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Worksheets

Competency Based Questions

Total questions: 100

Worksheet time: 1hrs 13mins

Name
Class
Date
1.

Three bulbs red, green and yellow flash at intervals of 80 seconds, 90 seconds and 110 seconds. All three flash together at 8:00 am. At what time will the three bulbs flash altogether again?

a)

9:00 am

b)

9:12 am

c)

10:00 am

d)

10:12 am

2.

Which of the following is an irrational number?

a)
b)
c)
d)
3.

Rahul has 40 cm long red and 84 cm long blue ribbon. He cuts each ribbon into pieces such that all pieces are of equal length. What is the length of each piece?

a)

4 cm as it is the LCM of 40 and 84

b)

4 cm as it is the HCF of 40 and 84

c)

8 cm as it is the LCM of 40 and 84

d)

8 cm as it is the HCF of 40 and 84

4.

Which of the following is rational?

a)
b)
c)
d)
5.

If ‘p’ is multiple of ‘q’, then HCF and LCM of ‘p’ and ‘q’ is:

a)

HCF = p, LCM = q

b)

HCF = q, LCM = p

c)

HCF = p x q = LCM

d)

None of these

6.

The prime factorization for 1729 is:

a)
b)
c)
d)
7.

Assertion (A): LCM of 26 and 91 is 182. Reason (R): The prime factorization of 26 = 2×13 and 91=7×13, hence LCM=13× 13 × 2×7.

a)

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

b)

Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

c)

Assertion (A) is true but reason (R) is false.

d)

Assertions (A) is false but reason (R) is true.

8.

Assertion (A): LCM of and is Reason (R): LCM is always a multiple of HCF.

a)

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

b)

Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

c)

Assertion (A) is true but reason (R) is false.

d)

Assertion (A) is false but reason (R) is true.

9.

A merchant has 120 soap cubes of 1st kind in box I, 180 soap cubes of 2nd kind in box II and 240 soap cubes of 3rd kind in box III. He wants to sell the soap cubes by filling three kinds of soap cubes in small packets of equal capacity. On the basis of above information, answer the following: What would be the largest capacity of such packets?

a)

30

b)

50

c)

60

d)

120

10.

Which of the following concept is used to find the largest capacity?

a)

HCF only

b)

LCM only

c)

HCF and LCM both

d)

None of these

11.

If he decided to put 3rd kind of soap cubes separately in small packets, how many packets are needed?

a)

2

b)

3

c)

4

d)

5

12.

How many total small packets are needed to pack all 3 kinds of soap cubes?

a)

4

b)

6

c)

7

d)

9

13.

If merchant decided to sell only second and third kinds of soap cubes then how many small packets are required?

a)

7

b)

6

c)

5

d)

4

14.

Amit, Ashutosh and Avinash started a race on a circular ground. Amit takes 24 minutes Ashutosh takes 12 minutes and Avinash takes 18 minutes to complete a round. They started the race at 7:35 AM. On the basis of above information, answer the following: After how many minutes they will meet again?

a)

144

b)

72

c)

60

d)

96

15.

Number of rounds taken by Amit when they met again after start?

a)

3

b)

4

c)

6

d)

5

16.

What is the time when they met again after start?

a)

8:47 AM

b)

9:12 AM

c)

9:47 AM

d)

7:47 AM

17.

How many total taken by all of them when they met again after start?

a)

12

b)

14

c)

13

d)

15

18.

Which of the following concept is used to find the number of rounds?

a)

HCF only

b)

LCM only

c)

HCF and LCM both

d)

None of these

19.

Find the number of zeroes of the given polynomial by its graph:

a)

2

b)

3

c)

1

d)

None of these

20.

If are zeroes of the polynomial then equals:

a)
b)
c)
d)
21.

If one zero of is reciprocal to the other then the value of is:

a)

3

b)
c)
d)

2

22.

A quadratic polynomial, whose zeroes are -3 and 4, is:

a)

x² - x + 12

b)

x² + x + 12

c)

x²−x−12

d)

2x² + 2x – 24

23.

If the zeroes of the quadratic polynomial are 2 and -3, then:

a)

a = -7, b = -1

b)

a = 5, b = -1

c)

a = 2, b = -6

d)

a = 0, b = -6

24.

If one zero of the quadratic polynomial is 2, then the value of k is:

a)

10

b)

– 10

c)

5

d)

– 5

25.

