CLASS 10th IMPORTANT QUESTIONS (FOR 90+ Marks)

MATHS

IMPORTANT QUESTIONS (FOR 90+ Marks):-

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CHAPTER 01    (6 Marks)

1. Find the LCM and HCF of 6 and 20 by the prime number factorisation method. (Ch.1 ex.06)

2. Find the HCF of 96 and 404 by the prime Factorisation method.hence, Find the LCM.

3. Express the each niuumber of its prime factor 

 (i)  5005        (ii)  3285

4. find the LCM and HCF following integers bu applying the prime factorization method.

(i) 12,15,and 21    (ii) 8,9and25

5. Give HCF (306,675)=9, find the LCM(306,657)

6. Show that 5-√3 is irrational (Ch.01 ex.10)

7. Show that 3√2 is irrational (Ch.01 ex.11)

8. Prove that 3+2√5 is irrational. (Ex.1.3)

9. Prove the irrationals of 1/2√5 and 6+2√5

         

  CHAPTER 02      (06 Marks)

1. Find the zeroes of the quadratic polynominal x²+7x+10, and verify the relationship between zeroes and the xoefficients.(Ch.02 Ex.02)

2. Find the zeroes of polynomial x²-3 and verify the relationship between the zeroes and the coefficients.(Ch.02 Ex.03)

3. Find the Zero of quadratic polynomials.(Ex.2.2 Q1)

(i) x²-2x-8        (ii) 6x²-3-7x

4. Find the quadratic polynominal each with the both numbers as the sum and product of its zeroes respictively.(Ex.2.2 Q2)

(i)√2,⅓        (ii)0,√5 (iii)-¼,¼

   

CHAPTER 03          (07 Marks)

1. On comparing the ratio a1/a2, b1/b2 and c1/c2, find out whether lines reporting the following pairs of linear equation intersec at a point, are parallel or coincident. (Ex.3.2 Q2)

(i) 5x-4y+8=0 ; 7x-6y-9=0

(ii) 9x+3y+12=0 ; 18x+6y+24=0

2. On Comparing the ratios a1/a2,b1/b2 and c1/c2 find out whether the following pair of linear equations are consistent, or inconsistent (Ex.3.2 Q3)

(i) 3x+2y=5 ; 2x-3y=7

(ii) (3/2)x + (5-3)y =7 ;

     9x-10y=14

3. Solve the following pair of linear equation by the submition method. (Ex.3.3 Q1)

(i) x - t = 3

    x/3 + 1/2 = 6

(ii) 3x/2 - 5y/3 = -2

     x/3 + y/2 = 13/6

4. Solve the 2x + 3y = 11 and  2x - 4y = -24 and hence find the value of 'm' for which y = mx + 3 (Ex. 3.3 Q2)

5. Solve the linear equation by the elimination method amd the substitution method: (Ex.3.4 Q.1)

(i) 3x + 4y = 10 and 2x - 2y = 2

(ii) x/2 + 2y/3 = -1 and x - y/3 = 3 

6. For which value of p does the pair of equation given below has unique solution? (Ex. 15)

4x + py + 8 = 0

2x + 2y + 2 = 0

7. For what value of k will the following pair of linear equation have infinitely many solution? (Ex.16)

8. For which value of k will the following pair of linear equation have no solution? {Ex.3.5Q2.(a)}

3x + y = 1

(2k - 1 x + (k - 1)y = 2k+1

9. Solve the pair of equations: (Ex. 17)

2/x + 3/y = 13

5/x  -  4/y = -2

10.  Solve the following pairs of equation by reducing them to a pair of linear equation. (Ex.3.6 Q.1)

(i) 1/2x + 1/3y = 2

    1/3x + 1/2y = 13/6

(ii) 2/√x + 3/√y = 2

     4/√x - 9/√y = -1

CHAPTER 04      (05 Marks)

1. Check the whether of the following are quadratic equations. (Ex.2)

(i) (x - 2)² + 1 = 2x - 3

(ii) x(x + 1)+ 8 = (x + 2) (x-1)

