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S

Shurbik 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Quadratic Equations

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?

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Sarvajeet Kumar replied | 23 Nov

6, 9.

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Balakumar 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Quadratic Equations

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?

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Suyash replied | 19 Nov

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

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K

Krishnat 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Quadratic Equations

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?

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Chandan replied | 22 Nov

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 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Relations

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

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Mamata replied | 24 Nov

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

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A

Aman 04 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Relations

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?

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Shikha replied | 23 Nov

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

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A

Anish 04 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Relations

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

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Shikha replied | 22 Nov

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

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M

Mayur 04 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Relations

How many relations are possible from a set a of m elements to another set B of n elements? Why?

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Shikha replied | 22 Nov

m*n. They are the Cartesian product of both the sets.

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B

Bonita 04 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Relations

If A = {1, 2, 3}, B = {a, b}, find A x A?

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Shikha replied | 22 Nov

A*A={(1,a), (1,b), (2,b),(3,a),(3,b)(2,a)}

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P

P 04 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Relations

If A = {1, 2, 3}, B = {a, b}, find A x B?

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A

Ashwini replied | 26 Nov

6

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M

Meghana 04 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Relations

If A = {1, 2, 3}, B = {a, b}, find B x B?

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Mamata replied | 18 Nov

BxB= {a,b} x{ a,b}
= {(a,a),(a,b),(b.a),b,b)}

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M

Mohd 04 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Relations

Find the range of the following functions: angle [cos (x)] - angle [sin (x)]?

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A

Ashwini replied | 26 Nov

-1 to 1

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D

Datta 02 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Surface Areas

What is the side of the square if the total surface area of a cube is 96 sq. cm?

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Ankit replied | 23 Nov

4 cm.

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H

Hariprasad 02 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Surface Areas

What do you mean by dimensions of any geometrical shapes?

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Chandan replied | 22 Nov

Two geometric shapes that share the same basic shape are called "similar to each other." If both shapes are the same size, they are called "congruent." Geometric shapes can be two-dimensional or flat. They can be three-dimensional, meaning they possess depth and volume.

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A

Arun 02 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Surface Areas

The volumes of the two spheres are in the ratio 64 : 27. Find the ratio of their surface areas?

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Ankit replied | 23 Nov

16 : 9.

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Answer

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R

Ravindra 02 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Probability

Two dice are thrown. What is the probability of obtaining a total of 10 or 11?

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Mamata replied | 25 Nov

Sample space = {(1,1), (1,2,), ........, (5,6), (6,1), (6,6)}
Number of sample space or cardinality of S = |s|= 36
Let A be the event of getting total of 10 or 11
A={(5,5),(5,6),(4,6),(6,4),(6,5)}.
|A|=5.
P(A)= |A|/|S|= 5 / 36.

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B

Baiju 02 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Trigonometry

What is the value of (tan 1 degree tan 2 degree tan 3 degree…...tan 89 degree)?

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Suyash replied | 19 Nov

Here,
tan 1°× tan 89° = tan 1° × cot 1 ° = 1
& Similarly,
tan 2°× tan 88° = 1 as so on.
So the value of,
tan1° × tan2° × ... tan 89° = tan 45° = 1

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R

Ramya 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Sets

Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. What is the value of m and n respectively?

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Ram Mohan replied | 23 Nov

The Values of m & n are : m=7 and n=4 for detailed solution, Please see the attachment.

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T

Tahir 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Sets

Power set of the set A = {1, 2} is _______ ?

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Chandan replied | 22 Nov

2 power 2 = 4 (Ans)

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A

Apoorva 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Sets

Define Universal set?

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Ram Mohan replied | 18 Nov

Universal set is a set, which is the union of all the sets involved in the context of the Question/ Problem.

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S

Shurbik 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Sets

Define set?

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Chandan replied | 22 Nov

A collection of "things" (objects or numbers, etc).
Each member is called an element of the set.
There should be only one of each member (all members are unique).
Here is a set of clothing items.
Another Example: {1,2,3,4} is the set of counting numbers less than 5

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N

Nagarunja 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Functions

Is the given relation a function: h = {(4, 6), (3, 9), (-11, 6), (3, 11)}? Given reasons for your answer

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T

Tarun 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Functions

Is f and g are real functions defined by f(x) = square of x + 7 and g(x) = x + 5?

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N

Natarajan 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Functions

Let f and g are two real valued functions defined as f(x) = 2x + 1, g(x) = square of x + 1, then find f + g?

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B

Balendra 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Functions

Express the following functions as set of ordered pairs and determine their range,
f: X - R, f(x) = cube of x + 1, where X = {-1, 0, 3, 9, 7}?

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P

Pradeep 03 Nov in  Class IX-X Tuition, Mathematics(Class IX-X Tuition), Functions

Find the values of x for which the functions: f(x) = 3 cube of x - 1 and g(x) = 3 + x are equal?

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