CBSE > Class 10 > Mathematics | CBSE Board | Homework Help

Diameter of cylindrical pipe = 7 cm
∴ Radius of cylindrical pipe = {tex}\frac { 7 } { 2 }{/tex}cm = 3.5 cm
Volume of water flows in 1 min = 192.5 litres
Volume of water that flows per hour = {tex}( 192.50 \times 60 ){/tex}litres
{tex}= ( 192.50 \times 60 \times 1000 ) \mathrm { cm } ^ { 3 }{/tex} ........(I)
{tex}{/tex} {tex}{/tex}Let h cm be the length of the column of water that flows in one hour.
Clearly, water column forms a cylinder of radius 3.5 cm and length h cm.
{tex}\therefore{/tex} Volume of water that flows in one hour
= πr² h
Volume of the cylinder of radius 3.5 cm and length h cm
{tex}= \left[ \frac { 22 } { 7 } \times ( 3.5 ) ^ { 2 } \times h \right] \mathrm { cm } ^ { 3 }{/tex} ...(ii)
From (i) and (ii), we have
πr²h = 192.50 × 60 × 1000
{tex}\frac { 22 } { 7 } \times 3.5 \times 3.5 \times h = 192.50 \times 60 \times 1000{/tex}
{tex}\Rightarrow \quad h = \frac { 192.50 \times 60 \times 1000 \times 7 } { 22 \times 3.5 \times 3.5 } \mathrm { cm }{/tex} = 300000 cm = 3 km
Hence, the rate of flow of water is 3 km per hour.

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A circle with centre o is inscribed in a right angle triangle abc in which angle b is 90 the circle touches its side ab bc and ac at point P Q and R respectively pb = 2cm find the diameter of the circle

Posted by Ajay Kumar 6 years, 11 months ago

CBSE > Class 10 > Mathematics

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Two vertices of triangle are (1,2) and (3,5). If the centroid of the triangle is at origin, find the coordinates of third vertex.

Posted by Zoya Khan 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let the coordinates of the third vertex be (x, y), Then
Coordinates of centroid of triangle are
{tex}\left( {\frac{{x + 1 + 3}}{3},\frac{{y + 2 + 5}}{3}} \right){/tex}
We have centroid is at origin (0, 0)
{tex}\therefore \frac{{x + 1 + 3}}{3} = 0{/tex} and {tex}\frac{{y + 2 + 5}}{3} = 0{/tex}
{tex}\Rightarrow{/tex} x + 4 = 0 {tex}\Rightarrow{/tex} y + 7 = 0
{tex}\Rightarrow{/tex} x = -4 {tex}\Rightarrow{/tex} y = -7
Hence, the coordinates of the third vertex are (-4, -7).

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2 cos²θ = 3 sin²θ Put the values of θ in given relations and check for which of these values it is true or false θ =30 45 60 90

Posted by Ashwin Patel 6 years, 11 months ago

CBSE > Class 10 > Mathematics

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tan²θ + cot²θ = 2 Put the values of θ in given relations and check for which of these values it is true or false θ=30 ,45,60,90

Posted by Ashwin Patel 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Ashwin Patel 6 years, 11 months ago

2 cos²θ = 3 sin²θ Put the values of θ in given relations and check for which of these values it is true or false θ =30 45 60 90

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Pravin Satyavolu 6 years, 11 months ago

For θ=45°,tan^2θ+Cot^2θ=2.

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If nth term of an ap is 2n+1 what is thw sum of its firts three terms

Posted by Kamal Gupta 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Nishant Dubey 6 years, 11 months ago

Pagal ha tu is the only one who can be in a position to help

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Gaurav Seth 6 years, 11 months ago

If nth term of an A.P = 2n+1

then, first term of A.P = 2(1)+1
= 2+1
= 3

then, second term = 2 (2) + 1

》4+1

》5

third term = 2 (3) +1

》6+1

》7

sum of terms = 3+5+7

sum of terms = 15

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If one zero of polynomial p(x)= (k+4)x2+13 x+3k is reciprocal of the other then find value of k

Posted by Anvika Rana 6 years, 11 months ago

CBSE > Class 10 > Mathematics

3 answers

Anvika Rana 6 years, 11 months ago

Pls give full solution...It will help me understand better☺☺

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Nishant Dubey 6 years, 11 months ago

The image is the only one I could think to do so it is the best I could do to help out the process for this one of those days when we were in our room

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Divya Garg 5 years, 8 months ago

The answer is 8.

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Root 3 sin theta minus cos theta equals to zero then find the value of theta

Posted by Karan Verma 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

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53. Each observation in a raw data is first multiplied by 3, then 6 is added. It is then divided by 3 and subsequently reduced by 6. Which of the following statement is true? (A) the new mean is equal to the original mean (B) the new mean is 4 more than the original mean (C) the new mean is 4 less than the original mean (D) the new mean is 2 more than the original mea

Posted by Jayesh Shrivastav 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

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The slant height of a frustum of a cone is 4 cm and 6 cm .find the curved surface area of the frustum.

Posted by Amit Raj 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Divya Garg 6 years, 11 months ago

Incorrect questions....slant height always remain constant in tue frustum....in this question 2 slant heights are given which is not possible....it may be that the given data is of radius...

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find the value of r

Posted by Arshad Kamar 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Divya Garg 6 years, 11 months ago

Incomplete question...