Assertion (A): has no real zeroes. Reason (R): A quadratic polynomial can have at the most two zeroes.

a)

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

b)

Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

c)

Assertion (A) is true but reason (R) is false.

d)

Assertions (A) is false but reason (R) is true.

26.

Assertion (A): If the sum of the zeroes of the quadratic polynomial is 2 then value of k is 1. Reason (R): Sum of zeroes of a quadratic polynomial is

a)

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

b)

Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

c)

Assertion (A) is true but reason (R) is false.

d)

Assertion (A) is false but reason (R) is true.

27.

A boy is playing with a ball and suddenly he throws that ball upwards and ball returns to the ground describing a parabolic path as shown in the figure. On the basis of above information, answer the following: The zeroes of the given curve are:

a)

0 and – 4

b)

0 and 4

c)

1 and 4

d)

-1 and 4

28.

The path traced by the ball, whose zeroes are given in the figure is:

a)
b)
c)
d)
29.

If then value of polynomial is:

a)

0

b)

1

c)

4

d)

3

30.

If we shift the parabola to right side by two units, then its polynomial expression becomes:

a)
b)
c)
d)
31.

If given curve is then the value of – is:

a)

11

b)

– 11

c)

21

d)

– 21

32.

In the standard form of quadratic polynomial a, b and c are:

a)

All are Polynomials.

b)

All are rational numbers.

c)

'a' is a non – zero real number and b and c are any polynomials.

d)

All are integers.

33.

If the roots of the quadratic polynomial are equal, where the discriminant – then:

a)

D > 0

b)

D < 0

c)

D ≥ 0

d)

D = 0

34.

If α and 1/α are the zeroes of the quadratic polynomial – then k is:

a)

4

b)

1/4

c)

-1/4

d)

2

35.

The graph of

a)

Intersects x – axis at two distinct points.

b)

Touches x – axis at a point.

c)

Neither touches nor intersects x – axis.

d)

Either touches or intersects x – axis.

36.

If the sum of the roots is –p and product of the roots is –1/p, then the quadratic polynomial is:

a)

b)

– –

c)

d)

37.

The pair of linear equations 2x + 3y = 4 and 3x + 4y = 9 has:

a)

infinitely many solutions

b)

no solution

c)

one unique solution

d)

two solutions

38.

The pair of equations x = a and y = b graphically represents lines which are

a)

parallel

b)

intersecting at (b, a)

c)

coincident

d)

intersecting at (a,b)

39.

The value of ‘k’ for which the system of equation x + 2y- 3=0 and 5x + ky + 7=0 has no solutions is

a)

k=10

b)

k=6

c)

k=3

d)

k=1

40.

For which value(s) of p, will the lines represented by the following pair of linear equations be parallel 3x -y -5= 0 6x-2 y-p = 0

a)

all real values except 10

b)

10

c)

5/2

d)

½

41.

x and y are 2 different digits. If the sum of the two digit numbers formed by using both the digits is a perfect square, then value of x+y is

a)

10

b)

11

c)

12

d)

13

42.

The pair of linear equations 2 kx + 5y = 7, 6x -5y = 11 has a unique solution, if

a)

k is not equal to - 3

b)

k is not equal to 3/2

c)

k is not equal to 5

d)

k is not equal to 9/2

43.

Assertion: System of linear equation given by x-7y+16=0 and 7x-49y-112=0 are dependent. Reason: Dependent system of equations can be obtained from each other by multiplying with a suitable constant.

a)

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

b)

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

c)

An assertion (A) is true but reasons (R) is false.

d)

Assertion (A) is false but reason (R) is true.

44.

Assertion: If 2x+3y=12 and 3x-2y=5 then x=3 , y=2. Reason: Method of elimination involves writing y in terms of x from any one of two equations and then putting this value of y in other equation to get value of x. Finally substituting value of x in any one equation gives value of y.

a)

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

b)

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

c)

Assertion (A) is true but reason (R) is false.

d)

Assertion (A) is false but reason (R) is true.

45.

Architect: An architect is a skilled professional who plans and designs buildings and generally plays a key role in their construction. Architects are highly trained in the art and science of building design. Since they bear responsibility for the safety of their buildings' occupants, architects must be professionally licensed. Riddhi is a licensed architect and design very innovative house. She has made a house layout for her client which is given below. In the layout, the design and measurements has been made such that area of two bedrooms and kitchen together is 95 m².

