Polynomial class 10 test yourself

 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.

CBSE Maths X Ch-6 : Trigonometry Identities

1 mark questions

Q. 1 Write the value of sin 620 sin 280 – cos620 cos 280

Q. 2 Write  cot A in terms of sin A.

Q. 3 Express sec790 + cot 610 in terms of trigonometrical ratios of angles between 00and 450 .

Q. 4 If 3tanθ = 4 , then write the value of tan θ + cot θ .

Q. 5 If sinq – cos θ = 0 , 00 <θ < 900 , then write the value of 'θ ' .

Q. 6 If 'q ' , then write the value of sin θ + cos 2θ .

Q. 7 Write the value of sin2 740 + sin2 160 .

Q. 8 In ΔABC, ∠B = 900 and sin C = 4/5 , what is the value of cos A?

Q. 9 If A and B are acute angles and sin A = cos   B , than write the value of A+B.

Q. 10 Write the value of tan2 300 + sec2 450 .

Q. 11 Write the value of 9 cosec2620 – 9 tan2 280 .

Q. 12 If sin q = 1/2, write the value of sin q – cosec θ .

Q. 13 What is the value of cos2490 – sin2 410 ?

Q. 14 If q = 450  , then what is the value of 2cos ec2θ + 3sec2q ?

Q. 15 Write the value of sin ( 900 –q ) cos q + cos(900 – q) Sinq

Q. 16 If tan (3x –150 ) =1, than write the value of 'x'.

Q. 17 In ΔABC, write tan (A+ B)/2  in terms of angle 'C'.

Q. 18 If q = 300 , then write the value of 1 – tan2 2q .

Q. 19 If tanq + cotq = 3, then what is the value of tan2θ + cot2θ ?

Q 20 Write the value of cot (350 +q ) – tan (550 – q )

2/3 marks questions

Q. 21 If sin 2q = cos (q – 36)0, 2θ and (q – 360) are acute angles. Find the value of 'q ' .

Q. 22 If tan (320 +q ) = cotq , θ and (320 +q ) are acute angles, find the value of 'q '.

Q. 23 If sin ( A+ B) =1 and cos(A – B) = √3 /2 ,  00 ≤ ( A+ B) ≤ 900 , A > B, then find the values of A and B.

Q. 24 If q = 300 , then find the value of (1– tan2q)/(1+ tan2q)

Q. 25 If tan q = √2 –1, then find the value of (2 tanq) /(1+ tan2q)

Q. 26 If q = 300 , then verify : cos 3q = 4cos3q – cosq .

Q. 27 Simplify: tan 2 600 + 4cos2 450 + 3sec2 300 + 5cos2 900

Q. 28 Find the value of :-

(sin 620)/ cos 28  +  2 (tan 730)/ cot170 –  (2sin 28 .sec620 )/(cot170 7sec 320 – 7cot 580)

Q. 29 find the value of

(11 sin 700 ) / ( 7 cos200 ) –  (4/7) [(cos530 .cos 370) / (tan150 .tan350 tan550 tan750)

Q. 30 Find the value of :-

3(sin2 740 sin216 )/( 4sin 620 .sec280) + 3(tan2 280 – cosec 2620 )/ tan 250 .tan 350tan 550 tan 650)

CBSE :10th Real Numbers Extra score Test paper

1. Express 140 as a product of its prime factors

2. Find the LCM and HCF of 12, 15 and 21 by the prime factorization method.

3. Find the LCM and HCF of 6 and 20 by the prime factorization method.

4. State whether13/3125 will have a terminating decimal expansion or a non-terminating repeating decimal.

5. State whether 17/8 will have a terminating decimal expansion or a non-terminating repeating decimal.

6. Find the LCM and HCF of 26 and 91 and verify that LCM × HCF = product of the two numbers.

7. Use Euclid’s division algorithm to find the HCF of 135 and 225

8.Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m

9. Prove that √3 is irrational.

10.Show that 5 – √3 is irrational

11. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

12. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

13. Express 156 as a product of its prime factors.

14. Find the LCM and HCF of 17, 23 and 29 by the prime factorization method.

15. Find the HCF and LCM of 12, 36 and 160, using the prime factorization method.

MATH ADDA "10TH MATHS BY JSUNIL": 10th Number system solved important question

MATH ADDA "10TH MATHS BY JSUNIL": 10th Number system solved important question: 1. Prove that one of every three consecutive integers is divisible by 3. Ans: n,n+1,n+2 be three consecutive positive integers We k...

JSUNIL TUTORIAL’S CBSE SAMPLE PAPER CHAPTER - SIMILAR TRIANGLE CLASS 10TH

1. If a straight line divides any two sides of a triangle in the same ratio, then prove that the line must be parallel to the third side.

2. Prove that, the internal (external) bisector of an angle of a triangle divides the opposite side internally (externally) in the ratio of the corresponding sides containing the angle.

