When x^13 + 1 is divided by x –1, the remainder is : -Maths 9th

When x^13 + 1 is divided by x –1, the remainder is : -Maths 9th
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If the polynomial x^19 + x^17 + x^13 + x^11 + x^7 + x^5 + x^3 is divided by (x^2 + 1), then the remainder is : -Maths 9th

Description : If the polynomial x^19 + x^17 + x^13 + x^11 + x^7 + x^5 + x^3 is divided by (x^2 + 1), then the remainder is : -Maths 9th

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Determine the remainder when polynomial p(x) is divided by x - 2 . -Maths 9th

Description : Determine the remainder when polynomial p(x) is divided by x - 2 . -Maths 9th

Last Answer : p(x) = x4 - 3x2 + 2x - 5 According to remainder theorem, the required remainder will be = p(2) p(x) = x4 - 3x2 + 2x - 5 ∴ p(2) = 24 - 3(2)2 + 2(2) - 5 =16 - 12 + 4 - 5 = 3

If x51 + 51 is divided by x + 1, then the remainder is -Maths 9th

Description : If x51 + 51 is divided by x + 1, then the remainder is -Maths 9th

Last Answer : (d) Let p(x) = x51 + 51 . …(i) When we divide p(x) by x+1, we get the remainder p(-1) On putting x= -1 in Eq. (i), we get p(-1) = (-1)51 + 51 = -1 + 51 = 50 Hence, the remainder is 50.

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The polynomial p{x = x4 -2x3 + 3x2 -ax+3a-7 when divided by x+1 leaves the remainder 19. -Maths 9th

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Determine the remainder when polynomial p(x) is divided by x - 2 . -Maths 9th

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Last Answer : p(x) = x4 - 3x2 + 2x - 5 According to remainder theorem, the required remainder will be = p(2) p(x) = x4 - 3x2 + 2x - 5 ∴ p(2) = 24 - 3(2)2 + 2(2) - 5 =16 - 12 + 4 - 5 = 3

If x51 + 51 is divided by x + 1, then the remainder is -Maths 9th

Description : If x51 + 51 is divided by x + 1, then the remainder is -Maths 9th

Last Answer : (d) Let p(x) = x51 + 51 . …(i) When we divide p(x) by x+1, we get the remainder p(-1) On putting x= -1 in Eq. (i), we get p(-1) = (-1)51 + 51 = -1 + 51 = 50 Hence, the remainder is 50.

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Last Answer : Given that the following polynomials leave the same remainder when divided by (x - 4) : We are to find the value of a. Remainder theorem: When (x - b) divides a polynomial p(x), then the remainder is p(b). So, from (i) and (ii), we get Thus, the required value of a is 1.

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If the polynomials ax^3 + 4x^2 + 3x – 4 and x^3 – 4x + a leave the same remainder when divided by (x – 3), the value of a is : -Maths 9th

Description : If the polynomials ax^3 + 4x^2 + 3x – 4 and x^3 – 4x + a leave the same remainder when divided by (x – 3), the value of a is : -Maths 9th

Last Answer : Given ax^3 + 4x^2 + 3x - 4 and x^3 - 4x + a leave the same remainder when divided by x - 3. Let p(x) = ax^3 + 4x^2 + 3x - 4 and g(x) = x^3 - 4x + a By remainder theorem, if f(x) is divided by (x − a) then ... 4 27a+41 g(3)=27-4(3)+a 15+a f(3)=G(3) 27a+41=15+a 26a=15-41 a=15-41/26 a=-26/26 a=-1

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Description : If the expression ax^2 + bx + c is equal to 4, when x = 0, leaves a remainder 4 when divided by x + 1 and leaves a -Maths 9th

Last Answer : Given exp. f(x) = ax2 + bx + c ∴ When x = 0, a.0 + b.0 + c = 4 ⇒ c = 4. The remainders when f(x) is divided by (x + 1) and (x + 2) respectively are f(–1) and f(–2). ∴ f( ... 2b = 2 ...(ii) Solving (i) and (ii) simultaneously we get, a = 1, b = 1.

