Important question on Number game -Maths 9th

Important question on Number game -Maths 9th
by

1 Answer

Answer :

Let  x2 + 19x + 92 = k2 Multiplying both sides by 4 we get, Factors of 7 are 7 and 1 as it is a prime number. 2k-m = 7 and 2k+m = 1 ------------ (1) 2k-2 = 7 and 2k+m = 7 -------------- (2) From equation (1), k = 2 From equation (2), k = 2 Hence the value of k = 2 Therefore, there are 2 integers for which x2 + 19x + 92 is a perfect square.
by

Related questions

Important question on Number game -Maths 9th

Description : Important question on Number game -Maths 9th

Last Answer : Let x2 + 19x + 92 = k2 Multiplying both sides by 4 we get, Factors of 7 are 7 and 1 as it is a prime number. 2k-m = 7 and 2k+m = 1 ------------ (1) 2k-2 = 7 and 2k+m = 7 ------ ... (2), k = 2 Hence the value of k = 2 Therefore, there are 2 integers for which x2 + 19x + 92 is a perfect square.

The game of “chuck-a-luck” is played at carnivals in some parts of Europe. Itsrules are asfollows: You pick a number from 1 to 6 and the operator -Maths 9th

Description : The game of “chuck-a-luck” is played at carnivals in some parts of Europe. Itsrules are asfollows: You pick a number from 1 to 6 and the operator -Maths 9th

Last Answer : (c) 0.42P(Particular number comes on the dice) = \(rac{1}{6}\)(∵ there are in all 6 numbers)P(particular number does not come on the dice) = 1 - \(rac{1}{6}\) = \(rac{5}{6}\)As there are 3 dices, so,P(Picked number ... (\big(rac{5}{6}\big)^3\) = \(rac{125}{216}\) ≈ 0.58∴ P(Winning) = 1 - 0.58 = 0.42

Three girls Reshma, Salma and Mandeep are playing a game by standing on a circle of radius 5 m drawn in a park. -Maths 9th

Description : Three girls Reshma, Salma and Mandeep are playing a game by standing on a circle of radius 5 m drawn in a park. -Maths 9th

Last Answer : Solution :- Let R, S and M represent the position of Reshma, Salma and Mandeep respectively. Clearly △RSM is an isosceles triangle as RS = SM = 6m Join OS which intersect RM at A. In △ROS and △MOS OR = OM ( ... . ∴ RM = 2RA RM = 2 x 4.8 = 9.6m Hence, distance between Reshma and Mandeep is 9.6m.

A and B throw a coin alternately till one of them gets a ‘head’ and wins the game. Find their respective probabilities of winning . -Maths 9th

Description : A and B throw a coin alternately till one of them gets a ‘head’ and wins the game. Find their respective probabilities of winning . -Maths 9th

Last Answer : Let A : Event of A getting a head ⇒ \(\bar{A}\) : Event of A not getting a head ∴ P(A) = \(rac{1}{2}\) and P(\(\bar{A}\)) = 1 - \(rac{1}{2}\) = \(rac{1}{2}\)Similarly, B : Event of B ... exclusive events, as either of them will win, P(B winning the game first) = 1 - \(rac{2}{3}\) = \(rac{1}{3}\).

Two players A and B play a game by alternately drawing a card from a well-shuffled pack of playing cards, replacing the card each time after draw. -Maths 9th

Description : Two players A and B play a game by alternately drawing a card from a well-shuffled pack of playing cards, replacing the card each time after draw. -Maths 9th

Last Answer : (a) \(rac{13}{25}\)Let E : Event of drawing a queen in a single draw the pack of 52 cards. As there are 4 queens in a pack of 52 cards,P(E) = \(rac{4}{52}\) = \(rac{1}{13}\)P(\(\bar{E}\)) = P(not ... {25}\). [Sum of a G.P with infinite terms = \(rac{a}{1-r}\) where a = 1st term, r = common ratio.]