3. In D PQR, given that S is a point on PQ such that ST II QR and PS/SQ= 3/5 If PR = 5.6 cm, then find PT.

4.  In D ABC, the internal bisector AD of < A meets the side BC at D. If BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm, then find DC.  

5.   D is the midpoint of the side BC of D ABC. If P and Q are points on AB and on AC such that DP bisects < BDA and DQ bisects < ADC, then prove that PQ II BC.

6.   In D ABC, < ABC=90° and BD^ AC. If AB=5 cm, BD=3 cm and CD=5cm, then find the value of BC.

7. In a quadrilateral ABCD, the bisectors of < B and < D intersect on AC at E. Prove that AB

 / BC = AD/DC

8. The internal bisector of < A of D ABC meets BC at D and the external bisector of < A meets BC produced at E. Prove that BD/BE = CD/CE

9. ABCD is a quadrilateral with AB =AD. If AE and AF are internal bisectors of < BAC and < DAC respectively, then prove that EF II BD.

10. A girl of height 120 cm is walking away from the base of a lamp-post at a speed of 0.6 m/sec. If the lamp is 3.6 m above the ground level, then find the length of her shadow after 4 seconds

11. Prove that In a right angled triangle, the square of the hypotenuse is equal to the sum of the  squares of the other two sides.

12. Prove that in any triangle the sum of the squares of any two sides is equal to twice the square of half of the third side, together with twice the square of the median which bisects the third side.

13. If ABC is an obtuse angled triangle, obtuse angled at B and if AD ^ CB then Prove that   

  AC²=AB² + BC²+2BCxBD

14. In equilateral triangle ABC, if ADBC, then prove that 3AB²= 4AD²

15. In a right triangle ABC, right angled at C, P and Q are points of the sides CA and CB respectively, which divide these sides in the ratio 2: 1.  Prove that (i) 9AQ²= 9AC² + 4BC²   (ii) 9BP²= 9BC² + 4AC²    (iii) 9 (AQ²+BP²) = 13AB² [ Hint Since P divides AC in the ratio 2 : 1, CP= 2/3 AC, QC= 2/3 BC]

16. P and Q are the mid points on the sides CA and CB respectively of triangle ABC  right angled at C. Prove that 4(AQ² +BP²) = 5AB²

17. In an equilateral D  ABC, the side BC is trisected at D. Prove that 9AD² = 7AB²

18. Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle.

19. If ABC is an obtuse angled triangle, obtuse angled at B and if AD^ CB Prove that AC2 =AB² + BC²+2BCxBD

20. If ABC is an acute angled triangle, acute angled at B and AD^ BC prove that AC² =AB² + BC² −2BCx BD

Sample Question Paper Class 10 Mathematics SA-1

Sample Question Paper Class 10 Mathematics SA-1: 1. ABC is right angled at A. The value of tan B . tan C is _______ (a) tan B (b) tan C (c) 0 ...

CBSE Sample Papers | SA Term-1 | Class 10 I 2011-1...

CBSE ADDA: CBSE Sample Papers | SA Term-1 | Class 10 I 2011-1...: Sample Question Papers for Term I (September 2011) Science (Class IX & X) ...

CBSE sample paper 10th Polynomials

1. Find a quadratic polynomial, the sum and product of whose zeroes are 0 and √5 respectively.

2. Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively

3. If a andb are the zeros of the quadratic polynomial f(x)= x2-5x+4, find the value of 1/a + 1/b-2a b

4. Find the zeroes of the quadratic polynomial 4 √3 x2 + 5 x - 2 √3 and verify the relationship between the zeroes and the coefficients.

5. Find the zeroes of the quadratic polynomial 4u2 + 8u and verify the relationship between the zeroes and the coefficients

6. Find the quadratic polynomial, the sum and product of whose zeroes are √2 and √3 respectively.

7. If a and b are the zeros of the given quadratic polynomial f(x)= 5x2 - 7x + 1, find the value 1/a + 1/b

8. Find the zeroes of the polynomial x2 – 3 and verify the relationship between the zeroes and the
Coefficients

9. Find the remainder when p(x)= x3-6x2+2x-4 when divided by 1 - 2x.

10. Find the remainder when x51+51 is divided by (x+1).

11. Find all the integral zeros of x3 -3x2 - 2x + 6

12. Obtain all zeros of 3x4 + 6x3 - 2x2 - 10x - 5, if two of its zeros are √5/√3 and - √5/√3

13. If (x - 2) and [x – ½ ] are the factors of the polynomials qx2 + 5x + r prove that q = r

14. If the zeroes of the polynomial are 3x2 − 5x + 2 are a+ b and a- b, find a and b.

15. On dividing 2x2 + 3x + 1 by a polynomial g(x), the quotient and the remainder were 2x-1 and 3 respectively. Find g (x). 

