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B

Basundhara 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

Simplify [square of (- square of a * cube of b)] * (square of c)?

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Daljit Kaur replied | 25/11/2016

(Fourth power of a) (sixth power of b) (c square).

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Mamata replied | 29/11/2016

Square of ( -a^2b^3) ) c^2
= a^4b^6c^2
= a fourth b sixth c squares.

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P

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

If l, b, h, S and V are length, breadth, height, surface area and volume respectively of a cuboid, prove that: 1/V = 2/S(1/l + 1/b + 1/h)?

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Ram Mohan replied | 02/12/2016

If l, b, h, S and V are length, breadth, height, surface area and volume respectively of a cuboid, Then, V = lbh
Let us take the relation S = 2 (lb +bh + lh). Now dividing both sides with V * S, we get:-
1/V = 2 ( lb + bh = lh )/ (V * S) = 2 ( lb + bh = lh )/ (lbh * S) ...... ( Substituting lbh for V)
==> 1/V = =2 [(lb/lbh )+( bh/lbh ) + (lh/ibh )] / S
==> 1/V...  more»
If l, b, h, S and V are length, breadth, height, surface area and volume respectively of a cuboid, Then, V = lbh
Let us take the relation S = 2 (lb +bh + lh). Now dividing both sides with V * S, we get:-
1/V = 2 ( lb + bh = lh )/ (V * S) = 2 ( lb + bh = lh )/ (lbh * S) ...... ( Substituting lbh for V)
==> 1/V = =2 [(lb/lbh )+( bh/lbh ) + (lh/ibh )] / S
==> 1/V = 2/S(1/l + 1/b + 1/h) proved. «less

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Ram Mohan replied | 02/12/2016

If l, b, h, S and V are length, breadth, height, surface area and volume respectively of a cuboid, Then
We have S = 2( lb + bh + lh ) and V = lbh
Let us take the relation S = 2(lb +bh + lh).
Now dividing both sides with V * S, we get
1/V = 2 ( lb + bh = lh )/ (V * S) = 2 ( lb + bh +lh )/ (lbh * S) ...... ( after Substituting lbh for V)
==> 1/V = 2 [(lb/lbh...  more»
If l, b, h, S and V are length, breadth, height, surface area and volume respectively of a cuboid, Then
We have S = 2( lb + bh + lh ) and V = lbh
Let us take the relation S = 2(lb +bh + lh).
Now dividing both sides with V * S, we get
1/V = 2 ( lb + bh = lh )/ (V * S) = 2 ( lb + bh +lh )/ (lbh * S) ...... ( after Substituting lbh for V)
==> 1/V = 2 [(lb/lbh )+( bh/lbh ) + (lh/lbh )] / S
==> 1/V = 2/S(1/l + 1/b + 1/h) proved. «less

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K

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

Is 2 + square root of 2 is not a rational number?

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Sridharla Ramesh replied | 18/11/2016

No

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Ram Mohan replied | 21/11/2016

Mr Kevin, the Author of the Question, wants to know, whether his presumption, that " (2 + sqrt 2) is not a RATIONAL NUMBER" is TRUE or FALSE.. "Sqrt 2" is an irrational number. "( 2 + sqrt 2)" is a compound number, containing an irrational part. Therefore the whole one, is an irrational number. That is; "(2+ sqrt2)" is not a rational number. Therefore the presumption of Mr Kevin...  more»
Mr Kevin, the Author of the Question, wants to know, whether his presumption, that " (2 + sqrt 2) is not a RATIONAL NUMBER" is TRUE or FALSE.. "Sqrt 2" is an irrational number. "( 2 + sqrt 2)" is a compound number, containing an irrational part. Therefore the whole one, is an irrational number. That is; "(2+ sqrt2)" is not a rational number. Therefore the presumption of Mr Kevin the Author is TRUE. Hence the answer to this Question should be Either 'TRUE' OR " YES" But not the "NO" given by Mr Sreedharlaramesh and Mr Dheerendra. Please verify . «less

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S

Sanjeevani 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Functions

Find the value of x and y, if (2x, x + y) = (6, 2)?

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Chandan replied | 22/11/2016

2x=6
x=3,
Now x+y=2
3+y=2
y=-1.
Hence x=3
y=-1

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Answer

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B

Basundhara 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

Which property is used to write a(x + y) = ax +ay?

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Shikha replied | 23/11/2016

Distributive property.

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Answer

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P

Prabhu 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

For what value of k is the point (-2, k) on the line with equation: -3x + 3y = 4?

