Description : Find the value of k for 5x +2ky =3k, if x =1 and y =1 is its solution. -Maths 9th
Last Answer : Given, equation is 5x + 2ky = 3k. On putting x =1 and y =1 in this equation, we get 5(1) + 2k(1) =3k ⇒ 5 + 2k =3k ⇒ 5 = 3k - 2k ⇒ k = 5 Hence, required value of k is 5.
Description : If x = 0 and y = k is a solution of the equation 5x - 3 y = 0, find the value of k. -Maths 9th
Last Answer : Solution :-
Description : Find the value of k if (x-2)is a factor of polynomial p(x) = 2x(cube) - 6x(square) + 5x + k. -Maths 9th
Description : If x^3 + 5x^2 + 10k leaves remainder – 2x when divided by x^2 + 2, then what is the value of k ? -Maths 9th
Last Answer : x3+5x2+10k =(x2+2)(x+5)+10k−2x−10 ⇒10k−2x−10=−2x ⇒10k−10=0 or k=1.
Description : If the three points (k, 2k), (2k, 3k) and (3, 1) are collinear then k is equal to -Maths 9th
Last Answer : (d) 3Let (x, y) be the co-ordinates of the third vertex of the triangle. Then\(rac{0+2+x}{3}\) = 1 and \(rac{0+0+y}{3}\) = 1⇒ 2 + \(x\) = 3 and y = 3 ⇒ \(x\) = 1, y = 3. ∴ Co-ordinates of vertices of the triangle ... - y3) + x2 (y2 - y3) + x3(y1 - y2)]= \(rac{1}{2}\) [0+6+0] = \(rac{6}{2}\) = 3.
Description : For what value of k will the roots of the equation kx^2 – 5x + 6 = 0 be in the ratio 2 : 3 ? -Maths 9th
Last Answer : (b) 1 Let the roots of the equation kx2 - 5x + 6 = 0 be α and β. Then, α + β = \(\frac{5}{k}\) ...(i) αβ = \(\frac{6}{k}\) ...(ii) Given \(\ ... frac{9}{k}\) ⇒ 9k2 - 9k = 0 k(k - 1) = 0 ⇒ k = 0 or 1 But k = 0 does not satisfy the condition, so k = 1.
Description : Find the solution set of x^2 – 5x + 6 > 0. -Maths 9th
Last Answer : answer:
Description : The point (2,3) lies on the graph of the linear equation 3x - (a -1)y =2a -1. If the same point also lies on the graph of the linear equation 5x + (1-2a)y = 3b, then find the value of b. -Maths 9th
Last Answer : Given, point (2,3) lies on the line. So, the point (2, 3) is the solution of 3x - (a -1) y = 2a - 1 On putting x = 2 and y = 3 in given solution. ∴ 3 2 - (a-1) 3 = 2a - 1 ⇒ 6 - 3a + 3 = 2a - 1 ⇒ - 3a ... 2 2) 3 = 3b ⇒ 10 - 9 = 3b ⇒ 1 = 3b ⇒ 1 / 3 = b Hence, the value of b is 1 / 3.
Description : Write a solution of the linear equation 5x + 0y +8 = 0 in two variables. -Maths 9th
Last Answer : Solution : -
Description : The value of the polynomial 5x – 4x2 + 3, when x = -1 is -Maths 9th
Last Answer : (a) Let p (x) = 5x – 4x2 + 3 …(i) On putting x = -1 in Eq. (i), we get p(-1) = 5(-1) -4(-1)2 + 3= - 5 - 4 + 3 = -6
Description : If the expressions (px^3 + 3x^2 – 3) and (2x^3 – 5x + p) when divided by (x – 4) leave the same remainder, then what is the value of p ? -Maths 9th
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.
Description : Find the value of the polynomial 5x – 4x2 + 3 at x = 2 and x = –1 -Maths 9th
Last Answer : Let the polynomial be f(x) = 5x – 4x2 + 3 Now, for x = 2, f(2) = 5(2) – 4(2)2 + 3 => f(2) = 10 – 16 + 3 = –3 Or, the value of the polynomial 5x – 4x2 + 3 at x = 2 ... (–1) = –5 –4 + 3 = -6 The value of the polynomial 5x – 4x2 + 3 at x = -1 is -6.
Description : What is the equation of the line having the y-intercept –1 and parallel to the line y = 5x – 7 ? -Maths 9th
Last Answer : Slope of AB = \(rac{2-4}{1-0}\) = -2, Slope of BC = \(rac{3-2}{3-1}\) = \(rac{1}{2}\)Slope of AC = \(rac{3-4}{3-0}\) = \(-rac{1}{3}\)Slope of AB × Slope of BC = -2 x \(rac{1}{2}\) = -1∴ AB ⊥ BC, i.e, ∠B = 90º ⇒ ΔABC is a right angled.
Description : A spring with a force constant k is cut into thirds. The force constant of each of the new springs is w) k x) 3k y) (1/3)k (read: one third k) z) 9k
Last Answer : ANSWER: X -- 3k
Description : If both x – 2 and x -(1/2) are factors of px2+ 5x+r, then show that p = r. -Maths 9th
Last Answer : Show that p = r.