polynomials grade 10 test paper

1. Every linear equation in two variables has ___ solution(s).

(a) No (b) one (c) two (d) infinitely many

2. For a pair to be consistent and dependent the pair must have

(a) no solution (b) unique solution

(c) infinitely many solutions (d) none of these

3. Graph of every linear equation in two variables represents a ___

(a) point (b) straight line(c) curve (d) triangle

4. Each point on the graph of pair of two lines is a common solution of he lines in case of 

(a) Infinitely many solutions (b) only one solution (c) no solution (d) none of these

5.The pair of linear equations is said to be inconsistent if they have

(a) only one solution (b) no solution (c) infinitely many solutions. (d) both a and c

6. Find the value of k so that the equations x + 2y = – 7, 2x + ky + 14 = 0 will represent coincident lines.

7. Give linear equations which is coincident with 2 x + 3y - 4 = 0 Find the value of K so that the pair of linear equations :

(3 K + 1) x + 3y – 2 = 0   

 (K² + 1) x + (k–2)y – 5 = 0 is inconsistent.

8. Solve for x and y :    

2^x + 3^y = 17

2^{x + 2} – 3 ^y+1 = 5.

9. The area of a rectangle remain the same if its length is increased by 7 cm and the breadth is decreased by 3 cm. The area remains unaffected if length is decreased by 7 cm and the breadth is increased by 5 cm. Find length and breadth.

10. A no. consists of three digits whose sum is 17. The middle one exceeds the sum of other two by 1. If the digits are reversed, the no. is diminished by 396. Find the no.

CBSE Maths Class VI to X

• 10th Math Test Paper (12)
• 6th Maths Test paper (9)
• 7th Maths (2)
• 7th Maths Test Paper (7)
• 8th Mathematics (11)
• 8th Maths (2)
• 9h The word 'geometry (3)
• 9th Maths (5)
• 9th Maths Test Paper (8)
• CTET (1)
• Geometry (3)
• maths glossary (3)

Polynomial test paper for class 10

CBSE TEST PAPER O1 

   10th Polynomial         

1. Write the zeroes of the polynomial x² -2x + 4.

2. Find a quadratic polynomial, the sum and product of whose zeroes are 0 and √5  respectively.

3. Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively

4. If a andb are the zeros of the quadratic polynomial f(x)= x²-5x+4, find the value of 1/a  + 1/b-2a b

5. Find the zeroes of the quadratic polynomial 4 √3 x² + 5 x - 2 √3 and verify the relationship between the zeroes and the coefficients.

6. Find the zeroes of the quadratic polynomial 4u² + 8u and verify the relationship between the zeroes and the coefficients

7. Find the quadratic polynomial, the sum and product of whose zeroes are √2 and √3 respectively.

8. If a and b are the zeros of the given quadratic polynomial f(x)= 5x² - 7x + 1, find the value  1/a  + 1/b

9. Find the zeroes of the polynomial x² – 3 and verify the relationship between the zeroes and theCoefficients

10. Find the remainder when p(x)= x³-6x²+2x-4 when divided by  1 - 2x.

11. Find the remainder when x⁵¹+51 is divided by (x+1).

12. Find all the integral zeros of x³ -3x² - 2x + 6

13. Obtain all zeros of 3x⁴ + 6x³ - 2x² - 10x - 5, if two of its zeros are √5/√3 and - √5/√3

14. If (x - 2) and [x – ½ ] are the factors of the polynomials qx² + 5x + r prove that q = r

15. If the zeroes of the polynomial are 3x² − 5x + 2 are a+ b and a- b, find a and  b.

16. On dividing 2x2 + 3x + 1 by a polynomial g(x), the quotient and the remainder were 2x-1 and 3 respectively. Find g (x).

What is a rational number?

What is a rational number?

 

Any ordinary number of arithmetic:  Any whole number, fraction, mixed number or decimal; together with its negative image.

A rational number is a nameable number, in the sense that we can name it according to the standard way of naming whole numbers, fractions, and mixed numbers.  "Five," "Six thousand eight hundred nine," "Nine hundred twelve millionths," "Three and one-quarter," and so on.

Q. Which of the following numbers are rational?

1

−6

3½

−

2 3

0

5.8

3.1415926535897932384626433

A rational number can always be written 

a b	, where a and b are integers (b  0).

An integer itself can be written as a fraction:  b = 1.  And fromarithmetic, we know that we can write a decimal as a fraction.

When a and b are positive, that is, when they are natural numbers, then we can always name their ratio.  Hence the term, rational number.

At this point, the student might wonder, What is a number that is not rational?

An example of such a number is  ("Square root of 2").  It is not possible to name any whole number, any fraction or any decimal whose

square is 2.

7 5

is close, because

7 5

·

7 5

=

49 25

-- which is almost 2.