Instructions: 1) Read the following question paper

and understand every question thoroughly without

writing anything. 15 minutes time is allotted for this.

2) Answer all the questions from the given four sec-

tions.

3) Write answer to the objective type questions

(Section − IV) on PART − B and attached withPART − A.

4) In Section − III, every question has internal choice.Answer to anyone alternative.

Time: 2 Hours PART - A Marks: 35

SECTION - I

I. i) Answer All the questions.

ii) Each question carries 1 mark. 7 ´ 1 = 7

1. Find HCF of 180 and 192.

2. If A = {2, 4, 6, 8}, B = {1} then find the value of

n(A) + n(B).

3. Sneha said that, slope of the points joining the line

A (2, 4) and B (4, 6) is 1. Justify your answer.

4. Write the polynomial whose zero’s are 2 + √3,

2 − √3.

5. How many multiples of 7 in between 1 to 100.

6. What would you say about the pair of linear equa-

tions 2x + 3y = 5, 6x + 9y = 15?

7. If the discriminant b2 − 4ac = 0 of quadratic equa-tion ax2 + bx + c = 0 then write the nature of roots.

SECTION - II

II. i) Answer All the questions.

ii) Each question carries 2 marks. 6 ´ 2 = 12

8. Write i) 5−3

= 1/125 ii) 73 = 343 logarithmic form.

9. If 3x + 4y = 7, 6x + 8y = k are coincident lines, then

find the value of k.

1 1 110. Solve − = (x is ≠ 0)

x x + 5 360

11. If x − 2, 4x − 1, 5x + 2 are in Arithmetic progres-sion. Then find the value ‘x’.

12. A(1, 2) B (3, −1) C (2, −4) are the vertices of a tri-angle then find the centroid and it lies in which

quadrant.

13. If A = {1, 3, 5} then find A ∩ A, A ∩ φ.

SECTION - III

III. i) Answer All the questions.

ii) Each question carries 4 marks.

ii) Each question has internal choice. 4 ´ 4 = 16

14. a) Prove that 3√2 − √

5 is irrational number.

(OR)

b) Solve the equation 5x2 − 7x + 2 = 0 by themethod of completing square.

15. a) In the Geometric progressions 16807, 2401,

1 1 1343, ... & , , , .... nth terms are

243 81 27

same, then find n = ?

(OR)

b) A = {x/x ∈ prime, x < 20}, B = {x/x ∈ multiples of3, x < 21} then prove that n (A ∪ B) = n(A) +n(B) − n(A ∩ B)

16. a) A(1, 1) B (1, 5) C (5, 5) D (5, 1) are the vertices

of a square then find the area of a square.

(OR)

b) Find the points of trisection of the line segment

joining the points A (5, 7), B (8,14).

17. a) Solve the pair of Linear equations in two vari-

ables 2x − y = 2, 4x + 3y = 24 by using graph.(OR)

b) Solve y = x2 − 8x + 15 by using graph.

Time: 30 mins PART - B Marks: 5

SECTION - IV

Instructions: i) Answer All the questions.

ii) Each question carries 1/2 mark.

iii) Marks will not be given in any case of over writing

and re writing or erased answers.

iv) Write the capital letter (A, B, C, D) showing the cor-

rect answer for the following questions in brackets

provided against them. 10 ´ 1/2 = 5

18. Product of zero’s of a polynomial √3 x2 + 5x + 7√

3

is ( )

−5A) 7√

3 B) 7 C) −7 D)

√3

PUBLIC EXAMINATIONS - 2020

Time: 2 Hrs. 45 Min. MATHEMATICS PAPER - I Max. Marks: 40

TENTH CLASS MODEL PAPER

P20. if 0.7

−= then P + Q = ( )

Q

A) 7 B) 9 C) 15 D) 16

22. Distance between (tan 45°, cot 45°)(2, 2) is ( )

A) √2 B) 2 C) 1 D) 0

23. If a, b, c are Geometric

Progression. Then which of the fol-

lowing is true. ( )

a + cA) b2 = a + c B) b =

2

C) b2 = ac D) √b = ac

24. If a = 5, r = 2 then a5

= ( )

A) 32 B) 10 C) 40 D) 80

25. log10

107

+ log101 + log

1010 = ( )

A) 8 B) 7 C) 9 D) 10

26. If x + y = 4, 2x + ky = 3 are parallel

then k = ( )

A) 1 B) 2 C) −2 D) 3

57

1

2

346

A B

1. The angle between velocity and accelera-

tion during the retarded motion is ..