(iii) x(2x + 3) = x³ + 1

(iv) (x + 2)³ = x³ - 4

2. Check whether following are quadratic equation:

(i) (x +1)² = 2(x - 3)

(ii) (x -2)(x + 1) = (x - 1)(x + 3)

3. Find the roots of the quadratic equation 6x quadratic equation 3x² -2√6x +2 =0.      (Ex.5)

4. Find the roots of the following quadratic equation by factorisation: (Ex.4.2 Q.1)

(i) x² - 3x -10 = 0

(ii) 2x² + x - 6 = 0

5. Find the roots of the following quadratic equation, if they exist, using the quadratic formula:   (Ex.13)

(i) 3x² - 5x + 2 = 0

(ii) x² + 4x + 5 = 0

(iii) 2x² - 2√2x + 1 = 0

6. Find the discriminant of the equation of the equation 3x² - 2x + ⅓ =0 and hence find the nature of its roots, if they are real. (Ex.18)

7. Find the nature of the roots of the following quadratic equation. if the real roots exist, find them.(Ex.4.4 Q.1)

(i) 2x² - 3x + 5 = 0

(ii) 3x² - 4√3x =4 = 0

8. Find the value of k for each of the following quadratic equation, so that they have two equal roots. (Ex.4.4 Q.2)

(i) 2x² + Kx + 3 = 0

(ii) Kx (x - 2) + 6 = 0

CHAPTER 05      (05 Marks)

1. For the AP: 3/2, 1/2, -1/2, -3/2, ……., write the first term a and the common difference d.    (Ex.01)

2. write the four terms of the AP, when the first term a and the common difference d given us follows: (Ex.5.1 Q.02)

(i) a = 10, d = 10

(ii) a = -1, d = ½ 

3. Find the folowing APs, write the first term and the common difference: (Ex.5.1 Q.02)

(i) 1/3, 5/3, 9/3, 13/3, …..

(ii) 0.6, 1.7, 2.8, 3.9,........

4. Find the 10th term of AP: 2, 7, 12, ……....    (Ex.3)

5. Determine the AP whose 3rd term is 5 and the 7th term is 9. (Ex.5)

6. Which of the term AP: 3, 8, 13, 18, …… is 78 ? (Ex 5.2 Q.4)

7. The 17th term of an AP exceeds its 10th term by 7. which of the common difference. (Ex. 5.2 Q. 10)

8. Find the sum of the first 22 term of the AP; 8, 3, -2,......    (Ex.11)

CHAPTER 06      (05 Marks)

1. Give statement of Basic Propotionality Theorem (BPT) ? only statement.

2. In figure (i) and (ii), DE||BC. Find EC in (i) and AD i  (

3. E and F are points on the sides PQ and PR respectively of a Triangle PQR. For each of the following cases ,state whether EF||QR :

1. PE = 3.9cm ,PF = 3.6cm and FR = 2.4 

2. PE = 4cm, QE = 4.5cm , PF = 8cmand RF = 9cm.

3. PQ = 1.28cm, PR = 2.56cm, PE = 0.18cm and PF = 0.36cm.

4. Write the criteria for similarity of triangles. Only statement. (6.2)

5. Write the criteria of Angle, Angle, Angle. Only statement. (6.3)

6. Write the criteria of Side, Side, Side. Only statement. (6.4)

7. Write the criteria of Side, Angle, Side. Only statement. (6.5)

8. Write the statement of Area of similar triangle.Only statement. (6.6)

9. Write the statement of pythagoras the prem.(6.8)

10. Write the statement of congress of statement of pythagoras theorem. (6.9)

11. In figure if PQ||RS, prove that triangle POQ~SOR. (Ex.4)

12. Let triangles ABC~DEF and there areas be, respectively ,64cm² and 121cms². If EF = 15.4cm, find BC.

13. Side of two similar triangle are in the ratio 4:9 Area of these triangle are in the ratio.

(i) 2:3     (ii) 4:9     (iii) 81:16     (iv) 16:81

14. Sides Of triangle are given below. Determine which of the right triangle in case of a right triangle, write the length of its hypotension (Ex.6.5 Q1)

(i) 7cm, 24cm, 25cm.