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Description : When x^40 + 2 is divided by x^4 + 1, what is the remainder ? -Maths 9th

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Description : If the remainder of the polynomial a0 + a1x + a2x^2 + ....... + anx^n when divided by (x – 1) is 1, then which one of the following is correct ? -Maths 9th

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Description : The remainder when 1 + x + x^2 + x^3 + ........ + x^(1007) is divided by (x – 1) is -Maths 9th

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When a polynomial f(x) is divided by (x – 3) and (x + 6), the respective remainders are 7 and 22. What is the remainder when f(x) is -Maths 9th

Description : When a polynomial f(x) is divided by (x – 3) and (x + 6), the respective remainders are 7 and 22. What is the remainder when f(x) is -Maths 9th

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The remainder, when x^(200) is divided by x^2 – 3^x + 2 is -Maths 9th

Description : The remainder, when x^(200) is divided by x^2 – 3^x + 2 is -Maths 9th

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When x^3 + 2x^2 + 4x + b is divided by (x + 1), the quotient is x^2 + ax + 3 and the remainder -Maths 9th

Description : When x^3 + 2x^2 + 4x + b is divided by (x + 1), the quotient is x^2 + ax + 3 and the remainder -Maths 9th

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If ax^3 + bx^2 + x – 6 has (x + 2) as a factor and leaves a remainder 4, when divided by (x – 2), the value of a and b respectively are : -Maths 9th

Description : If ax^3 + bx^2 + x – 6 has (x + 2) as a factor and leaves a remainder 4, when divided by (x – 2), the value of a and b respectively are : -Maths 9th

Last Answer : Let p(x) = ax³ + bx² + x - 6 A/C to question, (x + 2) is the factor of p(x) , and we know this is possible only when p(-2) = 0 So, p(2) = a(-2)³ + b(-2)² - 2 - 6 = 0 ⇒ ... --(2) solve equations (1) and (2), 4a = 0 ⇒a = 0 and b = 2 Then, equation will be 2x² + x - 6

Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Description : Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Last Answer : Remainder = 145 Again, we should evaluate p(5) Let p(y) = y3 + y2 - 2y + 5 ∴ p(5) = 53 + 52 - 2 x 5 + 5 = 125 + 25 - 10 + 5 = 145 Thus , we find that p(5) is the remainder when p(y) is divided by y - 5 .

If the polynomials az3 +4z2 + 3z-4 and z3-4z + 0 leave the same remainder when divided by z – 3, -Maths 9th

Description : If the polynomials az3 +4z2 + 3z-4 and z3-4z + 0 leave the same remainder when divided by z – 3, -Maths 9th

Last Answer : Let p1(z) = az3 +4z2 + 3z-4 and p2(z) = z3-4z + o When we divide p1(z) by z - 3, then we get the remainder p,(3). Now, p1(3) = a(3)3 + 4(3)2 + 3(3) - 4 = 27a+ 36+ 9-4= 27a+ 41 When we ... to' the question, both the remainders are same. p1(3)= p2(3) 27a+41 = 15+a 27a-a = 15 - 41 . 26a = 26 a = -1

Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Description : Find the remainder when y3 + y2 - 2y + 5 is divided by y - 5. -Maths 9th

Last Answer : Remainder = 145 Again, we should evaluate p(5) Let p(y) = y3 + y2 - 2y + 5 ∴ p(5) = 53 + 52 - 2 x 5 + 5 = 125 + 25 - 10 + 5 = 145 Thus , we find that p(5) is the remainder when p(y) is divided by y - 5 .

If the polynomials az3 +4z2 + 3z-4 and z3-4z + 0 leave the same remainder when divided by z – 3, -Maths 9th

Description : If the polynomials az3 +4z2 + 3z-4 and z3-4z + 0 leave the same remainder when divided by z – 3, -Maths 9th

Last Answer : Let p1(z) = az3 +4z2 + 3z-4 and p2(z) = z3-4z + o When we divide p1(z) by z - 3, then we get the remainder p,(3). Now, p1(3) = a(3)3 + 4(3)2 + 3(3) - 4 = 27a+ 36+ 9-4= 27a+ 41 When we ... to' the question, both the remainders are same. p1(3)= p2(3) 27a+41 = 15+a 27a-a = 15 - 41 . 26a = 26 a = -1

If the polynomials az3 + 42z2 + 3z – 4 and z3 - 4z + a leave the same remainder when divided by z – 3, find the value of a. -Maths 9th

