Download CBSE - Maths - Chapterwise Competency Based Questions. and more Exercises Mathematics in PDF only on Docsity!
KENDRIYA VIDYALAYA SANGATHAN AHMEDABAD REGION
COPETENCY BASED QUESTIONS
CLASS: X
NAME OF CHAPTER 1 : REAL NUMBERS
________________________________________________________
MULTIPLE CHOICE QUSTIONS
Q1 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 Q2 Which of the following is an irrational number?
(a)
(b)
(c)
(d)
Q3 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 Q4 Which of the following is rational? (a) (b)
(c) (d)
Q 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
Q 6 The prime factorization for 1729 is:
(a) (b) (c) (d) ASSERTION – REASON
Q 07 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.
Q 08 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. CASE BASED/SOURCE BASED
5. 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
Q 10 CASE – STUDY 2
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: 1. After how many minutes they will meet again? (a) 144 (b) 72 (c) 60 (d) 96 2. Number of rounds taken by Amit when they met again after start? (a) 3 (b) 4 (c) 6 (d) 5 3. 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
ANSWER KEY
4. How many total taken by all of them when they met again after start? (a) 12 (b) 14 (c) 13 (d) 15 5. 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
1. d
2. b
3. b
4. c
5. b
6. d
7. c
8. b
9. 1. c 2. a 3. c 4. d 5. a
10. 1. b 2. a 3. a 4. c 5. b
(d) 2x² + 2x – 24
Q 5 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
Q 6 If one zero of the quadratic polynomial is 2, then the
value of k is: (a) 10 (b) – 10 (c) 5 (d) – 5 ASSERTION – REASON
Q 07 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.
Q 08 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. CASE BASED/SOURCE BASED
Q 09 CASE – STUDY 1
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: 1. The zeroes of the given curve are: (a) 0 and – 4 (b) 0 and 4 (c) 1 and 4 (d) - 1 and 4 2. The path traced by the ball, whose zeroes are given in the figure is: (a) (b) (c) (d) 3. If then value of polynomial is: (a) 0 (c) 4 (b) 1 (d) 3 4. If we shift the parabola to right side by two units, then its polynomial expression becomes: (a) (b)
discriminant – then: (a) D > 0 (b) D < 0 (c) D ≥ 0 (d) D = 0
3. If α and 1/α are the zeroes of the quadratic polynomial - then k is: (a) 4 (b) 1/ (c) – 1/ (d) 2 4. 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.
5. 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) –
ANSWER KEY
NAME OF TEACHER: ASHUTOSH RAI, PGT – MATHS
NAME OF KV : KV NO 3 GANDHINAGAR CANTT
1 B
2 C
3 D
4 C
5 D
6 B
7 B
8 A
9 1. b 2. a 3. a 4. d 5. b
10 1. c 2. d 3. d 4. c 5. c
3x - y - 5= 0
6x-2 y-p = 0
(a) all real values except 10
(b) 10
(c) 5/
(d) ½
Q 5 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
Q 6 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/
(c) k is not equal to 5
(d) k is not equal to 9/
ASSERTION- REASON / VERY SHORT
Q 07 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
Q 08 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.
CASE BASED/SOURCE BASED
Q 09 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
and Rs 134500 was collected.
i) Let the number of children visited be x and the number of adults visited be y. Which of the following is the correct system of equation that models the problem? (a) x + y = 480 and 3x + 8y = 2690 (b) x + 2y = 480 and 3x + 4y = 2690 (c) x + y = 480 and 3x + 4y = 2690 (d) x + 2y = 480 and 3x + 8y = 2690
ii) How many children attended?
a) 250 b) 500 c) 230 d) 460
iii) How many adults attended?
(a) 250 (b) 500 (c) 230 (d) 460
iv) How much amount collected if 300 children and 350 adults attended?
(a) Rs 225400
(b) Rs 154000
(c) Rs 112500
(d) Rs 185000
ANSWERS:
- a
- d
- a
- a
- b
- a
- d
- a
9 i) 2x + y = 19 and x + y = 13 pair of linear equations describe this situation
ii) Outer boundary of layout = 2(L + B) = 2(15 + 12) = 2 x 27 = 54 m.
iii) Area of Bedroom 1 = L x B = x x 5 = 6 x 5 = 30m².
Area of Living room = 7(2 + y) + x * 2 = 7(2 + 7) + 6 x 2 = 7 x 9 + 12 = 63 + 12 = 75 m².
iv) Cost of laying tiles in kitchen = Rate / m² x Area of kitchen = 50 x ( x y) = 250 x 7 = Rs.1750.
- i) Since 480 people visited thus x + y = 480. Collected amount is Rs 134500 thus 150x + 400y = 134500 & 3x + 8y = 2690. Thus (a) is correct option.
ii) Solving the equations x + y = 480 and 3x + 8y = 2690 we get x = 230 and y = 250 Number of children attended = 230 Number of adults attended = 250. Thus (c) is correct option.
iii) Number of adults attended = 250. Thus (a) is correct option.
iv) Amount = 150 x 300 + 400 x 350 = 1, 85,000 Rs.Thus (d) is correct option.
reciprocal of the other, then
(a) b= c
(b) a = b
(c) ac = 1
(d) a= c
Q 6 Which of the following equations has 2 as one of the roots?
a) x^2 +4x− 5
b) x^2 +3x +
c) 2x^2 - 7x+
d) 3x^2 - 6x+
ASSERTION – REASON / VERY SHORT
Q 07 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.
Q 08 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.
CASE BASED/SOURCE BASED
Q 09 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?
Q 10 (^) 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.
