K

Karunanidhi 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Solve: (square of y) = a [(square of b) - (square of x)]?

Sarvajeet replied | 02/12/2016

dy/dx=-ax/y. Where, (square of y) = a [(square of b) - (square of x)].

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M

Manu 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

What is the formula of derivative of sin inverse x?

D Chandra replied | 30/11/2016

d/dx(sin^-1)=1/(root(1-x^2))

Sarvajeet replied | 03/12/2016

1/square root (1-square of x).

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S

Sumit 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

What is the derivative of log x?

P

Prabha replied | 11/12/2016

1/x.

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D

Dr. 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

What do you mean by L. H. L and R. H. L?

Sourabh Sharma replied | 06/12/2016

Left and Right Hand Limit

Sarvajeet replied | 07/12/2016

Left and Right Hand Limit.

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S

Santosh 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Find the rate of change of the area of a circle with respect to its radius r when r = 5 cm?

Sarvajeet replied | 07/12/2016

41.4 cm.

Prassan replied | 08/12/2016

Suppose A is area of circle.A=piXr2
dA/dr=2XpiXr.
=2XpiX5
=2X3.14X5
=31.4. (Ans)

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R

Rajendra 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

The volume of a cube is increasing at the rate of 8 cubic cm/sec. How fast is the surface area increasing when the length of an edge is 12 cm?

Sarvajeet replied | 02/12/2016

(8/3) square cm/sec or 2.6667 square cm/sec.

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V

Vinodha 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

An edge of a variable cube is increasing at the rate of 3 cm per second. How fast is the volume of the cube increasing when the edge if 10 cm long?

Sarvajeet replied | 07/12/2016

900 cube cm per second.

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M

Mahender 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of its circumference?

Sarvajeet replied | 07/12/2016

4.4 cm/s.

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A

Ankit 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

A balloon, which always remains spherical has a variables radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm?

Sarvajeet replied | 26/11/2016

1257.14 cube cm/cm=1257.14 square cm

Tapas replied | 04/12/2016

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A

Ankit 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Differentiate the equation with respect to x: (square of x) + (square of y) = 25?

Sarvajeet replied | 02/12/2016

Differentiation of the equation with respect to x = -x/y.

Tapas replied | 04/12/2016

The given equation: x^2 + y^2 = 25.
Differentiating with respect to x:
2x + 2y(dy/dx) = 0
=> dy/dx = - 2x/2y = - x/y.

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A

Abinaya 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

The radius of an air bubble is increasing at the rate of 1 / 2 cm per second. At what rate is the volume of the bubble increasing when the radius is 1?

Sarvajeet replied | 26/11/2016

6.289 cube cm/sec

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A

Aishwarya 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

A balloon which always remains spherical, has a variable diameter 3 / 2 (2x + 1). Find the rate of change of its volume with respect to x?

Sarvajeet replied | 02/12/2016

-((27.pie)/8) ((2x+1) power(-4)).

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Y

Yusufali 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Determine the continuity of the function: f(x) = sin x + cos x?

Hussam Uddin replied | 22/11/2016

f(x) = sin x - sin (x+ 90), 2 sin (x + 45 ). sin (-45) = -2/sin 45.
sin (x+45) = constant.
sin (x+45 ) which is a continuous function for all values of x.

Siva Naga Raju replied | 22/11/2016

Both sin x and cos x are continuous functions.
The sum or difference of continuous functions is also a continuous function.
Alternate way is multiply and divide the equation by sqrt (2), sin x + cos x can be written as sqrt (2) * sin(x+45).

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M

Maliha 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Determine the continuity of cosine x?

A

Anjali replied | 23/11/2016

It is evident that as h approaches 0, the coordinate of P approach the corresponding coordinate of B.
But by definition we know,
sin(0) = 0 and cos(0) = 1
The values of the functions match with those of the limits as x goes to 0 (Remind the definition of continuity we have).
limx tends to 0 sin(x) = sin(0) = 0 limx tends to 0 cos(x) = cos(0) = 1

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A

Amit 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

What do you mean by the function is strictly increasing and decreasing with respect to continuity?

Rama Krishna replied | 08/12/2016

Dear Student,
Increasing Functions:
A function is "increasing" when the y-value increases as the x-value increases.
Decreasing Functions:
The y-value decreases as the x-value increases.

Ankit replied | 09/12/2016

At no point slope is zero. It is of same symbol throughout the domain.

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S

Selvi 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Find the value of k: f(x) = kx; 3 if x < 2 at x = 2?

S

Srinivas replied | 25/11/2016

Let x--->2 kx=3
k*2=3
k=3/2.

Sarvajeet replied | 07/12/2016

kx=3
2k=3;
k=3/2;

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A

Asif 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Find the value of k: f(x) = kx + 1; 3x - 5 if x < 5 at x = 5?

Ankit replied | 09/12/2016

9/5.

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I

Ishfaque 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Is 3! + 4! = 7!?

Tapas replied | 28/11/2016

No.
3! + 4! = (1x2x3) + (1x2x3x4) = 6 + 24 = 30
But, 7! = 1x2x3x4x5x6x7 = 5040.
So they are different.

Sarvajeet replied | 03/12/2016

No.

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R

Ritu 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?

Abhilash replied | 30/11/2016

5C2 *2! = 20 Out of 5 flags choosing any two will give you a signal. Now these flags can be interchanged (suppose red on top and blue below it, now blue on top and red below it) Hence 2! for this arrangement among these two colours themselves.

Sarvajeet replied | 06/12/2016

20.

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D

Dileep 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Find n, if (n - 1) P (3) : (n) P (4) = 1 : 9?

Eti replied | 21/11/2016

n = 9

Sarvajeet replied | 03/12/2016

9

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V

Vaibhav 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

Find r, if (5) P ® = 2 * (6) P (r - 1)?

Sarvajeet replied | 02/12/2016

3

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T

Thamaraikannan 10/11/2016 in  Mathematics(Class XI-XII Tuition (PUC)),

How many 5 - digit numbers can be constructed using the digits 0 to 9 if each number starts with 76 and no digit appears more than once?

Sarvajeet replied | 26/11/2016

336

Gururaj replied | 28/11/2016

8 x 7 x 6
i.e., 336

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