(ii) 50cm, 80cm, 100cm.

15. ABC is an isosceles triangle right angled at C. Prove that AB² = 2AC².   (Ex.6.5. Q4)

16. ABC is an isolated triangle with AC = BC. if AB² =2AC² prove that ABC is a right triangle.   (Ex.6.5 Q5)

CHAPTER 07      (05 Marks)

1. Find the distance between the pairs (EX.7.1 Q1)

(i) (2,3),(4,1)

(ii) (a,b),(-a,-b)

2. Find the cordinate of the point which divides the line segment joint the point (4,-3) and (8,5) is the ratio 3:1 internally. (Ex.06)

3. Find the cordinates of the points which devides the joins of (-1,7) and (4,-3) in the ratio (2;3) (Ex.7.2 Q.01)

4. Find the cordinates of a point A, where AB is he distance of a circle, whose centre is (2,-3) and 

B is (1,4) (Ex.7.2 Q.07)

CHAPTER 08      (05 Marks)

1. Give tan A= 4/3, find the other trignometric ratios of the angle A. (Ex.01)

2. Given 15 cot A=8.find sin A and sec A. (Ex.8.1 Q.04)

3. Given secθ = 13/12, calculate all other trignomatic ratios. (Ex.8.1 Q.05)

4. In ∆ PQR, right angled at Q , PQ = 3cm and PR = 6cm determine ∠QPR ∠PRQ (Ex. 07)

5. If sin(A-B)=1/2, cot(A+B)= 1/2, 0° <A+B ≤ 90°,A>B, find A and B. (Ex. 08)

6. Evalute the following: (Ex.8.2 Q.01)

(i) sin 60° cos 30° + sin 30° cos60°

(ii)  2tan² 45° + cos² 30°- sin² 60°

(iii) 5 cos² 60°+4 sec² 30° - tan² 45°/ sin² 30°+ cos² 30°

7. If tan(A+B)= √3 and tan (A-B)= 1/√3;0°<A+B ≤ 90°; A>B, find A and B. (Ex.8.2 Q.03)

8. Evaluate tan65° / cot 25° (Ex.09)

9. If sin 3A + cos (A-26°), where 3A is an acute angle, find the value of A. (Ex.10)

10. Express cot85° + cot65° in a term of trignomatric ratio of angles between 0° and 45°. (Ex.11)

11.  Evalute: (Ex.8.3 Q1)

(i) sin18°/ cos72°

(ii) tan 26°/ cot64°

(iii) cos 48° -sin42° 

(iv) cosec31° -sec59°

12. Show that: (Ex.8.3 Q2)

(i) tan48°tan23°tan42°tan67°= 1

(ii) cos38°cos52°- sin38°sin52°=0

13. If tan2A= cot(A-18°), where 2A is actual angle, find tha value of A (Ex.8.3 Q3)

14.  If tan A = cot B, Prove that A+B = 90°. (Ex.8.3 Q4)

15. Evalute sin²63°+ sin²27°/cos²17°+ cos²73° (Ex.8.4 Q3)

CHAPTER 09      (05 Marks)

1.  An observer 1.5m tall is 28.5m away from the chimney. The angle of the elevation of the top of the chimney from her eyes is 45°. What is the High of the chimney. (Ex. 03)

2. The shadow of atower standing on a level ground is found to be 40m longer when the sun attitude is 30° then when it is 60° what is the height of the tower.(Ex. 05)

3. When a tree break due to strom and the broken part bends to the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8m. Find the height of the tree . (Ex.9.1 Q 2)

4. A kite is flying at hight of  60m above from the ground the string attached to the kite is temporarily tied to the point of ground. The inclination of the string with the ground is 60°. Find the length of the string assuming that there is no stack in the string. (Ex 9.1 Q.5) 

5. From the top of 7m high building. The angle of elevation of the top of a cable tower is 60° and the angle of depreciation of its foot is  45°. Determine the hight of the tower. (Ex.09 Q.12)

CHAPTER 10      (05 Marks)

1. A Tangent PQ at a point P of a circle of radius 5cm meets a line thought the centre O at a point Q so that OQ=12cm length PQ is:

