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M

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

Is the rational number: 3/5 is terminating or non-terminating decimal?

Chandan replied | 22/11/2016

3/5=0.6
hence terminating decimal

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S

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

Is square of x = 5 a rational number or not?

A

Ashwini replied | 26/11/2016

Yes

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K

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

Express 7/64 as a decimal form?

Tapas replied | 29/11/2016

7/64 = 0.109375 = 0.11 (approximately)

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M

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

Express 12/125 as a decimal fraction?

Tapas replied | 29/11/2016

12/125 is a fraction. In decimal form 12/125 = 0.096.

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K

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

What is the largest number which divides 70 and 125, leaving remainders 5 and 8?

Tapas replied | 29/11/2016

So, we need to find out the largest number which divides (70-5) = 65, and (125 - 8) = 117 leaving no remainder.
So, we need to find the HCF of 65 and 117, which is 13.

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M

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

Solve: 1457/1250?

Tapas replied | 29/11/2016

1457/1250 = 1.1656.

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K

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

Write whether every positive integer can be of the form 4(q) + 2, where q is an integer. Justify your answer?

Ram Mohan replied | 21/11/2016

The expression, 4(q) + 2 , yields a sequence of all even + ve Numbers which are in Arithmetic Progression with a Common Difference equal to '4' , for all q >= 0. Hence, every positive inter cannot expressed in the form 4 q+2 .

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A

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

Check whether the following equation is quadratic or not: square of x - 6 x - 4 = 0?

Tapas replied | 30/11/2016

This is a quadratic equation as highest power of x is 2.

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R

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

Determine whether the given value of x is a solution of the given equation or not: 2(square of x) - 6x + 3 = 0; x = 1/2 ?

Chandan replied | 22/11/2016

No, the given value of x is a solution of the given equation
since by putting the value of x in left hand side it is not making L.H.S= R.H.S.
So, x=1/2 is not the solution for the given quadratic equation.

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P

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

Determine whether the given value of x is a solution of the given equation or not: (2x + 3)(3x - 2) = 0; x = 2/3 ?

Ram Mohan replied | 21/11/2016

Yes.
The Given equation (2x+3) (3x-2)= 0 is True, ===> 3x-2 =0 ===> 3x=2 ===> x = 2/3.
Hence x = 2/3 is one solution, while, x= -3/2, is the other solution.

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U

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

Using factorization, find the roots of the quadratic equation: 9(square of x) - 16 = 0?

Tapas replied | 30/11/2016

9x^2 - 16 = 0
=> (3x)^2 = 4^2 =0
=> (3x + 4)(3x - 4)=0
so, 3x=4 --> x = 4/3
or, 3x=-4 --> x = -4/3
Answer: x = 4/3 or -4/3.

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P

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

Solve: 4(square of x) + 2x + 1 = 0?

Jeet replied | 02/12/2016

{-1+i(root3)}/4 and {-1-i(root3)}/4.

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A

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

Determine the value of p for which the given quadratic equation has real roots: p(square of x) + 4x + 1 = 0?

Tapas replied | 29/11/2016

The equation: px^2 + 4x + 1 = 0. The roots are real if the discriminant is zero or positive.
So, 4^2 - 4p >= 0 (>= means greater than or equal to).
=> p is smaller than or equal to 4.
Answer: p must be equal to 4 or smaller.

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A

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

The sum of a number and its reciprocal is 10/3, find the number?

Mamata replied | 24/11/2016

Let the number be a
a+(1/a)= 10/3
=> a^2+1)/a = 10/3
=> 3a^2+3-10a=0
=> 3a^2-10a+3=0
=> 3a^2-9a-a+3=0
=> 3a(a-3)-1(a-3)=0
=> (3a-1)(a-3)=0
=> a= 3 and a = 1/3

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P

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

A two digit number is such that the product of its digits is 12. When 36 is added to this number, the digits interchange their places. Find the number?

Sarvajeet replied | 23/11/2016

36.

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A

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

Find two consecutive odd natural numbers, the sum of whose squares is 202?

Chandan replied | 22/11/2016

x2+square of (x+2) =202.
Solving the quadratic equation we get
two odd natural numbers = 9,11 or -9,-11

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D

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

Determine two consecutive even positive integers, the sum of whose squares is 100?

