10th maths Chapter Polynomial extrascore questions

Math Adda  

Chapter: POLYNOMIALS        

LEVEL-I

1. The zeroes of the polynomial 2x²-3x-2 are

a. 1, 2        b. -1/2,1    

c. ½,-2      d. -1/2,2                       [Ans- (d)]

2. If a and b are zeroes of the polynomial 2x²+7x-3, then the value of a² +b² is

a. 49/4                b. 37/4       

c. 61/4                d. 61/2                                                      
Ans-( c ) 

3. If the polynomial 6x³+16x²+px -5 is exactly divisible by 3x+ 5 , then the value of p is

a. -7      b. -5     

c.5        d.7                                                                                  
[Ans- (d )]

4. If 2 is a zero of the polynomials 3x2+ax-14 and 2x3+bx2+x-2, then the value of 2 - 2b is

a. -1       b. 5         

c. 9       d. -9                         

[Ans-( c ) ]

5. A quadratic polynomial whose product and sum of zeroes are 1/3 and √2 respectively is

(a) 3x² – x +3√ 2 (b) 3x² + x - 3√2 (c) 3x² + 3√2x +1 (d) 3x² – 3√2x +1         
[ Ans: (d)]

LEVEL-II

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

2. For what value of k, (-4) is zero of the polynomial x² – x – (2k+2)?                          
Ans: k=9

3. Write a quadratic polynomial, the sum and product of whose zeroes are 3 and -2. 
Ans: x² -3x-2

4. Find the zeroes of the quadratic polynomial 2x²-9-3x and verify the relationship between the zeroes and the coefficients.                                   Ans: 3, -3/2

5. Write the polynomial whose zeroes are 2 +√3 and 2 - √3.          Ans: p(x)=x2-4x+1

LEVEL – III

1. Find all the zeroes of the polynomial 2x³+x²-6x-3, if two of its zeroes are -√3 and √3. 
Ans: x=-1/2

2. If the polynomial x⁴ + 2x³ + 8x²+12x+18 is divided by another polynomial x² + 5, the remainder comes out to be  px+q. 

Find the value of p and q.                                                         Ans:p=2,q=3

3. If the polynomial 6x⁴+8x³+17x²+21x+7 is divided by another polynomial 3x²+4x+1, the remainder  comes out to  be (ax+b), find a and b.                      Ans:a=1, b=2

4. If two zeroes of the polynomial f(x)= x³-4x²-3x+12 are √3 and -√3, then find its third zero. Ans: 4

5. If a, b are zeroes of the polynomial x²-2x-15 then form a quadratic polynomial whose zeroes are  (2a) and (2b).              Ans: x²-4x-60

LEVEL – IV

1. Find other zeroes of the polynomial p(x)=2x⁴ +7x³19x²-14x +30 if two of its zeroes are √2 and -
√2.

Ans: 3/2 and -5

2. Divide 30x⁴ +11x³-82x²-12x-48 by (3x² +2x-4) and verify the result by division algorithm.

3. If the polynomial 6x⁴ +8x³-5x²+ax+b is exactly divisible by the polynomial 2x²-5, then find the 
value of a and b.     
Ans: a = -2 0 , b = - 2 5

4. Obtain all other zeroes of 3x⁴ -15x³+13x²+25x-30, if two of its zeroes are and ±√5/3. 
Ans: 
±√5/3,3,2

5. If a, b are zeroes of the quadratic polynomial p(x)=kx²+4x+4 such that a² +b²=24, find the value 
of k.                                                                        
Ans: k=2/3 or k= -1

SELF EVALUATION

1. If a, b are zeroes of the quadratic polynomial ax²+bx+c then find (a) a/b +b/a (b) a² +b²

2. If a, b are zeroes of the quadratic polynomial ax²+bx+c then find the value of a² - b²

3. If a, b are zeroes of the quadratic polynomial ax²+bx+c then find the value of a³ +b³

4. What must be added to 6x⁵+5x⁴+11x³-3x²+x+5 so that it may be exactly divisible by 3x² -2x+4 ?

5. If the square of difference of the zeroes of the quadratic polynomial f(x)= x²+px+45 is equal to 144, 
find the value of p.

FORMATIVE TEST 2 GUESS PAPER CLASS 10 MATHS

Section -A

CBSE GUESS

1.The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have

(A) a unique solution (B) exactly two solutions        (C) infinitely many solutions (D) no solution

2. If a pair of linear equations is consistent, then the lines will be

(A) parallel      (B) always coincident             (C) intersecting or coincident             (D) always intersecting

3. The pair of equations y = 0 and y = –7 has

(A) one solution          (B) two solutions        (C) infinitely many solutions              (D) no solution

4.If sinA + sin2A = 1, then the value of the expression (cos2A + cos4A) is

(A) 1                                        (B)1/2                          (C) 2                                                  (D) 3

5. Given that sinα =1/2 and cosβ =1/2 , then the value of (α + β) is

(A) 0°              (B) 30°                                    (C) 60°                                                           (D) 90°

Section - B

1.For which values of p and q, will the following pair of linear equations have infinitely many solutions?

4x + 5y = 2    and            (2p + 7q) x + (p + 8q) y = 2q – p + 1.

2. In a competitive examination, one mark is awarded for each correct answer while1/2 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly

3. Given that α + β = 90°, show that  = sinα

4. A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number

5.An aeroplane leaves an Airport and flies due North at 300 km/h. At the same time, another aeroplane leaves the same Airport and flies due West at 400 km/h. How far apart the two aeroplanes would be after 1and 1/2  hours?       Or,

In an equilateral triangle ABC, D is a point on side BC such that BD =1/3 BC. Prove that 9 AD²= 7 AB².

6. Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle.

7. Show that tan⁴θ + tan²θ = sec⁴θ – sec²θ.

8. If sin θ + cos θ = √3 , then prove that tan θ + cot θ = 1

9. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians

10. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.