class 10 Application of trigonometry solved Board Questions

Class 10 Application of Trigonometry [Height and Distance] Solved Problems (14Q)

Question 01: The angle of elevation of an aeroplane from a point on the ground is 45 o. After a flight of 15 seconds, the elevation changes to 30 o. If the aeroplane is flying at a constant height of 3000 meters, find the speed of the plane.

Questions 02: A around balloon of radius r subtends an angle a at the eye of the observer while the angle of elevation of its centre is b , prove that the height of the centre of the balloon is r sin b cosec a/2

Class 10 Polynomial Test paper

1. If x=1 is a zero of a polynomial f(x) = x³-2x²+4x+k. Write the value of k                        (Ans. k= -3)

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

3. Verify whether 3 and 2 are the zeros of the poly. (x - 2)(x -3)?

4. Find the zeros of the polynomial f(x) =4x²+8x               (Ans. 0, -2)

5. Find a quadratic polynomial each with the given zeros as sum and the product of its zeros respectively      

(a) ¼, -1              (b) √2  , 1/3                                       
{Ans.(a).4x²-x-4,(b) 3x²-3√2 x+1}

3 marks questions

1. Using division algorithm, find the quotient and the remainder on dividing f(x) by g(x) , where

f(x) =6x³ +13x² + x - 2 and g(x) =2x+1                                              

[Ans.q (x) =3x²+5x-2, r(x)=0]

2. If α , β are the zeros of 2y2+7y+5 write the value of α+ β +α β.   
(Ans. -1)

3. Find the zeros of a quadratic polynomial 5x2-4-8x and verify the relationship between the zeros and the coefficients of the polynomial.                                                                                            (Ans.2,-2/5 )

4. If α, β are the zeros of the poly. f(x)=x²-px+q, find the value of  (a) α²+β²       (b)1/α +1β        

(Ans. P² -2q, p/q ) 

5. On dividing x³+2x²-5x-6 by a polynomial g(x) the quotient and remainder were x+1 and - 4x -4 respectively Find the polynomial g(x)      

(Ans. x²+ x - 2)

6. If (x + a) is a factor of 2x²+2ax+5x+10. Find a.              (Ans. a = 2)

7. Find all the zeros of 2x⁴-9x³+5x²+3x-1, if two of its zeros are 2+√3 & 2- √3

8. 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.

9. Find all other zeroes of the polynomial p(x) = 2x³ + 3x² – 11x – 6, if one of its zero is –3.

10. If one zero of the polynomial (a² +9)x² +13x +6a is reciprocal of the other . Find the value of a.

CBSE Class 10 Self Evaluation Tests for chapter Polynomial

Section-A

1. The zeroes of the quadratic polynomial x² + 99x + 127 are

(A) both positive (B) both negative (C) one positive and one negative (D) both equal

2. The zeroes of the quadratic polynomial x² + k x + k, k ≠ 0,

(A) cannot both be positive (B) cannot both be negative (C) are always unequal (D) are always equal

3. If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then

(A) c and a have opposite signs (B) c and b have opposite signs (C) c and a have the same sign (D) c and b have the same sign

4. If one of the zeroes of a quadratic polynomial of the form x²+ax + b is the negative of the other, then it

(A) has no linear term and the constant term is negative.

(B) has no linear term and the constant term is positive.

(C) can have a linear term but the constant term is negative.

(D) can have a linear term but the constant term is positive.

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

(A) 1 (B) 2 (C) 3 (D) more than 3

Section-B

1. Find the zeroes of 2x³ – 11x² + 17x – 6.

 2. Find the quadratic polynomial, the sum and the product of whose zeroes are ¹/₂, and –2 .

 3. Find the values of m and n for which x = 2 and –3 are zeroes of the polynomial:
 3x² – 2mx + 2n.

 4. Check whether x² + 4 is factor of x⁴ + 9x² + 20

Section-C

 5. Divide the polynomial (x⁴ + 1) by (x – 1) and verify the division algorithm.

 6. Find all zeroes of x⁴ – 3x³ – 5x² + 21x – 14, if two of its zeroes are √7 and – √7 

 7. On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4 respectively, find g(x). 

Section-D

8. Given that √2 is a zero of the cubic polynomial 6x³ + √2 x² – 10x – 4 √2 , find  its other two zeroes.

9. Find k so that x² + 2x + k is a factor of 2x⁴ + x³ – 14 x² + 5x + 6. Also find all the zeroes of the two polynomials.

10. Given that x – √5 is a factor of the cubic polynomial x³ – 3√ 5x² + 13x – 3 √5 , find all the zeroes of the polynomial.