Ram Mohan replied | 21/11/2016

Let the two consecutive even numbers be ' 2 a ' and ( 2 a + 2) where, a > 0 . Since the sum of their squares = 100; we get
4 a*a+ 4 ( a*a+2a+1) = 100==> 2a*a+2a+1 = 25==> 2 a*a + 2 a -24 =0 solving this,
we get a = 3 and a= -4. taking only +ve value of a=3, the required numbers are '6' and '8'.

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D

Dr. Rajani 03/11/2016 in  Mathematics(Class IX-X Tuition),

There are three consecutive positive integers such that the sum of the square of the first and the product of the other two is 154. What are the integers?

Shikha replied | 22/11/2016

Let first three consecutive numbers are x, x+1, x+2 . According to the question, x2+(x+1)(x+2)=154. Final answer is x=8. Hence numbers are 8,9,10.

Ankit replied | 23/11/2016

8, 9, 10.

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S

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

The hypotenuse of a grassy land in the shape of right triangle is 1 meter more than twice the shortest side. If the third side is 7 meters more than the shortest side, find the sides of the grassy land?

Tapas replied | 29/11/2016

Let the length of the shortest side be x. Then, the two sides other than the hypotenuse are x and (x + 7). So, by the given condition:
(2x +1)^2 = x^2 + (x + 7)^2.

Tapas replied | 29/11/2016

Let the length of the shortest side be x. Then, the two sides other than the hypotenuse are x and (x + 7). So, by the given condition:
(2x +1)^2 = x^2 + (x + 7)^2
=> 4x^2 + 4x + 1 = 2x^2 + 14x + 49
=> 2x^2 -10x - 48 = 0
=> x^2 - 5x - 24 = 0
=> x^2 - 8x + 3x -24 = 0
=> (x - 8)(x + 3) = 0
x = 8 or - 3. But the length of a side of a land cannot be negative....  more»
Let the length of the shortest side be x. Then, the two sides other than the hypotenuse are x and (x + 7). So, by the given condition:
(2x +1)^2 = x^2 + (x + 7)^2
=> 4x^2 + 4x + 1 = 2x^2 + 14x + 49
=> 2x^2 -10x - 48 = 0
=> x^2 - 5x - 24 = 0
=> x^2 - 8x + 3x -24 = 0
=> (x - 8)(x + 3) = 0
x = 8 or - 3. But the length of a side of a land cannot be negative.
So, x = 8m and the other sides are x + 7 = 15m, and (2x + 1) = 17m.
So, the sides of the land are 8m, 15m, and 17m. «less

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S

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

The difference of the squares of two numbers is 45. The squares of the smaller number is 4 times the larger number. Determine the numbers?

Sarvajeet replied | 23/11/2016

6, 9.

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B

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

The sum of ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages?

Suyash replied | 19/11/2016

Given,
F+S = 45
(F-5)×(S-5) = 124
On solving ,
F = 36 years
& S = 9 years

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K

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

A passenger train takes 2 hours less for a journey of 300 km, if its speed is increased by 5 km/hr from its usual speed. Find its usual speed?

Chandan replied | 22/11/2016

Let usual speed be x km/h
(300/x) - (300/(x+5)) = 2
solving it we get quadratic equation x2+5x-750=0
solving it get x=25 km/h.
Hence usual speed of train is 25 km/h.

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J

Joydev 04/11/2016 in  Mathematics(Class IX-X Tuition),

Let A = {2, 3} and B = {3, 4}. Write all subsets of A x B?

Mamata replied | 24/11/2016

A x B= { (2,3), (2,4), (3,3), (3,4) }.

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A

Aman 04/11/2016 in  Mathematics(Class IX-X Tuition),

Let R be the relation on Z defined by a R b if and only if a - b is an even integer. Find domain of R and range of R?

Shikha replied | 23/11/2016

Domain would be set of all integer while range would be set of all even numbers.

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A

Anish 04/11/2016 in  Mathematics(Class IX-X Tuition),

Determine the domain and the range of the relation R, where R = {(x, cube of x) : x is a prime number less than 10}?

Shikha replied | 22/11/2016

Domain: {2,3,5,7} while Range = {8,27,125,343}.

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