1) 0° 2) 45° 3) 90° 4) 180°

2. The distance travelled by a particle in a

straight line motion is directly proportional to

t1/2, where t = time elapsed. What is the

nature of motion?

1) increasing acceleration

2) decreasing acceleration

3) increasing retardation

4) decreasing retardation

3. Two balls of different masses m1

and m2

are

dropped from two different heights h1

and

h2. The ratio of times taken by the two to

drop through these distances is ..

1) h1

: h2

2) h2

: h1

3) √h

1: √

h

24) h

1

2: h

2

2

4. A particle moves along X-axis in such a way

that its position co-ordinate (x) varies

with time (t) according to the expression

x = 2 − 5t + 6t2. Its initial velocity is 1) 2 m/s 2) 3 m/s 3) 6 m/s 4) −5 m/s

5. When the speed of a car is u, the minimum

distance over which it can be stopped is s.

If the speed becomes nu, then what will be

the minimum distance over which it can be

stopped during the same time?

s s1) ns 2) 3) 4) n2s

n n2

6. A person is throwing two balls into the air

one after the other. He throws the second

ball when first ball is at the highest point. If

he is throwing the balls every second, how

high do they rise?

1) 1.25 m 2) 2.50 m 3) 3.75 m 4) 5 m

7. The relation between time t and distance

x is, t = αx2 + βx where α and β areconstants. Then the retardation is ..

1) 2αv3 2) 2βv3 3) 2αβv3 4) 2α2βv3

8. A man is walking along a straight road. He

takes 5 steps forward and 3 steps backward

and so on. Each step is 1 m long and takes

1 s. There is a pit on the road 11 m away

from the starting point. The man will fall into

the pit after ..

1) 21 s 2) 23 s 3) 29 s 4) 31 s

9. A ball is thrown from the top of a tower in

vertically upward direction. Velocity at a

point h meters below the point of projection

is twice of the velocity at a point h meters

above the point of projection. Then the max-

imum height reached by the ball above the

top of the tower is ..

5 21) 2h 2) 3h 3) ()h 4) ()h

3 3

10. A man is walking on a road with a velocity

3kmh−1. Rain started falling with a velocity

10 kmh−1 in vertically downward direction.

Then the relative velocity of the rain w.r.t.

man is ..

1) √7 kmh−1 2) √

13 kmh−1

3) √109 kmh−1 4) √

119 kmh−1

11. A bird is flying towards north with a veloci-

ty 40 kmh−1 and a train is moving with a

velocity 40 kmh−1 towards east. What is the

velocity of the bird noted by a man in the

train?

1) 40√2 kmh−1 N−E 2) 40√

2 kmh−1 S−E

3) 40√2 kmh−1N−W 4) 40√

2 kmh−1 S−W

12. The maximum height reached by a projec-

tile is 4 m. The horizontal range is 12 m.

Then the velocity projection (in ms−1) is ..

1 g 1 g1) √ 2) √ 3 2 5 2

g g

3) 3 √ 4) 5 √ 2 213. The maximum height attained by a projec-

tile is increased by 10%. Keeping the angle

of projection constant, what is the percent-

age increase in the time of flight?

1) 5% 2) 10% 3) 15% 4) 20%

14. The equation of motion of a projectile is

3y = 12x − x2. The horizontal component

4

of velocity is 3 ms-1. Then the range of the

projectile is ..

1) 12 m 2) 16 m 3) 9 m 4) 18 m

15. A projectile is fired from the level ground at

an angle θ above the horizontal. The ele-vation angle Φ of the highest point as seenfrom the launch point is related to θ by therelation ..

11) tanΦ = tanθ 2) tanΦ = tanθ

2

13) tanΦ = 2 tanθ 4) tanΦ = tanθ

4

16. A block of mass M is pulled along a hori-

zontal friction less surface by a rope of

mass m. Force P is applied at one end of

the rope. Then the force which the rope

exerts on the block is ..