Description : If the polynomials az3 + 42z2 + 3z – 4 and z3 - 4z + a leave the same remainder when divided by z – 3, find the value of a. -Maths 9th

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When a + b + c + 3a^(1/3) b^(2/3) + 3a(2/3) b^(1/3) is divided by a^(1/3) + b^(1/3) + c^(1/3), what is the remainder ? -Maths 9th

Description : When a + b + c + 3a^(1/3) b^(2/3) + 3a(2/3) b^(1/3) is divided by a^(1/3) + b^(1/3) + c^(1/3), what is the remainder ? -Maths 9th

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If 9x^2 + 3px + 6q when divided by (3x + 1) leaves a remainder (-3/4) -Maths 9th

Description : If 9x^2 + 3px + 6q when divided by (3x + 1) leaves a remainder (-3/4) -Maths 9th

Last Answer : Given, (9x2 + 3px + 6q), when divided by (3x + 1) leaves a remainder −34−34 ∴ f(x) = 9x2 + 3px + 6q – (−34)(−34) = (9x2+3px+6q+34)(9x2+3px+6q+34) is exactly divisible by (3x + 1) ... ...(ii) Solving equations (i) and (ii), we get q = 0, p = 7474.

If x^5 – 9x^2 + 12x – 14 is divisible by (x – 3), what is the remainder ? -Maths 9th

Description : If x^5 – 9x^2 + 12x – 14 is divisible by (x – 3), what is the remainder ? -Maths 9th

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Explain Remainder Theorem. -Maths 9th

Description : Explain Remainder Theorem. -Maths 9th

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What is 91 divided by 13 with remainder?

Description : What is 91 divided by 13 with remainder?

Last Answer : 7

What is 91 divided by 13 with remainder?

Description : What is 91 divided by 13 with remainder?

Last Answer : 7

Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in ascending order. -Maths 9th

Description : Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in ascending order. -Maths 9th

Last Answer : Here, the arranged data is 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34, 43 Total number of observations = 10 Here, 10 is an even number , therefore median will be the mean of (10 / 2)th and (10 / 2 + 1)th observation. ... ⇒ 3x + 12 / 2 = 24 ⇒ 3x - 12 = 48 ⇒ 3x = 60 ⇒ x = 20 ∴ The value of x = 20

Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in ascending order. -Maths 9th

Description : Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in ascending order. -Maths 9th

Last Answer : Here, the arranged data is 6, 14, 15, 17, x + 1, 2x - 13, 30, 32, 34, 43 Total number of observations = 10 Here, 10 is an even number , therefore median will be the mean of (10 / 2)th and (10 / 2 + 1)th observation. ... ⇒ 3x + 12 / 2 = 24 ⇒ 3x - 12 = 48 ⇒ 3x = 60 ⇒ x = 20 ∴ The value of x = 20

In the linear equation y = 4x + 13, if x is the number of hours a labourer is on work and y are his wages in rupees then draw the graph. Also find the wages when work is done for 6 hours. -Maths 9th

Description : In the linear equation y = 4x + 13, if x is the number of hours a labourer is on work and y are his wages in rupees then draw the graph. Also find the wages when work is done for 6 hours. -Maths 9th

Last Answer : when the work is done for 6 hours x=6 y=4(6)+13 y=24+13 y=37 the labourer gets Rs.37 if he works for 6hrs

Ten observations 6, 14, 15, 17, x+1, 2x -13, -Maths 9th

Description : Ten observations 6, 14, 15, 17, x+1, 2x -13, -Maths 9th

Last Answer : 6, 14, 15, 17, x + 1, 2x -13, 30, 32, 34, 43, Here, n = 10 Since the number of observations is 10 (an even number), therefore, the median = (10/2)th observation + (10/2 + 1)th observation/2 = 5th observation + 6th ... = x + 1 + 2x - 13/2 ⇒ 48 = 3x - 12 ⇒ 3x = 48 + 12 = 60 ⇒ x = 20

What is/are the factors of (x^29 – x^24 + x^13 – 1) ? -Maths 9th

Description : What is/are the factors of (x^29 – x^24 + x^13 – 1) ? -Maths 9th

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The line L is given by x/5 + y/b = 1 passes through the point (13, 32). The line K is parallel to L and has the equation -Maths 9th

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Last Answer : (a) 45º The equations of the given lines are: A\(x\) + By = A + B ⇒ By = -A\(x\) + (A + B) ⇒ y = \(-rac{A}{B}x\) + \(rac{(A+B)}{B}\) ....(i)and A(\(x\) - y) + B(\(x\) ... (ii) = m2 = \(rac{(A+B)}{B-A}\)Let θ be the angle between both the lines, then∴ tan θ = 1 ⇒ θ = tan-1 (1) = 45°.