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The sum of the radii of two circkes is 7cm,and the difference of their circumference is 8cm.find the circumferences of the circles

Posted by Satyam Gupta 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

If secQ + tanQ =.then find the value of cosec Q

Posted by Juhi Kumari 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

If sec theta + tan theta = p , then find cosec theta

Posted by S Sihag Ji 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Abhishek Mishra 6 years, 11 months ago

Sec=1/cos and tan= sin/cos then cos lcm and 1+sin/cos so, 1+sin/cos=p:1+sin=pcos andsin=pcoss-1andsin=1/cosectocosec=1/pcoss-1

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show that an even integer is of the form 6q and 6q+2 for 6q+4 where q is a positive integer

Posted by Rohit Yadav 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Saumya Saini 6 years, 11 months ago

let a be any positive integer then b= 6 a= bq+r 0≤r<b 0≤r<6 r= 0,1,2,3,4,5 case 1. r=0 a= bq+r 6q+0 6q case 2. r=1 a= 6q+1 6q+1 case3. r=2 a=6q+2 case 4. r=3 a=6q+3 case 5 r=4 a=6q+4 case 6.. r=5 a=6q+5 hence from above it is proved that any even positive integer is of the form 6q ,6q+2,6q+4

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If the angle between two tangents drawn from an external point P to a circle of radius a and center O, is 60° then find the lenhth of OP

Posted by Sheshnath Chauhan 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

We know that tangent is always perpendicular to the radius at the point of contact.
So, ∠OAP = 90
We know that if 2 tangents are drawn from an external point, then they are equally inclined to the line segment joining the centre to that point.
So, ∠OPA = 12∠APB = 12{tex}\times{/tex}60° = 30°
According to the angle sum property of triangle-
In ∆AOP, ∠AOP + ∠OAP + ∠OPA = 180°
{tex}\Rightarrow{/tex} ∠AOP + 90° + 30° = 180°
{tex}\Rightarrow{/tex} ∠AOP = 60°
So, in triangle AOP
tan angle AOP = AP/ OA
{tex}\sqrt 3 = \frac{{AP}}{a}{/tex}
therefore, {tex}AP = \sqrt 3 a{/tex}
hence, proved

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Find the nature of roots in the quadratic equation x2-4x-3under root 2

Posted by Shreya Gupta 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

S Sihag Ji 6 years, 11 months ago

Real and diff. root

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A number N When divided by 15 give the reminder is 4 what is the reminder when the same number divided by 15

Posted by Deepshikha Yadav 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Aashu Kumar 6 years, 11 months ago

4?????

2Thank You

S Sihag Ji 6 years, 11 months ago

4Thank You

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Find the least number of square tiles which can cover the floor of a rectangular shape haveing length and breadth 16m and 58cm and 8m 32cm respectively?

Posted by Aashu Kumar 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

ANSWER

Prove that the points (3,0),(6,4),(-1,3)are the vertices of a right angled isosceles triangle

Posted by Suhail Khan 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Given A(3, 0), B(6, 4) and C(-1, 3)

AB² = (3 - 6)² + (0 - 4)² = 9 + 16 = 25
BC² = (6 + 1)² + (4 - 3)² = 49 + 1 = 50
CA² = (-1 - 3)² + (3 - 0)² = 16 + 9 = 25
AB² = CA² or, AB = CA
Triangle is isoceles
Also, 25 + 25 = 50
or, AB² + CA² = BC²
Since, pythagoras theorem is verified, therefore triangle is right-angled triangle.

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How value of h will be calculated in step deviation method of statistics if class interval is not uniform or same?

Posted by Jitendra Dangra 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Garima Bhardwaj 6 years, 11 months ago

we could not use step deviation when h is not uniform.

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In a triangle ABC a circle is drawn with AB as the diameter which interscet hypoteneus AC at point P Prove PB =PC

Posted by Aditya Raj 6 years, 11 months ago

CBSE > Class 10 > Mathematics

0 answers

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How to solve sin theotta+ cos thetta

Posted by Nandana Santhosh 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Divya Garg 6 years, 11 months ago

Sin theta+cos theta is in the simplest form. It cannot be simplified furthur.....

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If tan A= ntan B and sin A= msinB , then prove that cos squre A = m square -1 / n square -1

Posted by Anjali Singh 5 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Given,
tan A = n tan B
{tex} \Rightarrow{/tex} tanB = {tex}\frac{1}{n}{/tex}tan A
{tex}\Rightarrow{/tex} cotB = {tex}\frac { n } { \tan A }{/tex}..........(1)
Also given,
sin A = m sin B
{tex}\Rightarrow{/tex} sin B = {tex}\frac{1}{m}{/tex}sin A
{tex}\Rightarrow{/tex} cosec B = {tex}\frac { m } { \sin A }{/tex}.....(2)
We know that, cosec²B - cot²B = 1, hence from (1) & (2) :-
{tex} \quad \frac { m ^ { 2 } } { \sin ^ { 2 } A } - \frac { n ^ { 2 } } { \tan ^ { 2 } A } = 1{/tex}
{tex}\Rightarrow \quad \frac { m ^ { 2 } } { \sin ^ { 2 } A } - \frac { n ^ { 2 } \cos ^ { 2 } A } { \sin ^ { 2 } A } = 1{/tex}
{tex}\Rightarrow \quad \frac { m ^ { 2 } - n ^ { 2 } \cos ^ { 2 } A } { \sin ^ { 2 } A } = 1{/tex}
{tex}\Rightarrow{/tex} m² - n²cos²A = sin²A
{tex}\Rightarrow{/tex} m² - n²cos²A = 1 - cos²A
{tex}\Rightarrow{/tex} m² - 1 = n²cos²A - cos²A
{tex}\Rightarrow{/tex} m² - 1 = (n² - 1) cos²A
{tex}\Rightarrow \quad \frac { m ^ { 2 } - 1 } { n ^ { 2 } - 1 } ={/tex} cos²A