In a chess tournament, where participants were to play one game with one another, two players fell ill, having played 6 games each without playing -Maths 9th

Description : In a chess tournament, where participants were to play one game with one another, two players fell ill, having played 6 games each without playing -Maths 9th

Last Answer : answer:

In how many ways can a mixed doubles game be arranged from amongst 8 married couples if no husband and wife play in the same game? -Maths 9th

Description : In how many ways can a mixed doubles game be arranged from amongst 8 married couples if no husband and wife play in the same game? -Maths 9th

Last Answer : For mixed doubles, we have 2 men and 2 women. 2 men out of 9 can be selected in 9C8 ways Out of 9 women, 2 will be there wife 30 only 7 are remaining for selecting 2 Now out of them 2 possible combinations can be made. So, ... =3024 Hence the answer is 3024.

I want contact number of study ranker who give answers of our question on whatsapp I am having that number earlier but plzzz it's my request please provide me your number I am PREMIUM MEMBER -Maths 9th

Description : I want contact number of study ranker who give answers of our question on whatsapp I am having that number earlier but plzzz it's my request please provide me your number I am PREMIUM MEMBER -Maths 9th

Last Answer : NEED ANSWER

I want contact number of study ranker who give answers of our question on whatsapp I am having that number earlier but plzzz it's my request please provide me your number I am PREMIUM MEMBER -Maths 9th

Description : I want contact number of study ranker who give answers of our question on whatsapp I am having that number earlier but plzzz it's my request please provide me your number I am PREMIUM MEMBER -Maths 9th

Last Answer : Hi there, You can ask your doubts here. Just post your question by clicking on Ask Question button select the subject and enter the chapter name in tag. Thanks.

prove the following question -Maths 9th

Description : prove the following question -Maths 9th

Last Answer : Let ABCD is a quadrilateral in which P, Q, R, and S are the mid-points of sides AB, BC, CD, and DA respectively. Join PQ, QR, RS, SP, and BD. In ΔABD, S and P are the mid- ... SPQR is a parallelogram. We know that diagonals of a parallelogram bisect each other. Hence, PR and QS bisect each other.

Simplify the question -Maths 9th

Description : Simplify the question -Maths 9th

Last Answer : After rationalizing it 42/11

Simplify the following question -Maths 9th

Description : Simplify the following question -Maths 9th

Last Answer : Simplification of following question

Factorise this question -Maths 9th

Description : Factorise this question -Maths 9th

Last Answer : (i) The greatest monomial that is a common factor of the three terms is 6xy. ∴ 30x3y + 24x2y2 - 6xy = 6xy (5x2 + 4xy - 1) (ii) Here the polynomial (a-b) is a common factor. ∴ 5x(a-b) + 6y(a-b) = (a-b) (5x + 6y)

Factorise this question -Maths 9th

Description : Factorise this question -Maths 9th

Last Answer : (i) 7a3 + 7a - 2a2 - 2 = 7a(a2 + 1) - 2 (a2 + 1) = (a2 + 1) (7a - 2) (ii) The term of 4ax + 3by - 3ay - 4bx can be rearranged and factorized . 4ax - 4bx - 3ay + 3by = 4x(a-b) - 3y(a-b) = (a-b) (4x - 3y) (iii) x3 + y3 + x2y + xy2 = x3 + x2y + xy2 + y3 = x2(x+y) + y2 (x+y) = (x+y) (x2+y2)

Factorise this question -Maths 9th

Description : Factorise this question -Maths 9th

Last Answer : (i) 9x2 + 30xy + 25y2 = (3x2 + 2(3x) (5y) + (5y)2 = (3x + 5y)2 (ii) 9x2 - 30xy + 25y2 = (3x)2 - 2(3x) (5y) + 5y2 = (3x - 5y)2

Factorize this question -Maths 9th

Description : Factorize this question -Maths 9th

Last Answer : (i) 9x2 - y2 = (3x)2 - (y)2 = (3x + y) (3x - y) (ii) (3 - x)2 - 36x2 = (3 - x)2 - (6x)2 = (3 - x + 6x) (3 - x - 6x) = (3 + 5x) (3 - 7x) (iii) (2x - 3y)2 - (3y + 4y)2 = (2x - 3y + ... + 7y) (iv) 16x4 - y4 = (4x2)2 - (y2)2 = (4x2 + y2) (4x2 - y2) = (4x2 + y2) (2x + y) (2x - y)

