X Polynomial MCQ Assignments in Mathematics Class X (Term I)

X Polynomial MCQ Assignments in Mathematics Class X (Term I)

1. If α,β are zeroes of the polynomial f(x) = x2 + px + q, then polynomial having 1/α and 1/β as its zeroes is

(a) x2 + qx + p (b) x2 – px + q (c) qx2 + px + 1 (d) px2 + qx + 1

2. If α and β are zeroes of x2 – 4x + 1, then 1/α + 1/β – αβ is

(a) 3 (b) 5 (c) –5 (d) –3

3. The quadratic polynomial having zeroes as 1 and –2 is :

(a) x2 – x + 2 (b) x2 – x – 2 (c) x2 + x – 2 (d) x2 + x + 2

4. If α, β are zeroes of x2 – 6x + k, what is the value of k if 3α+2β=20 ?

(a)–16 (b) 8 (c) 2 (d) –8

5. If one zero of 2x2 – 3x + k is reciprocal to the other, then the value of k is

(a) 2 (b) −23 (c) −32 (d) –3

6. The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is –2 is

(a) x2 + 3x – 2 (b) x2 – 2x + 3 (c) x2 – 3x + 2 (d) x2 – 3x – 2

7. If (x + 1) is a factor of x2 – 3ax + 3a – 7, then the value of a is :

(a)1 (b) –1 (c) 0 (d) –2

8. The number of polynomials having zeroes –2 and 5 is :

(a)1 (b) 2(c)3 (d) more than 3

9. The quadratic polynomial p(y) with –15 and–7 as sum and one of the zeroes respectively is :

(a) y2 – 15y – 56 (b) y2 – 15y + 56 (c) y2+ 15y + 56 (d) y2 + 15y – 56

10.The value of p for which the polynomial x3 + 4x2 – px + 8 is exactly divisible by (x – 2) is :

(a) 0 (b) 3 (c) 5 (d) 16

11. If 1 is a zero of the polynomial p(x) = ax2– 3(a – 1)x – 1, then the value of a is :

(a) 1 (b) –1 (c) 2 (d) –2

12. If –4 is a zero of the polynomial x2 – x – (2 + 2k), then the value of k is :

(a) 3 (b) 9 (c) 6 (d) –9

13.The degree of the polynomial (x + 1)(x2 – x – x4 + 1) is :  (a) 2 (b) 3 (c) 4 (d) 5

14. If (x + 1) is a factor of x2– 3ax + 3a – 7, then the value of a is :

(a) 1 (b) –1 (c) 0 (d) –2

15. If sum of the squares of zeroes of the quadratic polynomial f(x) = x2 – 8x + k is 40, the value of k is :

(a) 10 (b) 12 (c) 14 (d) 16

X math's Chapter: 02 Polynomials CBSE Test paper New

Download 

Class X Polynomial Test Paper-1
Download File

Class X Polynomial Test Paper-2 
Download File

Class X Polynomial Test Paper-3 
Download File

Class X Polynomial Test Paper-4 
Download File

9th Linear Equation in two Variable [Guess paper] 2013

9th Linear Equation in two Variable [Sample Guess paper] 2013

[1 Mark Questions]

1. Which of the following is not a linear equation?

(a) ax + by + c = 0                 (b) 0x + 0y + c = 0              

(c) 0x + by + c = 0                 (d) ax + 0y + c = 0

2. Age of ‘x’ exceeds age of ‘y’ by 7 yrs. This statement can be expressed as linear equation as  

(a) x + y + 7 = 0                  (b) x – y + 7 = 0      

(c) x – y – 7 = 0                  (d) x + y – 7 = 0

3. Linear equation in one variable is :

(a) 2x = y      (b) y2 = 3y + 5   (c) 4x – y = 5   (d) 3t + 5 = 9t – 7

4. The condition that the equation ax + by + c = 0 represent a linear equation in two variables is

(a) a ≠ 0, b = 0              (b) b ≠ 0, a = 0               

c) a = 0, b = 0               (d) a ≠ 0, b ≠ 0             

5. How many linear equations in x and y can be satisfied by x = 1 and y = 2?

(a) only one   (b) two  (c) infinitely many (d) three

6. The general form of a linear equation in two variables is :

(a) ax + by + c = 0, where a, b, c are real  umbers and a, b ≠ 0  

(b) ax + b = 0, where a, b are real numbers and a ≠0

(c) ax² + bx + c = 0, where a, b, c are real numbers and a, b ≠ 0    

(d) none of these

7. The equation of the line whose graph passes through the origin, is :  

(a) 2x + 3y = 1              (b) 2x + 3y = 0  

(c) 2x + 3y = 6             (d) none of these              

[(b){form x = my}]

8. The equation of y-axis is : 

(a) y = 0 (b) x = 0(c) y = a (d) x = a        

[ (b) The equation of y-axis is x = 0 ]

9. The equation of x-axis is : 

(a) y = 0 (b) x = 0 (c) y = a (d) x = a      

[(a) The equation of x-axis is y = 0 ]

10. Any point on the x-axis is of the form: 

(a) (x, y)  (b) (0, y) (c) (x, 0) (d) (x, x)  

[(c) On x-axis y-coordinate will be 0].

11. Any point on the line y = x is of the form : 

(a) (a, a) (b) (0, a)  (c) (a, 0) (d) (a, – a)

[(a) Any point on the line y = x is of the form (a, a).

12. The point of the form (a, – a) always lies on the line : 

(a) x = a (b) y = – a  (c) y = x (d) x + y = 0

[d) The point (a, – a) always lies on the line x + y = 0.]

