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Prakash 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Determine the A.p whose third term is 16 and the difference of 5th from 7th term is 12?

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Chandan replied | 22/11/2016

an= a+(n-1)d
an=10+(30-1)*(-3)
=10-87=-77
30th term is -77

a + (3 ? 1) d = 16
a + 2d = 16 ... (i)
a7 ? a5 = 12
[a+ (7 ? 1) d] ? [a + (5 ? 1) d]= 12
(a + 6d) ? (a + 4d) = 12
2d = 12
d = 6
From equation (i), we get,
a + 2 (6) = 16
a + 12 = 16
a = 4
Therefore, A.P. will be
4, 10, 16, 22, …

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Granth 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

The sum of the first six terms of an A.p is zero and the fourth term is 2. Find the sum of its first 30 terms?

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Tapas replied | 01/12/2016

Let the first term be (a - 5b) and the common difference be 2b.
So the six terms are: (a - 5b), (a - 3b), (a - b), (a + b), (a + 3b), (a + 5b).
By the given conditions:-
Sum of six terms = (a - 5b) + (a - 3b) + (a - b) + (a + b) + (a + 3b) + (a + 5b) = 6a = 0.
So, a = 0.
The fourth term=a + b=2 --> 0 + b=2 --> b = 2.
So, for the A.P. the first term...  more»
Let the first term be (a - 5b) and the common difference be 2b.
So the six terms are: (a - 5b), (a - 3b), (a - b), (a + b), (a + 3b), (a + 5b).
By the given conditions:-
Sum of six terms = (a - 5b) + (a - 3b) + (a - b) + (a + b) + (a + 3b) + (a + 5b) = 6a = 0.
So, a = 0.
The fourth term=a + b=2 --> 0 + b=2 --> b = 2.
So, for the A.P. the first term x = (a - 5b) = -10. The common difference, y = 2b = 4.
Sum of 1st 30 terms, S30 = (n/2)[2x + (n-1)y] = 15 x [ -20 + 29 x 4] = 1440. (Answer) «less

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Supriyo 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

An A.P consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term?

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Tapas replied | 01/12/2016

Let the first term be a and the common difference be b. So,
t1 = a = 7 and t60 = a + 59b = 125.
From above, we get:-
t60 - t1 = 59b = 125 - 7 = 118.
So, b = 118/59 = 2.
Hence, the 32nd term, t32 = a + 31b = =7 + 31x2 = 69. (Answer)

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N

Nitesh 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers?

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Tapas replied | 01/12/2016

Let the 3 terms are (a - b), a, and (a + b).
So,
(a - b) + a + ( a + b) = 27
=> 3a = 27
=> a = 9.
Now the product is 648. So,
(9 - b) x 9 x (9 + b) = 648
=> (81 - b^2) = 648/9 = 72
=> b^2 = 81 - 72 = 9
=> b = =3 or b = -3.
For, b = 3, the numbers are:
(9 - 3), 9, (9 + 3) = 6, 9, 12
or
(9 - (-3)), 9 , (9 + (-3)) = 12, 9, 6
The...  more»
Let the 3 terms are (a - b), a, and (a + b).
So,
(a - b) + a + ( a + b) = 27
=> 3a = 27
=> a = 9.
Now the product is 648. So,
(9 - b) x 9 x (9 + b) = 648
=> (81 - b^2) = 648/9 = 72
=> b^2 = 81 - 72 = 9
=> b = =3 or b = -3.
For, b = 3, the numbers are:
(9 - 3), 9, (9 + 3) = 6, 9, 12
or
(9 - (-3)), 9 , (9 + (-3)) = 12, 9, 6
The three numbers are 6, 9, 12 or 12, 9, 6 (Answer) «less

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A

Anmol 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Write the first four terms of the A.p, when the first term a and the common difference d are given: a = 10, d = 10?

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Tapas replied | 01/12/2016

The first four terms are 10, 10 + 10, 10 + 2x10, and 10 + 3x10.
So, the terms are: 10, 20, 30, 40.

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S

Samskriti 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

For the given A.P write the first term and the common difference: 3, 1, -1, -3, …..?

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Tapas replied | 01/12/2016

The first term is 3.
The common difference = 1-3 = -2.

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R

Ramya 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

What is the 30th term of a given A.P: 10, 7, 4,....?

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Chandan replied | 22/11/2016

a3 = 16

a + (3 ? 1) d = 16
a + 2d = 16 ... (i)
a7 ? a5 = 12
[a+ (7 ? 1) d] ? [a + (5 ? 1) d]= 12
(a + 6d) ? (a + 4d) = 12
2d = 12
d = 6
From equation (i), we get,
a + 2 (6) = 16
a + 12 = 16
a = 4
Therefore, A.P. will be
4, 10, 16, 22, …

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S

Sarvepalli 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

Which term of the A.P: 3, 8, 13, 18, ……, is 78?

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Chandan replied | 22/11/2016

tn = a + (n - 1) d
78 = 3 + (n - 1)5
78 = 3 + 5n - 5
78 = - 2 + 5n
78 + 2 = 5n
80 = 5n
80/5 = n
16 = n
n= 16

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K

Krity 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

The 17th term of an A.P exceeds its 10th term by 7. Find the common difference?