When f(x) = x4 - 2x3 + 3x2 - ax is divided by x + 1 and x - 1 , we get remainders as 19 and 5 respectively . -Maths 9th

Description : When f(x) = x4 - 2x3 + 3x2 - ax is divided by x + 1 and x - 1 , we get remainders as 19 and 5 respectively . -Maths 9th

Last Answer : When f(x) is divided by (x+1) and (x-1) , the remainders are 19 and 5 respectively . ∴ f(-1) = 19 and f(1) = 5 ⇒ (-1)4 - 2 (-1)3 + 3(-1)2 - a (-1) + b = 19 ⇒ 1 +2 + 3 + a + b = 19 ∴ a + b = 13 ------- ... + 3x2 - 5x + 8 ⇒ f(3) = 34 - 2 33 + 3 32 - 5 3 + 8 = 81 - 54 + 27 - 15 + 8 = 47

When f(x) = x4 - 2x3 + 3x2 - ax is divided by x + 1 and x - 1 , we get remainders as 19 and 5 respectively . -Maths 9th

Description : When f(x) = x4 - 2x3 + 3x2 - ax is divided by x + 1 and x - 1 , we get remainders as 19 and 5 respectively . -Maths 9th

Last Answer : When f(x) is divided by (x+1) and (x-1) , the remainders are 19 and 5 respectively . ∴ f(-1) = 19 and f(1) = 5 ⇒ (-1)4 - 2 (-1)3 + 3(-1)2 - a (-1) + b = 19 ⇒ 1 +2 + 3 + a + b = 19 ∴ a + b = 13 ------- ... + 3x2 - 5x + 8 ⇒ f(3) = 34 - 2 33 + 3 32 - 5 3 + 8 = 81 - 54 + 27 - 15 + 8 = 47

BY REAMINDER THEOREM FIND THE REAMINDER, WHEN P(x) IS DIVIDED BY G(X), WHERE -Maths 9th

Description : BY REAMINDER THEOREM FIND THE REAMINDER, WHEN P(x) IS DIVIDED BY G(X), WHERE -Maths 9th

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BY REAMINDER THEOREM FIND THE REAMINDER, WHEN P(x) IS DIVIDED BY G(X), WHERE -Maths 9th

Description : BY REAMINDER THEOREM FIND THE REAMINDER, WHEN P(x) IS DIVIDED BY G(X), WHERE -Maths 9th

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Let R1 and R2 be the remainders when the polynomials x^3 + 2x^2 – 5ax – 7 and x^2 + ax^2 – 12x + 6 are divided by (x + 1) and (x – 2) respectively. -Maths 9th

Description : Let R1 and R2 be the remainders when the polynomials x^3 + 2x^2 – 5ax – 7 and x^2 + ax^2 – 12x + 6 are divided by (x + 1) and (x – 2) respectively. -Maths 9th

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f(x) = x^4 – 2x^3 + 3x^2 – ax + b is a polynomial such that when it is divided by (x – 1) and (x + 1), the remainders are respectively 5 and 19. -Maths 9th

Description : f(x) = x^4 – 2x^3 + 3x^2 – ax + b is a polynomial such that when it is divided by (x – 1) and (x + 1), the remainders are respectively 5 and 19. -Maths 9th

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In what ratio is the line joining the points (2, –3) and (5, 6) divided by the x-axis. -Maths 9th

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Last Answer : (b) (2, 1) (- 2, 1)Let PQRS be the required square and P(0, -1) and R(0, 3) be its two opposite vertices. Length of diagonal PR = \(\sqrt{(0-0)^2+(3+1)^2}\) = \(\sqrt{16}\) = 4∴ Length of each side = \( ... + 4 = 8 ⇒ a2 = 4 ⇒ a = 2. ∴ The other two vertices of the square are (+2, 1) and (-2, 1).