P P1) 2)

(M − m) M(m + M) mP P

3) 4) (M + m) (M + m)

17. Three forces are acting on a particle of

mass m initially in equilibrium. If the first

two forces (R1

and R2) are perpendicular to

each other and suddenly the third force

(R3) is removed, then the acceleration of

the particle is ..

R1

− R2

R1

+ R21) 2)

m m

R3

R1

3) 4) m m

18. A bob is hung from the ceiling of a train

compartment. The train moves on an

inclined track of inclination 30° with hori-zontal. Acceleration of the train up the

gplane is a = . Then the angle which the

2

string supporting the bob makes with

normal to the ceiling in equilibrium is ..

√3 2

1) tan−1 ( ) 2) tan−1 ( )2 √

3

3) 30° 4) 60°

19. A particle of mass m is joined to a heavy

body by a light string passing over a light

pulley. Both bodies are free to move. Then

the total downward force on the pulley is ..

1) mg 2) 2 mg 3) 3 mg 4) 4 mg

20. The upper half of an inclined plane with

inclination θ is perfectly smooth while thelower half is rough. A body starting from

rest at the top will again come to rest at the

bottom if the coefficient of friction for the

lower half is ..

11) tanθ 2) 2 tanθ 3) tanθ 4) √

2 tanθ

2

21. A body of mass m is launched up on a

rough inclined plane making an angle 45°

with horizontal. If the time ascent is half of

the time of descent, the coefficient of

friction between plane and the body is ..

2 3 4 31) 2) 3) 4)

5 5 5 4

22. Springs of spring constant K, 3K, 9K, 27K,

...., ∞ are connected in series. Then theequivalent spring constant of the combina-

tion is ..

3K 2K1) ∞ 2) 3) 4) K

2 3

23. A particle has initial velocity u = 3iΛ

+ 4jΛ

and a constant force F

= 4iΛ

− 3jΛ

acts on the

particle. Then the path of the particle is ..

1) Straight line 2) Circular

3) Parabolic 4) Elliptical

24. The first ball of mass m moving with a

velocity u collides head on with the second

ball of mass m at rest. If the coefficient of

restitution is e, then the ratio of the veloci-

ties of the first and the second ball after the

collision is ..

1 − e 1 + e 1 + e 1 − e1) 2) 3) 4)

1 + e 1 − e 2 2 25. A plastic ball is dropped from a height of 1

m and rebounds several times from the

floor. If 1.03 s elapse from the moment it is

dropped to the second impact with the

floor, what is the coefficient of restitution?

1) 0.02 2) 0.03 3) 0.64 4) 0.36

26. A body of mass 2 kg moving with a velocity

of 6 m/s strikes inelastically another body of

same mass at rest. Then the amount of

heat evolved during the collision is ..

1) 3J 2) 9J 3) 18J 4) 36J

27. A bomb of mass 12 kg at rest explodes into

two pieces of masses 4 kg and 8 kg. The

velocity of 8 kg mass is 6 m/s. Then the

kinetic energy of the other mass is ..

1) 24J 2) 144J 3) 264J 4) 288J

28. Two blocks of masses 6 kg and 4 kg are

attached to the two ends of a massless

string passing over a smooth fixed pulley. If

the system is released, the acceleration of

the centre of mass of the system will be

1) zero

2) g, vertically downwards

g3) , vertically downwards

5

g4) , vertically downwards

25

29. A car accelerates from rest at a constant late

α for some time after which it decelerates ata constant rate β to come to rest. If the totaltime elapsed is t, then the maximum velocity

acquired by the car is given by.

αβ α + β1) ()t 2) ( )t α + β αβ

α2 + β2 α2 − β23) ( )t 4) ( )t αβ αβ

30. Which of the following remains constant

during the motion of a projectile?

1) Kinetic energy 2) Momentum

3) Vertical component of velocity

4) Horizontal component of velocity

31. A body is projected with Kinetic energy K at

an angle of 60° with the horizontal. ItsKinetic energy at the highest point of its

trajectory will be ..

K K1) K 2) 3) 4) 2K

2 4

32. A body is projected at an angle θ with thehorizontal. When it is at the highest point,

the ratio of the potential and kinetic

energies of body is ..