13. Equation of the line y = 0 represents: 

(a) y-axis (b) x-axis (c) both x-axis and y-axis (d) origin

[(b) The equation of x-axis is y = 0]

14. The graph of the linear equation 2x + 3y = 9 cuts y-axis at the point : 

(a) 9/2 , 0  (b) (0, 9) (c) (0, 3) (d) (3,1) [C]

15. The point of the form (a, a) always lies on:

(a) x-axis(b) y-axis(c) on the line y = x(d) on the line x + y = 0  [C]                      

9th Linear Equation in two Variable [Guess paper] 2013 [2 Marks Questions]

1. The cost of a notebook is twice the cost  of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be Rs x and that of a pen to be Rs y.)

2. Which one of the following options is true, and why? y = 3x + 5 has (i) a unique solution (ii) only two solutions (iii) infinitely many solutions.

[ infinitely many solutions. It is because a linear equation in two variables has infinitely many solutions. We keep changing the value of x and solve the linear equation for the corresponding value of y]

3. Write any four solutions for  (i) 2x + y = 7 or, (ii) x = 4y

4. Check (4, 0) is a solution For the equation x – 2y = 4

5. If (2, 0) is a solution of linear equation 2x + 3y = k, then find the value of k.

6. If the point (2 – 1) lies on the graph of the equation 3x + ky = 4, then find the value of k.

7. Give the geometric representations of y = 3 as an equation 

(i) in one variable (ii) in two variables

8. Check whether the graph of the linear equation x + 2y = 7 passes through the point (0, 7).

9. Mayank and Sujata two students of class IX together contributed Rs 1000 towards PM Relief fund. Write a linear equation satisfying the data

10. The cost of a table exceeds the cost of the chair by Rs 150. Write a linear equation in two variables to represent this statement. Also, find two solutions of the same equation.

8th Polygons Solved Questions Paper[CBSE Maths]

1.Q. Find the number of diagonals in an octagon?

Ans: Number Of Diagonals Of Polygon = n(n-3) / 2     

Where n is Number Of Sides

Here n = 8

Diagonals= [8(8-3)5]/2 = 20

2.Q. Find the number of sides of a polygon whose each exterior angle is 45⁰ .

Ans: Measure of Each Exterior Angle of a Polygon = 360/n

Each Exterior Angle = 45

45 = 360/n

Number of Sides = 360/45 =8

So Number of Sides = 8

3. Q. The sum of the interior angles of a regular polygon is 3 times the sum of its exterior angles. Determine the number of sides of the polygon.

Ans: sum of the interior angles of a regular polygon is 3 times the sum of its exterior angles.

We know that in a regular polygon sum of all the exterior angles = 360°

Therefore, sum of interior angles = 3 × 360° = 1080°

Again, we have sum of interior angles, S = (n - 2)180°, where n is the number of sides of the polygon

⇒ (n - 2)180° = 1080°
⇒ n - 2 = 6
⇒ n = 8
4. Q.  (a) What is the minimum interior angle possible for a regular polygon? Why?

 (b) What is the maximum exterior angle possible for a regular polygon?

Answer: The polygon with minimum number of sides is a triangle, and each angle of an equilateral triangle measures 60°, so 60° is the minimum value of the possible interior angle for a regular polygon. For an equilateral triangle the exterior angle is 180°-60°=120° and this is the maximum possible value of an exterior angle for a regular polygon.
The sum of the exterior angles of any polygon= 360⁰
Hence, the polygon of 8 sides is octagon.

5. Q. Find the measure of each exterior angle of a regular polygon of 9 sides.

Ans: Total measure of all exterior angles = 360

No. of sides = 9

Measure of each exterior angle = 360/9 = 40

6.Q. If the sum of the measures of the interior angles of a polygon equals the sum of the measures of the exterior angles, how many sides does the polygon have?

Ans:The sum of the measures of the interior angles of a polygon with n sides =(n-2)x180⁰

(n-2) x180⁰ = 360⁰            Þ      n=2+2=4

7.Q. The sum of the interior angles of a regular polygon is:(n - 2) × 180° where n is the number of sides of the polygon.

Solution: The sum of its exterior angles of regular polygon= 360°

The exterior angle of a regular polygon

Interior angle of a regular polygon = sum of interior angles ÷ number of sides

8. Q.What is the measure of the each angle of regular Hexagon?

Ans: No. of sides in regular hexagon = 6

The measure of the each angle =[(2n – 4)x90⁰ /n ]=[2x6-4]x90⁰/6 =720⁰ /6 =120⁰

9. Q. Find the number of sides of a polygon whose each interior angle is 156⁰ .

Ans each exterior angle = 180 - 1560 = 24⁰

Measure of Each Exterior Angle of a Polygon = 360/n

 Þ 24⁰  = 360/n       Þ n = 360/24 =15

10.Q.  Two regular polygons are such that the ratio between their no. of sides is 1:2 and the ratio of measures of their interior angle is 3:4. Find the number of sides of each polygon.

Ans: let the number of sides are x and 2x

then their interior angles will be [{(2n-4)/n}x90⁰]       and [{(4n-4)/n}x90⁰]

A/Q, the ratio of measures of their interior angle = 3:4

Þ [{(2n-4)/n}x90⁰] ¸ [{(4n-4)/n}x90⁰] = ¾

On solving this we get , n=5

So, the numbers of sides are 5 and 2x5=10

8th Polygons Solved Questions Paper Download File