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46.

Mr. RK Agrawal is owner of a famous amusement park in Delhi. Generally he does not go to park and it is managed by team of staff. The ticket charge for the park is Rs 150 for children and Rs 400 for adults. One day Mr. Agrawal decided to random check the park and went there. When he checked the cash counter, he found that 480 tickets were sold and Rs 134500 was collected.

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47.

ax² + bx + c = 0, a > 0, b = 0, c > 0 has

a)

two equal roots

b)

one real roots

c)

two distinct real roots

d)

no real roots

48.

The sum and product of the zeroes of a quadratic polynomial are 3 and -10 respectively. The quadratic polynomial is

a)

x² - 3x + 10

b)

x² - 3x - 10

c)

x² - 3x - 10

d)

x² + 3x + 10

49.

The quadratic equation x² + x−5 = has

a)

two distinct real roots

b)

two equal real roots

c)

no real roots

d)

more than 2 real roots

50.

If α, β are the zeros of the polynomial f(x) = x² − p(x+1) - c=0 such (α+1) (β+1) =0, then c=

a)

1

b)

0

c)

-1

d)

2

51.

If one root of the quadratic equation ax² + bx +c= 0 is the reciprocal of the other, then

a)

b= c

b)

a = b

c)

ac = 1

d)

a= c

52.

If one root of the quadratic equation ax^2 + bx + c = 0 is the reciprocal of the other, then

a)

b= c

b)

a = b

c)

ac = 1

d)

a= c

53.

Which of the following equations has 2 as one of the roots?

a)

x^2 + 4x - 5

b)

x^2 + 3x + 12

c)

2x^2 - 7x + 6

d)

3x^2 - 6x + 2

54.

Assertion: If one root of the quadratic equation 2x² + kx – 6 = 0 is 2, the value of k is -1 Reason: x = 2 is a root of the equation 2x² + kx - 6 = 0 Choose the correct answer out of the following choices:

a)

Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.

b)

Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.

c)

Assertion is correct statement but Reason is wrong statement.

d)

Assertion is wrong statement but Reason is correct statement.

55.

Assertion: The discriminant of the quadratic equation 2x^2 – 4x + 3 = 0, is -8 and hence the nature of its roots is no real roots. Reason: if b^2 - 4ac < 0, the nature of root is no real roots.

a)

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b)

Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c)

Assertion is true but the reason is false.

d)

Both assertion and reason are false.

56.

Maximum Profit: A kitchen utensils manufacturer can produce up to 200 utensils per day. The profit made from the sale of these utensils can be modelled by the function P(x) = - 0.5x² + 175x - 3300 , where P(x) is the profit in Rupees, and x is the number of utensils made and sold. Based on this model, (i) Find the y -intercept and explain what it means in this context. (ii) Find the x -intercepts and explain what they mean in this context. (iii) How many utensils should be sold to maximize profit?

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57.

Riya has a lawn with a flowerbed and grass land. The grass land is in the shape of rectangle while flowerbed is in the shape of square. The length of the grassland is found to be 3 m more than twice the length of the flowerbed. Total area of the whole lawn is 1260 m^2. i) If the length of the flowerbed is x m then what is the total length of the lawn? ii) What will be the perimeter of the whole field? iii) What is the area of grassland?

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58.

If x + 1, 3x and 4x + 2 are in AP, find the value of x.

a)

1

b)

2

c)

3

d)

4

59.

Two persons Shalini and Mira joined a Fintech company. Shalini and Mira started with an initial salary of Rs.50000 and Rs.64000 respectively with annual increment of Rs.2500 and Rs.2000 each respectively. In which year will Shalini start earning more salary than Mira?

a)

28th

b)

29th

c)

30th

d)

27th

60.

If a clock strikes once at 1pm, twice at 2pm, thrice at 3pm and so on and again once at 1pm and so on, then how many times will the bell be struck in the course of one and a half day?

a)

156

b)

312

c)

288

d)

234

61.

Find the sum of first 30 terms of an A. P. whose nth term is 5 + (n/5)

a)

243.5

b)

240.5

c)

248

d)

243

62.

Find the sum of all natural number between 1 and 100 which are divisible by 7

a)

753

b)

735

c)

14

d)

761

63.

Find the sum of the following (1- 1/n) + (1- 2/n) + (1- 3/n) + (1- 4/n) + .... Upto n terms.

a)

n(n+1)/2

b)

n^2

c)

n-1

d)

(n-1)/2

64.