1) tanθ 2) cotθ 3) tan2θ 4) cot2θ33. A body dropped from the top of a tower hits

the ground after 4 s. How much time does

it take to cover the first half of the distance

from the top of the tower?

1) 1 s 2) 2 s 3) 2√2 s 4) √

2 s

34. A projectile has a maximum range of

200 m. Then the maximum height attained

by it is ..

1) 25 m 2) 50 m 3) 75 m 4) 100 m

35. For a particle moving along a straight line,

the displacement x depends on time t as x

= At3 + Bt2 + Ct + D. Then the ratio of its

initial velocity to its initial acceleration

depends on

1) A, C 2) B, C 3) C 4) C, D

36. A stone is dropped from a balloon rising

with acceleration a. Then the acceleration

of the stone relative to the balloon is

1) g downward 2) (g + a) downward

3) (g − a) upward 4) (g + a) upward37. A particle has initial velocity of 17 ms−1

towards east and constant acceleration of

2 ms−2 due west. The distance covered by

it in 9th second of motion is

1) 0 m 2) 0.5 m 3) 72 m 4) 2 m

38. A body starts from rest and moves for n

seconds with uniform acceleration a. Its

velocity after n seconds is v. Then the dis-

placement of the body in last 3 seconds is

v(6n − 9) 2v(6n − 9)1) 2)

2n n

2v(2n + 1) 2v(2n − 1)3) 4)

n n

39. Water drops fall at regular intervals from a

roof. At an instant when a drop is about to

leave the roof, the separations between 3

successive drops below the roof are in the

ratio

1) 1 : 2 : 3 2) 1 : 4 : 9

3) 1 : 3 : 5 4) 1 : 5 : 13

40. A car accelerates from rest at constant rate

for the first 10 s and covers a distance x. It

covers a distance y in the next 10 s at the

same acceleration. Then which of the fol-

lowing is true

1) x = 3y 2) y = 3x 3) x = y 4) y = 2x

The path of the particle is..?

K.S.S. RajasekharSubject Expert

Writer

Kinematics and Laws of Motion

Answers

1-4, 2-4, 3-3, 4-4, 5-4, 6-4, 7-1, 8-3, 9-3,

10-3, 11-3, 12-4, 13-1, 14-2, 15-2, 16-4, 17-3,

18-2, 19-4, 20-2, 21-2, 22-3, 23-3, 24-1, 25-3,

26-3, 27-4, 28-4, 29-1, 30-4, 31-3, 32-3, 33-3,

34-2, 35-2, 36-2, 37-2, 38-1, 39-3, 40-2.

NEETPhysics

19. From venn dia-

gram B − A = ( )

A) {3}

B) {2, 3, 4, 5}

C) {3, 2} D) φ

21. If area of ∆OAB= 20 sq.units

then x = ( )

A) 3 B) 5

C) 4 D) 6O A(x, o)

(o, 8)

y

B

x

27.Zero’s of a poly

nomial is ( )

A) −1, 0, 1, 2

B) −1, 1, 2

C) −1, 2

D) 0, 1, 2

y

x0 1 2

Þœªô¢ªî¦ô¢Ù 28  2020 n email: help@eenadupratibha.net

17

Answers

18-B 19-C 20-D 21-B 22-A 23-C

24-D 25-A 26-B 27-A.

1. Show that the sum of all odd integers

between 1 to 500 which are divisible by 3 is

41,583.

Sol: Odd integers between 1 to 500 are 3, 6, 9,

.... 498

here, a = 3, d = 6 − 3 = 3, an = 498∴ an = a + (n − 1)d ⇒ 498 = 3 + (n − 1)3 ∴ 498 − 3 = (n − 1)3

495n − 1 = ∴ n = 165 + 1 = 166

3

∴ Sum of all odd integers between 1 to 500n 166

Sn = [a + l] ⇒ S166 = [3 + 498]2 2

= 83[501] ⇒ S166 = 41583Hence, Proved.

2. If two zeros of the polynomial P(x) = x4 − 9x3

+ 24x2 − 24x + 8 are 3 ± √5, find other zeros.