(i) 12 cm

(ii) √9 cm

2. The length of a Tangent drown from an external point is a circle are equal. (Theorem 10.2)

3. From a point Q. the length of Tangent to a circle is 24cm And the distance of Q from the centre is 25cm. The radius of circle is: (Ex.10.2 Q.1)

(i) 7cm

(ii) 12cm

4. Prove that the Tangent drown at the ends of a diameter of a circle are parallel. (Ex.10.2 Q.4)

5. Prove that the perpendicular of the point of contact to the target to a circle passes through the centre. (Ex.10.2 Q.5)

6. The length of Tangent from a point A at distance 5cm from the centre of the circle is 4cm find the radius of the circle.(Ex.10.2 Q.6)

7. Two concentric circles are of radius of 5cm and 3cm. Find the length of the chord of the larger circle which touches the smaller circle. (Ex.10.2 Q.7)

CHAPTER 12     (05 Marks) 

1. The cost of fencing a circular field at the range of 24 ₹ per metre is 5280 ₹. The field is to be plugged at the high rate of 0.50 ₹ per m². find the cost of ploughing the field (take x= -22/7).   (Ex.01)

2. The radius of the two circle are 19cm and 9cm respectively find the radius of the circle which has circumstance equal to the sum of circumstances of the two circles. (Ex.12.1 Q.01)

3. The radius of the circle are 8cm and 6cm respectively. Find the radius of the circle having equal area to the sum of the area of two circles. (Ex.12.1 Q.02)

4. Find the area of the sector of the circle with radius 4cm and of angle 30°, also find the area of corresponding mejor sector (use π =3.14)    (Ex.02)

5. A chord of circle of radius 10cm subtends a right angle at the centre. find the area of coresponding (use π =3.14) :    (Ex.12.2 Q.4)

(i) Minor segment

(ii) Major sector

6. A chord of the circle of a radius 15cm subtends an angle of 60° at the centre find the area of corresponding minor and Majorsegments of the circle.

(use π =3.14 and √3 = 1.73)     (Ex.12.2 Q.6)

7. A car has two wippers which do not overlap each wipper has a blade of lenght 25cm sweeping through an anve of 115°. find the total area cleaned at each sweep of the blades. (Ex.12.2 Q.11)

CHAPTER 13     (06 Marks) 

1. A toy is in the form of cone of radius 3.5cm mounded on a hemisphare of the same radius the total hight of the toy is 15.5cm find the total surface area of the toy.    (Ex.13.1 Q.3)

2. A medicine capsule is in the shape of a cylinder with two hemisphare stick to each of its ends in fig. the length of entire capsule is 14mm and the diameter of the capsule is 5mm.Find the surface area.    (Ex.13.1 Q.6)

3. Form.a solid cylinder whose hight is 2.4cm and diameter is 1.4cm. a conical cavity of a same height and same diameter is hollowed out. find the total surface area of the remaining solid to the nearest cm².    (Ex.13.1 Q.8)

4. A solid iron pole.consist of cylinder of height 220cm and base diameter is 24cm which is surounded by another cylinder of height 60cm and radius 8cm. find the mass of the pole. Given that 1cm² of iron has approximetly 8g mass. (use π = 3.14)    (Ex.13.2 Q.6)

CHAPTER 14     (05 Marks)

1. EX. 03

2. EX.14.1 Ques no.02

3. EX.14.1 Ques no.06

4. EX.14.1 Ques no.09

5. EX.14.2 Ques no.01

6. EX.14.2 Ques no.02

7. EX.14.3 Ques no.01

CHAPTER 15    (06 Marks)

1. EX.01

2. EX.02

3. EX.03

4. EX.04

5. EX.05

6. EX.08

7. EX.15.1 Ques no.05

8. EX.15.1 Ques no.07

9. EX.15.1 Ques no.08

10. EX.15.1 Ques no.12

11. EX.15.1 Ques no.13

12. EX.15.1 Ques no.14

13. EX.15.1 Ques no.16

14. EX.15.1 Ques no.17

15. EX.15.1 Ques no.18

16. EX.15.1 Ques no.19