Assertion: The 10th term of the AP where S_n = 5n^2 is 95 Reason: If S_n is the sum of the first n terms of an A.P., then its nth term a_n is given by a_n = S_n – S_n – 1.

a)

Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

b)

Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

c)

Assertion is correct but Reason is incorrect.

d)

Assertion is incorrect but Reason is correct.

65.

Assertion: 21, 27, 33 are in A.P. Reason: Three terms a, b, c taken in order are in A.P. if (a-c)/2 = b

a)

Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

b)

Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

c)

Assertion is correct but Reason is incorrect.

d)

Assertion is incorrect but Reason is correct.

66.

Amitabh Kacchan wants to buy a car and plans to take a loan from a bank. He repays his total loan of Rs 1,18,000 through monthly instalments with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month. Based on this answer the following questions: (i) The amount paid by him in 30th instalment is (ii) The amount paid by him in the 30 instalments is (iii) In how many years will the loan be repaid?

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67.

To reach the Handi during a Dahi-Handi competition in Mumbai, many groups formed a pyramid with multiple rows having one person lesser in each succeeding row compared to the previous row. Group A started with the base row containing 51 persons and the only person in the top row broke the Handi and won. Based on this answer the following questions: (i) To find the total number of persons in a pyramid, which mathematical concept can be used in this situation? (ii) How many rows were there in total? (iii) How many persons were there in the middle most row? (iv) If the group C had 70 persons in the base row, find the total number of persons in the pyramid.

4 lines
68.

In the given figure, ∠T and ∠B are right angles. If the length of AT, BC and AS (in centimeters) are 15, 16, and 17 respectively, then the length of TC (in centimeters) is:

a)

18

b)

16

c)

19

d)

12

69.

In the given figure, value of x(in cm) is

a)

4

b)

5

c)

6

d)

8

70.

In ΔABC, if DE || BC, AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, then value of x is

a)

3

b)

4

c)

5

d)

3.5

71.

Find the value of x in the figure below if DE || AB.

a)

x = 2

b)

x = 1

c)

x = 6

d)

x = 4

72.

If in Figure O is the point of intersection of two chords AB and CD such that OB = OD, then triangles OAC and ODB are

a)

equilateral but not similar

b)

isosceles but not similar

c)

equilateral and similar

d)

isosceles and similar

73.

Assertion (A): In the given figure, PA || QB || RC || SD. Reason (R): If three or more line segments are perpendiculars to one line, then they are parallel to each other.

a)

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

b)

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

c)

Assertion (A) is true but reason (R) is false.

d)

Assertion (A) is false but reason (R) is true.

74.

Assertion (A): Two similar triangles are always congruent. Reason (R): If areas of two similar triangles are equal, then the triangles are congruent.

a)

Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

b)

Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

c)

Assertion (A) is true but reason (R) is false.

d)

Assertion (A) is false but reason (R) is true.

75.

Rohan is very intelligent in maths. He always try to relate the concept of maths in daily life. One day he is walking away from the base of a lamp post at a speed of 1 m/s. Lamp is 4.5 m above the ground. (i) If after 2 second, length of shadow is 1 meter, what is the height of Rohan ? (ii) What is the minimum time after which his shadow will become larger than his original height? (iii) What is the distance of Rohan from pole at this point ? (iv) What will be the length of his shadow after 4 seconds? (v) Which similarity criterion is used in solving the above problem

a)

1 sec

b)

145 cm

c)

120 cm

d)

150 cm

e)

175 cm

76.

The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection. Ramesh places a mirror on level ground to determine the height of a pole (with traffic light fired on it). He stands at a certain distance so that he can see the top of the pole reflected from the mirror. Ramesh’s eye level is 1.5 m above the ground. The distance of Ramesh and the pole from the mirror are 1.8 m and 6 m respectively (i) Which criterion of similarity is applicable to similar triangles? (ii) What is the height of the pole? (iii) Now Ramesh move behind such that distance between pole and Ramesh is 13 meters. He place mirror between him and pole to see the reflection of light in right position. What is the distance between mirror and Ramesh ? (iv) What is the distance between mirror and pole?

a)

AA

b)

ASA

c)

6 metres

d)

SSA

e)

SSS

77.