The probability of guessing the correct answer to a certain question is x/ 2. -Maths 9th

Description : The probability of guessing the correct answer to a certain question is x/ 2. -Maths 9th

Last Answer : Here, probability of guessing the correct answer = x / 2 And probability of not guessing the correct answer = 2 / 3 Now, x / 2 + 2 / 3 = 1 ⇒ 3x + 4 = 6 ⇒ 3x = 2 ⇒ x = 2 / 3

Simplify the following question : -Maths 9th

Description : Simplify the following question : -Maths 9th

Last Answer : Simplification of following number

Simplify the following question : -Maths 9th

Description : Simplify the following question : -Maths 9th

Last Answer : Simplification

prove the following question -Maths 9th

Description : prove the following question -Maths 9th

Last Answer : Let ABCD is a quadrilateral in which P, Q, R, and S are the mid-points of sides AB, BC, CD, and DA respectively. Join PQ, QR, RS, SP, and BD. In ΔABD, S and P are the mid- ... SPQR is a parallelogram. We know that diagonals of a parallelogram bisect each other. Hence, PR and QS bisect each other.

Simplify the question -Maths 9th

Description : Simplify the question -Maths 9th

Last Answer : After rationalizing it 42/11

Simplify the following question -Maths 9th

Description : Simplify the following question -Maths 9th

Last Answer : Simplification of following question

Factorise this question -Maths 9th

Description : Factorise this question -Maths 9th

Last Answer : (i) The greatest monomial that is a common factor of the three terms is 6xy. ∴ 30x3y + 24x2y2 - 6xy = 6xy (5x2 + 4xy - 1) (ii) Here the polynomial (a-b) is a common factor. ∴ 5x(a-b) + 6y(a-b) = (a-b) (5x + 6y)

Factorise this question -Maths 9th

Description : Factorise this question -Maths 9th

Last Answer : (i) 7a3 + 7a - 2a2 - 2 = 7a(a2 + 1) - 2 (a2 + 1) = (a2 + 1) (7a - 2) (ii) The term of 4ax + 3by - 3ay - 4bx can be rearranged and factorized . 4ax - 4bx - 3ay + 3by = 4x(a-b) - 3y(a-b) = (a-b) (4x - 3y) (iii) x3 + y3 + x2y + xy2 = x3 + x2y + xy2 + y3 = x2(x+y) + y2 (x+y) = (x+y) (x2+y2)

Factorise this question -Maths 9th

Description : Factorise this question -Maths 9th

Last Answer : (i) 9x2 + 30xy + 25y2 = (3x2 + 2(3x) (5y) + (5y)2 = (3x + 5y)2 (ii) 9x2 - 30xy + 25y2 = (3x)2 - 2(3x) (5y) + 5y2 = (3x - 5y)2

Factorize this question -Maths 9th

Description : Factorize this question -Maths 9th

Last Answer : (i) 9x2 - y2 = (3x)2 - (y)2 = (3x + y) (3x - y) (ii) (3 - x)2 - 36x2 = (3 - x)2 - (6x)2 = (3 - x + 6x) (3 - x - 6x) = (3 + 5x) (3 - 7x) (iii) (2x - 3y)2 - (3y + 4y)2 = (2x - 3y + ... + 7y) (iv) 16x4 - y4 = (4x2)2 - (y2)2 = (4x2 + y2) (4x2 - y2) = (4x2 + y2) (2x + y) (2x - y)

The probability of guessing the correct answer to a certain question is x/ 2. -Maths 9th

Description : The probability of guessing the correct answer to a certain question is x/ 2. -Maths 9th

Last Answer : Here, probability of guessing the correct answer = x / 2 And probability of not guessing the correct answer = 2 / 3 Now, x / 2 + 2 / 3 = 1 ⇒ 3x + 4 = 6 ⇒ 3x = 2 ⇒ x = 2 / 3

Simplify the following question : -Maths 9th

Description : Simplify the following question : -Maths 9th

Last Answer : Simplification of following number

Simplify the following question : -Maths 9th

Description : Simplify the following question : -Maths 9th

Last Answer : Simplification

In an examination there are 3 multiple choice questions and each question has 4 choices. If a student randomly selects answer for all -Maths 9th