Sol: It is given that 3 + √5 and 3 − √

5 are two

zeros of P(x). Therefore (x − (3 + √5 ) and

(x − (3 − √5 )) are factors of f(x)

But, {x − 3 − √5 } {x − 3 + √

5 } = (x − 3)2

− (√5 )2 = x2 + 9 − 6x − 5 = x2 − 6x + 4

Using long division method, we obtain

x2 − 6x + 4) x4 − 9x3 + 24x2 − 24x + 8 (x2 − 3x + 2x4 − 6x3 + 4x2− + −

−3x3 + 20x2 − 24x + 8−3x3 + 18x2 − 12x+ − +

2x2 − 12x + 82x2 − 12x + 8

Then, quotient q(x) = x2 − 3x + 2 and remain-der = 0

By division algorithm, we obtain

P(x) = (x2 − 6x + 4) (x2 − 3x + 2)Hence, other two zeros of P(x) are the zeros

of the polynomial.

x2 − 3x + 2 = x2 − 2x − x + 2 = x(x − 2) −1(x − 2) = (x − 1)(x − 2)∴ x = 1 and 2∴ Other two zeros of P(x) are 1 and 2

3. A shop keeper buys a number of books for

Rs.100. If he had bought 5 more books for the

same amount, each book would have cost

Rs.1 less. How many books did he buy?

Sol: Let the number of books bought be x. then

Cost of x books = Rs.100

100∴ Cost of 1 book = Rs.

x

If the number of books bought is x + 5, then

100Cost of one book = Rs. ,

x + 5

It is given that the cost of one book is

reduced by Rs.1

100 100 x + 5 − x∴ = = 1 ⇒ 100 [] = 1x x + 5 x(x + 5)500 = x2 + 5x ⇒ ∴ x2 + 5x − 500 = 0x2 + 25x − 20x − 500 = 0x(x + 25) −20(x + 25) = 0(x − 20)(x + 25) = 0 ∴ x = 20 or x = −25⇒ x = 20 (... x cannot be negative)Hence the number of books = 20

4. If A (1, 7) B (9, 7) and C (5, 1) are the vertices

of ∆ABC mid points of the sides AB, BC, CAare P, Q, R. Then find the area of ∆PQR.

Sol: Mid point of A (1, 7) B (9, 7) is

x1 + x2 y1 + y2P = ( , )2 2

1 + 9 7 + 7= ( , ) = (5, 7)2 2 Mid point of B (9, 7) C (5, 1) is

9 + 5 7 + 1Q = ( , ) = (7, 4)2 2Mid point of C (5, 1) A (1, 7) is

5 + 1 1 + 7R = ( , ) = (3, 4)2 2Area for ∆PQR

1= |x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)|2

1= |5(4 − 4) + 7(4 − 7) + 3(7 − 4)|

2

1 1= |0 − 21 + 9| = |−12|

2 2

= 6 sq.units

Important Questions (4 M)

1, 2 Marks

1. If 2x, x + 10, 3x + 5 are in A.P. find the value

of x.

Sol: Since 2x, x + 10, 3x + 5 are in A.P

x + 10 − 2x = 3x + 5 − (x + 10)−x + 10 = 2x − 5 ⇒ 10 + 5 = 3x

15x = = 5

3

Sol: A − B = {3}, B − A = {4}∴ (A − B) ∩ (B − A) = φ

3. Solve the following system of linear equations

substitution method x − y = 1, 2x + y = 8Sol: x = 1 + y

Substitute in 2x + y = 8

2(1 + y) + y = 8 ⇒ 2 + 2y + y = 86

3y = 8 − 2 = 6 ⇒ y = = 23

∴ x = 1 + y = 1 + 2 = 3 ∴ x = 3, y = 24. A = {x/x∈N, x < 5} B = {x/x∈W, x < 5} then find

A − (A − B) = ?Sol: A = {1, 2, 3, 4} B = {0, 1, 2, 3, 4 }

A − B = φ∴ A − (A − B) = {1, 2, 3, 4} − }}

= {1, 2, 3, 4} = A

5. If α, β are the zeroes of ax2 + bx + c then α2 + β2 = ?

−b cSol: α + β = , αβ =

a a

∴ α2 + β2 = (α + β)2 − 2αβ

−b 2 c= () − 2()a a

b2 2c b2 − 2ac= − =

a2 a a2

−1

1

243

2. A B

Find (A − B) ∩ (B − A)

- P. Venugopal