ABCD is a rectangle whose three vertices are B(4, 0), C(4, 3) and D(0, 3). The length of one of its diagonals is

a)

5

b)

4

c)

3

d)

25

78.

If the point C (k, 4) divides the join of the points A (2,6 ) and B(5, 1) in the ratio 2 : 3 then the value of k is

a)

16

b)
c)
d)
79.

If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (–2, 5), then the coordinates of the other end of the diameter are

a)

(–6, 7)

b)

(6, –7)

c)

(4, 2)

d)

(5, 3)

80.

If R (5,6) is the midpoint of the line segment AB joining the points A(6,5) and B(4, y) then y equals

a)

5

b)

7

c)

12

d)

6

81.

The point P which divides the line segment joining the points A(2, –5) and B(5, 2) in the ratio 2 : 3 lies in the quadrant

a)

I

b)

II

c)

III

d)

IV

82.

If A( 1, 3), B(–1, 2), C(2, 5) and D(x, 4) are the vertices of a||gm ABCD then the value of x is

a)

3

b)

4

c)

0

d)
83.

Assertion : The coordinates of the point which divides the line segment joining the points (3,4) and (-5,-7) internally in the ratio 2:3 is ( , ) Reason : The section formula is ( , )

a)

Both A and R are true and R is the correct explanation of A.

b)

Both A and R are true but R is not the correct explanation of A.

c)

A is true but R is false.

d)

A is false but R is true.

84.

If the point P (k-1 ,2) is equidistant from the points A (3, k) and B(k, 5) find the values of k.

4 lines
85.

Ronit is the captain of his school football team. He has decided to use 4-4-2-1 formation in the next match. The above figure shows the position of the players in 4-4-2-1 formation on a coordinate grid (Q-1) Which of the following coordinates represents the position of the goalkeeper?

a)

(9, –9)

b)

(0, 9)

c)

(–9, 0)

d)

(0, –9)

86.

What is the distance between the two centre forward positions in Ronit’s plan?

a)

3 units

b)

6 units

c)

5√3 units

d)

16 units

87.

Mention two positions which are not equidistant from any axis.

4 lines
88.

Which position are on the line x+2y-4 = 0?

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89.

If the quadratic equation x² - 5x + k = 0 has equal roots, what is the value of k?

a)

4

b)

1

c)

6

d)

5

90.

What is the sum of the roots of the quadratic polynomial 3x² + 12x + 9?

a)

-4

b)

-6

c)

-3

d)

-2

91.

Which of the following represents a quadratic polynomial?

a)

5x³ + 2

b)

3/x

c)

x² - 4x + 4

d)

2x + 3

92.

What is the value of k for which the quadratic equation x² + kx + 16 = 0 has no real roots?

a)

k = -4

b)

k = -8

c)

k = 4

d)

k = 8

93.

If the sum of the roots of the quadratic equation 3x² + 5x + c = 0 is 2, what is the value of c?

a)

6

b)

5

c)

4

d)

3

94.

Which of the following equations represents a line parallel to the line 2x - 3y + 6 = 0?

a)

4x - 6y + 12 = 0

b)

6x - 4y + 9 = 0

c)

3x + 2y - 5 = 0

d)

2x + 3y - 6 = 0

95.

What is the value of k if the quadratic polynomial is given by kx² + 4x + 4 and one of its roots is -2?

a)

0

b)

1

c)

2

d)

3

96.

If the quadratic polynomial f(x) = x² + px + q has roots 3 and -1, what is the value of p + q?

a)

2

b)

1

c)

3

d)

4

97.

In a circular track, if two runners start at the same point and run at speeds of 5 m/s and 7 m/s respectively, after how many seconds will they meet again if the track length is 120 meters?

a)

120

b)

90

c)

60

d)

30

98.

What is the value of k for which the quadratic equation x² + kx + 4 = 0 has no real roots?

a)

k = 8

b)

k > 8

c)

-8 < k < 8

d)

k < -8

99.

If the roots of the quadratic polynomial are 1 and 4, then the polynomial can be expressed as:

a)

x² - 5x - 4

b)

x² + 5x + 4

c)

x² - 5x + 4

d)

x² + 5x - 4

100.

Which of the following equations represents a pair of parallel lines?

a)

3x + 2y = 5 and 3x + 2y = 10

b)

x + y = 2 and 2x + 2y = 4

c)

x - y = 1 and 2x - 2y = 3

d)

2x + 3y = 6 and 4x + 6y = 12