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Tapas replied | 01/12/2016

For the given point:
-3(-2) + 3k = 4 --> 6 + 3k = 4 --> 3k = 4-6 = 2 --> k = 2/3 (Answer).

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A

Agastya 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

Which line given by its equation: [2 (3x - 2)] - 3 = 7?

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Shikha replied | 22/11/2016

6x=14

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B

Briyal 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

Solve for x the equation: (1/2) square of x + mx - 2 = 0?

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Shikha replied | 23/11/2016

After equating coefficients, square of x-4+2 m x = 0.
So, x=[-m+-square root of (m 2+4)] / 2.

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Answer

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K

Kunal 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

For what values of b the equation square of x - 4x + 4b = 0 has two real solutions?

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Shikha replied | 23/11/2016

x = 4b/3.
Hence, real solutions for b would be 3/4, -3/-4, 6/8, 9/12 [i.e., any factors of 3/4].

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Daljit Kaur replied | 25/11/2016

This equation will have real solutions for b less than or equal to one

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Answer

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P

Priya 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

Simplify: -2(x - 3) + 4(-2x + 8)?

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Shikha replied | 23/11/2016

-2x + 6- 8x +32 = 0
-10x + 38 = 0
X= -38/-10 = 3.8.

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Answer

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A

Abdul 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

Find the product: (2a + 5b) (4 square of a - 6ab + 9 square of b)?

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Shikha replied | 23/11/2016

8*cube of a + 8 * square of a*b-12 a*square of b+45 *cube of b.

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J

Joydip 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

Divide: 4 (square of x) + 3x by 2 (square of x)?

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Jeet replied | 02/12/2016

2 + (3/2x).

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Answer

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C

Chandan 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

What is the value of f(5): f(x) = 5(square of x) - 4x?

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Sreedevi replied | 02/12/2016

f(x) = 5x^2 - 4x (given).
on substituting x = 5 in the above,
f(5) = 5( 25) - 20 = 105.

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Answer

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P

Praveen 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

Define Algebra in terms of Mathematics?

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Sreedevi replied | 02/12/2016

Algebra is a branch of mathematics which deals with unknowns or variables. In algebra, we can find the solution of the given problem using unknowns (variables).

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Answer

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P

Praveen 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

Find any real solutions for the quadratic equation: 2 (square of x) - 8 = 0?

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Tapas replied | 01/12/2016

2 x^2 -8=0 --> x^2 = 4 --> x = +2 or -2.

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Answer

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A

Ashok 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

Solve: x + 3 < 0?

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Chandan replied | 22/11/2016

x>-3

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Ram Mohan replied | 22/11/2016

The answer should be (x < -3).

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Answer

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G

Gaurav 03/11/2016 in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Algebra

What is the point of intersection of the lines x - y = 3 and -5x - 2y = -22?

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Sreedevi replied | 02/12/2016

The point of intersection is (4,1).

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Answer

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U

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

Find the A.P whose 10th term is 5 and 18th term is 77?

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Tapas replied | 01/12/2016

Let the first term be a and the common difference be b.
So, the 10th term: t10 = a + 9b = 5.
and, the 18th term: t18 = a + 17b = 77.
So, from t17 - t10 we get: 8b = 77 - 5 = 72.
This gives: b = 9.
From t10 we get: a = 5 - 9b = 5 - 9x9 = -76.
So, a = -76, b = 9 and the A.P is:-
-76, -67, -58, -49, ..... (Answer).

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Answer

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S

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

In a certain A.P the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term?

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Tapas replied | 01/12/2016

Let the first term be a and the common difference be b.
So, by the given condition:-
t24 = 2 x t10 --> a + 23 b = 2 ( a + 9b) = 2a + 18b.
This gives: a = 5b.
So, the 72nd term: t72 = a +71b = 5b + 71b = 76b.
and the 34th term: t34 = a + 33b = 5b + 33b = 38b = 76b/2 = t72/2.
So, the 72nd term is twice the 34th term. (Proved)

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P

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

If 9th term of an A.P is zero, prove that its 29th term is double the 19th term?

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Ram Mohan replied | 22/11/2016

Let 'a' be the first term and 'd' be the common difference of the given A P. If Tn stands for nth term of this A P, then we get T9 = a + 8d= 0 ( Given).
T19 = a + 18 d = ( a + 8 d) + 10 d = T9 + 10 d = 0 +10 d = 10d
T29 = a + 28 d = (a + 8 d) +20 d = T9 + 20 d = 0 + 20 d = 20d =2 *10 d= 2 * T19.

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P

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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G

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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S

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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