Description : In an examination there are 3 multiple choice questions and each question has 4 choices. If a student randomly selects answer for all -Maths 9th

Last Answer : Probability of selecting a correct choice for a question = \(rac{1}{4}\)(∵ Out of 4 choices only one is correct)∴ Probability of answering all the three questions correctly = \(rac{1}{4}\)x \(rac{1}{4}\)x\ ... of not answering all the three questions correctly = 1 - \(rac{1}{64}\) = \(rac{63}{64}\).

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. -Maths 9th

Description : A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. -Maths 9th

Last Answer : (c) \(rac{11}{3^5}\)Probability of guessing a correct answer = \(rac{1}{3}\)Probability of guessing an incorrect answer = \(rac{2}{3}\)∴ Probability of guessing 4 or more correct answers = 5C4 \(\big(rac{1}{3}\big)^4\)\(\big(rac{2 ... )^5\) = 5 x \(rac{2}{3^5}\) + \(rac{1}{3^5}\) = \(rac{11}{3^5}\).

Important properties of triangles: -Maths 9th

Description : Important properties of triangles: -Maths 9th

Last Answer : answer:

Important Theorems on Triangles. -Maths 9th

Description : Important Theorems on Triangles. -Maths 9th

Last Answer : answer:

1. Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points? -Maths 9th

Description : 1. Draw different pairs of circles. How many points does each pair have in common? What is the maximum number of common points? -Maths 9th

Last Answer : As we can see from the figure, that two circles have two points in common. Two circles cannot intersect each other at more than two points. Let us assume that two circles cut each other at ... circle can pass. So, two circles if intersect each other will intersect at maximum two points.

Construct a histogram for the marks of the student given below : - Marks 0-10,10-30,30-45,45-50,50-60 and number of students 8,32,18,10,6 -Maths 9th

Description : Construct a histogram for the marks of the student given below : - Marks 0-10,10-30,30-45,45-50,50-60 and number of students 8,32,18,10,6 -Maths 9th

Last Answer : see in book okay!!!

Express the following number in standard form 4730000000 -Maths 9th

Description : Express the following number in standard form 4730000000 -Maths 9th

Last Answer : The standard form of 4,730,000,000 is 4.73 * 10^9 Explanation :- = 4730000000. * 10^0 = 4.73 * 10^9

If a is a positive rational number and n is a positive integer greater than 1, prove that an is a rational number . -Maths 9th

Description : If a is a positive rational number and n is a positive integer greater than 1, prove that an is a rational number . -Maths 9th

Last Answer : We know that product of two rational number is always a rational number. Hence if a is a rational number then a2 = a x a is a rational number, a3 = 4:2 x a is a rational number. ∴ an = an-1 x a is a rational number.

Insert a rational and an irrational number between 2 and 3. -Maths 9th

Description : Insert a rational and an irrational number between 2 and 3. -Maths 9th

Last Answer : A rational number between 2 and 3 = 2 + 3 / 2 = 2.5 An irrational number between 2 and 3 is √5 .

Give an example to show that the product of a rational number and an irrational number may be a rational number . -Maths 9th

Description : Give an example to show that the product of a rational number and an irrational number may be a rational number . -Maths 9th

Last Answer : A rational number 0 multiplied by an irrational number gives the irrational number 0.

Give two examples to show that the product of two irrational numbers may be a rational number . -Maths 9th

Description : Give two examples to show that the product of two irrational numbers may be a rational number . -Maths 9th

Last Answer : Take a = (2+ √3) and b =(2 - √3 ); a and b are irrational numbers, but their product = 4-3 = 1, is a rational number. Take c = √3 and d = -√3; c and d are irrational numbers. but their product = -3, is a rational number.