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Sarvajeet replied | 23/11/2016

1.

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S

Shreyansh 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Progressions

If the 3rd and the 9th terms of an A.P are 4 and -8 respectively, which term of this A.P is zero?

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Tapas replied | 01/12/2016

Let the first term and the common difference are a and b.
So, the third term: t3 = a + 2b = 4.
and, the 9th term: t9 = a + 8b = -8.

So, t9 - t6=6b = -8 - 4=-12 --> b = - 2.

So, from the expression of t3, we get:
a = 4 - 2b = 4 + 4 = 8.

Let us consider that the nth term is zero. So:

tn = a + (n-1)b = 0 --> 8 + (n-1)(-2)...  more»
Let the first term and the common difference are a and b.
So, the third term: t3 = a + 2b = 4.
and, the 9th term: t9 = a + 8b = -8.

So, t9 - t6=6b = -8 - 4=-12 --> b = - 2.

So, from the expression of t3, we get:
a = 4 - 2b = 4 + 4 = 8.

Let us consider that the nth term is zero. So:

tn = a + (n-1)b = 0 --> 8 + (n-1)(-2) = 0 --> 8 -2n +2 = 0 --> 2n=10 --> n = 5.

Answer: The 5th term of the series is zero. «less

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M

Melvin 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Volumes

A solid cylinder has a total surface area of 213 sq. cm. Its curved surface area 2/3 of the total surface area. Find the volume of the cylinder?

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Tapas replied | 30/11/2016

Please see the attachment:

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Answer

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A

Ankita 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Volumes

The dimensions of a cuboid are in the ratio 1 : 2 : 3 and its total surface area is 88 sq. m. Find the dimensions?

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Sarvajeet replied | 23/11/2016

2, 4, 6.

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G

Girija Sankar 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Volumes

Find the longest pole length that can be put in a room of 10 m * 10 m * 5 m dimensions?

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Tapas replied | 30/11/2016

The longest pole has the length equal to the principal diagonal of the rectangular room (box).
So, the length = Sq. root ( 10^2 + 10^2 + 5^2) = sq. root (225) = 15 m
Answer: The longest pole length is 15 m.

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S

Saurabh replied | 01/12/2016

15 m

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Answer

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C

Chiranjib 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Volumes

A circus tent consists of cylindrical base surmounted by a conical roof. The radius of the cylinder is 20 m. The height of the tent is 63 m and that of the cone is 21 m. Find the volume of the tent and the area of the canvas used for making it?

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Tapas replied | 30/11/2016

Please see the attachment.

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Answer

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V

Vivek 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Volumes

The volume of two hemispheres are in the ratio 8: 27. Find the ratio of their radii?

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Sarvajeet replied | 23/11/2016

2 : 3.

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P

Pankaj 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Volumes

Find the volume of a cube whose total surface area is 486 sq. cm?

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Tapas replied | 30/11/2016

Please see the attachment.

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Answer

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S

Sajini 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Volumes

The length of a cinema hall is 20 m and breadth is 16 m. the sum of the areas of floor and flat roof is equal to the area of four walls. Find the height and volume of the hall?

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Tapas replied | 30/11/2016

Please see the attachment.

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Answer

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A

Ajit 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Volumes

Find the volume of a sphere whose radius is 2.1 cm?

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Suyash replied | 19/11/2016

Volume = 4/3 ?r^3
= 4/3 ? 2.1^3
= 388.08 cc

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Answer

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T

Twinkle 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Volumes

A closed cuboid water tank is made of steel sheet that is 2.5 cm thick. The outer dimensions of the tank are 2.15 m * 1.5 m * 1.1 m. find the capacity of the tank and the volume of steel used to construct it?

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Tapas replied | 30/11/2016

Please see the attachment.

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Answer

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M

Mukund 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Volumes

What is the formula for volume of a sphere?

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Tapas replied | 01/12/2016

Please see the attachment.

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Answer

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S

Sumimolss 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Volumes

What is the formula for volume of a cuboid?

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Chandan replied | 22/11/2016

Volume of a cuboid = (length × breadth × height) cubic units.

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Answer

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P

Pinaki 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Volumes

Find the volume of a sphere whose radius is 6 cm?

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Tapas replied | 01/12/2016

Please see the attachment.

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Answer

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A

Avinesh 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Real Numbers

Find twenty rational numbers lying between 0 and 0.5?

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Sreedevi replied | 01/12/2016

1/100,2/100, 3/100, ....,2/10 are the 20 rational numbers in between 0 and 0.5.
You can also use mean method to find the 20 rational numbers that lie between 0 an 0.5.
for example: 0< (0+1/2)/2<1/2 that is the average of the two given numbers always lie in between the two given rational numbers. by proceeding like that we can find 'n' rational numbers in between any two rational numbers.

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Answer

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R

Rosary 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Real Numbers

Determine any number of rational numbers between 0 and 0.3?

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Shikha replied | 23/11/2016

1/10, 2/10.

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A

A.mohamed 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Real Numbers

Every point on the number line corresponds to a ____ number which may be either ____ or ______ ?

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S

Sadhana replied | 01/12/2016

real, positive, negative

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