Description : What must be added to 2x(square) - 5x + 6 to get x(cube) - 3x(square) + 3x - 5? -Maths 9th
Description : If both (x -2) and (x - 1/2) are factors of px2 + 5x + r, show that p = r. -Maths 9th
Description : Solve x^2 – 5x + 4 > 0. -Maths 9th
Description : If both (x – 2) and (x – 1/2) are factors of px^2 + 5x + r, then: -Maths 9th
Description : What is (x^2-3x+2)/(x^2-5x +6)÷(x^2-5x+4)/(x^2-7x+12) equal to? -Maths 9th
Description : If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is -Maths 9th
Last Answer : (a) Since, (2, 0) is a solution of the given linear equation 2x + 3y = k, then put x =2 and y= 0 in the equation. ⇒ 2 (2) + 3 (0) = k ⇒ k = 4 Hence, the value of k is 4.
Description : For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution? -Maths 9th
Last Answer : The given linear equation is 2x + cy= 8. …(i) Now, by condition, x and y-coordinate of given linear equation are same, i.e., x = y. Put y = x in Eq. (i), we get
Description : For what value of c, the linear equation 2x + cy = 8 has equal values of x and y as its solution? -Maths 9th
Description : Find the value of k,if y+3 is a factor of 3y(to the power square) + ky + 6. -Maths 9th
Description : Find the value of k if the line on 2x + y = k passes through the point (3,5). -Maths 9th
Description : Degree of the polynomial 4x4 + Ox3 + Ox5 + 5x+ 7 is -Maths 9th
Last Answer : (a) Degree of 4x4 + Ox3 + Ox5 + 5x + 7 is equal to the highest power of variable x. Here, the highest power of x is 4, Hence, the degree of a polynomial is 4.
Description : One of the factors of (25x2 – 1) + (1 + 5x)2 is -Maths 9th
Last Answer : (d) Now, (25x2 -1) + (1 + 5x)2 = 25x2 -1 + 1 + 25x2 + 10x [using identity, (a + b)2 = a2 + b2 + 2ab] = 50x2 + 10x = 10x (5x+ 1) Hence, one of the factor of given polynomial is 10x.
Description : Give the geometric interpretations of 5x + 3 = 3x – 7 as an equation (i) in one variable (ii) in two variables. -Maths 9th
Description : if (1.-2) is a solution of the equation 2x-y=p,then find the value of p. -Maths 9th
Last Answer : x = 1 y = -2 2x-y = p Therefore, p = 2(1)-(-2) = 2 + 2 = 4
Last Answer : 2x-y=p put x-1,y=-2 =2(1)-(-2)=p p=4
Description : The temperature of a liquid can be measured in Kelvin units as x K or in Fahrenheit units as y°F. The relation between the two system of measurement of temperature is given by the linear equation y = 9/5 ( x - 273 ) + 32 -Maths 9th
Description : If y = (1/(a^(1-loga x))), z = (1/(a^(1-loga y))) and x = a^k, then k = -Maths 9th
Last Answer : (b) \(rac{1}{{1-log_az}}\) y = \(rac{1}{a^{1-log_ax}}\) = \(a^{-(1-log_ax)}\)⇒ logay = \(rac{1}{{1-log_ax}}\) and loga z = \(rac{1}{{1-log_ay}}\)∴ logaz = \(rac{1}{1-\bigg(rac{1}{1-log_ax}\bigg)}\) = \( ... x = \(rac{1}{{1-log_az}}\)⇒ x = \(a^{rac{1}{1-log_az}}\) = ak ⇒ k = \(rac{1}{{1-log_az}}\).
Description : 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
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°.
Description : A pair of linear equations which has a unique solution x = 2, y = -3 is (a) x + y = -1 ; 2x – 3y = -5 (b) 2x + 5y = -11 ; 4x + 10y = -22(c) 2x – y = 1 ; 3x + 2y = 0 (d) x – 4y – 14 = 0 ;5x – y – 13 = 0
Last Answer : (d) x – 4y – 14 = 0 ;5x – y – 13 = 0
Description : If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th
Last Answer : (c) Let p(x) = 2x2 + kx Since, (x + 1) is a factor of p(x), then p(-1)=0 2(-1)2 + k(-1) = 0 ⇒ 2-k = 0 ⇒ k= 2 Hence, the value of k is 2.
Description : FOR WHAT VALUE OF K, THE POLYNOMIAL X2+(4-K)X+2 IS DIVISIBLE BY X-2 -Maths 9th
Last Answer : As the given polynomial divisible by x-2 means the polynomial satisfies for the value x=2 So putting x=2 in x²+(4-k)x+2 yields 0 ⇒2²+(4-k)2+2=0 ⇒4+8-2k+2=0 ⇒ 2k=14 ⇒ k= ... ;-3x+2 if factorized yields (x-1)(x-2). Thus is divisible by x-2 as well as divisible by x-1.
Last Answer : The value of 'k' is 4
Description : If x+1 is a factor of the polynomial 3x(square) - kx,then find the value of k. -Maths 9th
Description : For what value of k,(x+1) is a factor of p(x) - kx(square) - x - 4 ? -Maths 9th
Description : One root of x^2 + kx – 8 = 0 is the square of the other, then the value of k is : -Maths 9th
Description : For what value of p is the coefficient of x^2 in the product (2x – 1) (x – k) (px + 1) equal to 0 and the constant term equal to 2 ? -Maths 9th
Description : For what value of k, will the expression (3x^3 – kx^2 + 4x + 16) be divisible by (x – k/2) ? -Maths 9th
Last Answer : Given f(x) = 3x³ - kx² + 4x + 16. Since (x - k/2) is a factor of polynomial. This means x = k/2 is the zero of the given polynomial. ⇒ f(k/2) = 3(k/2)³ - k(k/2)² + 4(k/2) + 16 ⇒ 0 ... - 4k + 32) + 4(k² - 4k + 32) ⇒ 0 = (k + 4)(k² - 4k + 32) ⇒ k = -4.