If a wooden box of dimensions 8 m x 7 m x 6 m is to carry boxes of dimensions 8 cm x 7 cm x 6 cm, then find the maximum number of boxes that can be carried in the wooden box. -Maths 9th

Description : If a wooden box of dimensions 8 m x 7 m x 6 m is to carry boxes of dimensions 8 cm x 7 cm x 6 cm, then find the maximum number of boxes that can be carried in the wooden box. -Maths 9th

Last Answer : Volume of wooden box = 800 cm × 700 cm × 600 cm Volume of box = 8 cm × 7 cm × 6 cm ∴ Number of boxes = volume of wooden box / volume of each box = 800 cm × 700 cm × 600 cm / 8 cm × 7 cm × 6 cm = 1000000

There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be – 3.5. Find the mean of the given numbers. -Maths 9th

Description : There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be – 3.5. Find the mean of the given numbers. -Maths 9th

Last Answer : Let x be the mean of 50 numbers. ∴ sum of 50 numbers = 50x Since each number is subtracted from 53. According to question, we have 53 × 50 - 50x / 50 = - 3.5 ⇒ 2650 - 50x = -175 ⇒ 50x = 2825 ⇒ x = 2825 / 50 = 56.5

Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows : -Maths 9th

Description : Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows : -Maths 9th

Last Answer : (i) Frequency distribution table (ii) From the above frequency distribution table, we observe that number of children in the class - interval 15 - 20 is 2. So, 2 children view television for 15 hours or more than 15 hours a week .

A dice is rolled number of times and its outcomes are recorded as below : -Maths 9th

Description : A dice is rolled number of times and its outcomes are recorded as below : -Maths 9th

Last Answer : Total number of outcomes = 250 Total number of outcomes of getting odd numbers = 35 + 50 + 53 = 138 P (getting an odd number) = 138 / 250 = 69 / 125

A die is thrown six times and number on it is noted as given below : -Maths 9th

Description : A die is thrown six times and number on it is noted as given below : -Maths 9th

Last Answer : Here, in 6 trials, each number occur once and total prime numbers i.e., 2, 3, 5 occur one time each Hence, the number of prime occur = 3 Probability of getting a prime = 3/6 =1/2

Two coins are tossed simultaneously for 360 times. The number of times ‘2 Tails’ appeared was three times ‘No Tail’ appeared and number of times ‘1 tail’ appeared is double the number of times ‘No Tail’ appeared. -Maths 9th

Description : Two coins are tossed simultaneously for 360 times. The number of times ‘2 Tails’ appeared was three times ‘No Tail’ appeared and number of times ‘1 tail’ appeared is double the number of times ‘No Tail’ appeared. -Maths 9th

Last Answer : Total number of outcomes = 360 Let the number of times ‘No Tail’ appeared be x Then, number of times ‘2 Tails’ appeared =3x Number of times ‘1 Tail’ appeared =2x Now, x + 2x + 3x =360 ⇒ 6x =360 ⇒ x= 60 P(of getting two tails)=(3 x 60) / 360 =1 / 2

A die was rolled 100 times and the number of times, 6 came up was noted. -Maths 9th

Description : A die was rolled 100 times and the number of times, 6 came up was noted. -Maths 9th

Last Answer : Here, total number of trials = 100 Let x be the number of times occuring 6. We know, Probability of an ever = Frequency of the event occuring / Total number of trials ⇒ x / 100 = 2 / 5 [∵ Probability is given] ⇒ x = 40

Insert a rational number and an irrational number between the following : -Maths 9th

Description : Insert a rational number and an irrational number between the following : -Maths 9th

Last Answer : We know that, there are infinitely many rational and irrational values between any two numbers. (i) A rational number between 2 and 3 is 2.1. To find an irrational number between 2 and 3. Find a ... and 6.375738 is 6.3753. An irrational number between 6.375289 and 6.375738 is 6.375414114111

If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation. -Maths 9th

Description : If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation. -Maths 9th

Last Answer : (b) By property, if we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation remains the same i.e., the solution of the linear equation is remains unchanged.

Construct a histogram for the marks of the student given below : - Marks 0-10,10-30,30-45,45-50,50-60 and number of students 8,32,18,10,6 -Maths 9th

Description : Construct a histogram for the marks of the student given below : - Marks 0-10,10-30,30-45,45-50,50-60 and number of students 8,32,18,10,6 -Maths 9th

Last Answer : see in book okay!!!