Class 6th Mathematical Reasoning...Class 6th Mathematical Reasoning Next Education India Pvt. Ltd....
Transcript of Class 6th Mathematical Reasoning...Class 6th Mathematical Reasoning Next Education India Pvt. Ltd....
Class 6th Mathematical Reasoning _________________________________________________________________________________________________
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Year Questions Marks
2012 20 20
2013 15 15
2014 20 20
2015 20 20
2016 20 20
Total 95 95
1. Neha is getting ready for the state assessment, and is planning mini-lessons for students focused on
particular difficulties that they are having with adding columns of numbers. To target her instruction more
effectively, she wants to work with group of students who are making the same kind of error, so she looks at
a recent quiz to see what they tend to do. She sees the following three student’s mistakes.
Which have the some kind of error? [2012]
(A) I and II (B) I and III (C) II and III (D) I, II and III
Ans: A
Solution: (I) and (II) adding the digits at unit place correctly which is not done by (iii).
2. Select the correct match. [2013]
(A) LXV = 75 (B) LXIX = 79 (C) XCVIII = 98 (D) LXXX = 90
Ans: C
Solution: XCVIII = (100 – 10) + 5 + 1 + 1 + 1 = 98.
3. The difference between place values of digit 5 in 456.385 is ______. [2014]
(A) 49995 (B) 499.95 (C) 49.995 (D) 49.999
Ans: C
4. The figure below is made up of 12 equilateral triangles.
If the length of PQ is 96 cm, find the total perimeter of the figure. [2015]
(A) 192 cm (B) 384 cm (C) 288 cm (D) 576 cm
Ans: B
5. The simplification of 2.002 + 7.9 {2.8 – 6.3(3.6 – 1.5) + 15.6} yields [2016]
(A) 2.002 (B) 4.2845 (C) 40.843 (D) 42.845
Ans: D
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6. This graph shows the number of people who used the Internet each year in India from 1997 to 2003.
Based on the information in the graph, between which two years did the smallest increase occur? [2012]
(A) 1998 and 1999 (B) 2001 and 2002 (C) 2002 and 2003 (D) 1997 and 1998
Ans: C
Solution: As per the graph the inclination is very less this duration.
7. Express the number of storybooks that Mohit read in December as a fraction of the total number of
storybooks read in four months. [2013]
(A) 1 (B) 1
2 (C)
1
3 (D) 2
Ans: C
Solution: Total number of storybooks = 24
Number of storybooks read in December = 8
Hence the ration will be 8/24 = 1/3
8. Find the least number which on adding 9 to it becomes exactly divisible by 15, 25, 30 and 45. [2014]
(A) 410 (B) 450 (C) 380 (D) 441
Ans: D
9. Which of the following options is INCORRECT? [2015]
(A) The number 48693 rounded off to nearest hundred is 48700.
(B) LXXV is greater than LXXIV.
(C) One million is equal to 10 crore.
(D) Place value of a digit = (face value of the digit) × (Value of the place)
Ans: C
10. If I = 13
4÷
5
6,
II = 13 ÷ [(4 ÷ 5)] ÷ 6],
III = [13 ÷ (4 ÷ 5)] ÷ 6 and
IV = 13 ÷ 4(5 ÷ 6) then, which of the following are equal? [2016]
(A) I and II (B) I and IV (C) I and III (D) All are equal
Ans: B
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11. Which of the following represents the fraction of Figure X that is shaded? [2012]
(A) 1
2 (B)
2
3 (C)
4
5 (D)
5
9
Ans: D
Solution: The shaded parts are 20 and the total number of small squares is 36.
So the fraction is 20/36 that is 5/9.
12. Which of the following numbers is completely divisible by 3? [2013]
(A) 297149 (B) 1790184 (C) 6392105 (D) 901352
Ans: B
Solution: Because, sum of digits for 1790184 = 1+7+9+0+1+8+4 = 30 is divisible by 3, therefore
1790184 is divisible by 3.
13. Which of the following square(s) must be shaded so that given figure is symmetric along both lines LM and
AB? [2014]
(A) R and S (B) P only (C) Q and P (D) Q only
Ans: C
14. Which of the following figures do not have any line of symmetry? [2015]
Ans: C
15. Which of the following statements is/are INCORRECT? [2016]
(i) Eighty four in Roman numeral is written as CXXXIV.
(ii) There are seven zeroes in 1 crore.
(iii) There are ten thousand milligrams formed by using all
(iv) The smallest 4-digit number formed by using all the digits 4, 3, 0, 8 without repetition is 3048.
(A) Both (i) and (iii) (B) Both (i) and (iv) (C) Only (i) (D) Only (iii)
Ans: A
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16. Raghav drew the line segments shown here on a piece of paper which of the following pairs of line
segments appears to be perpendicular? [2012]
(A) GH̅̅ ̅̅ and KL̅̅̅̅ (B) GH̅̅ ̅̅ and IJ̅ (C) EF̅̅̅̅ and KL̅̅̅̅ (D) EF̅̅̅̅ and GH̅̅ ̅̅
Ans: B
Solution: The line segments GH and U are perpendicular.
17. The given figure is made up of 10 squares of the same size. The perimeter of the figure is 80 cm.
Find the area of the figure. [2013]
(A) 250 cm2 (B) 150 cm2 (C) 280 cm2 (D) 190 cm2
Ans: A
Solution: Given perimeter of above figure = 16 a = 80 cm
Side of each square = a = 80/16 = 5cm
Area of each square = 5 × 5 = 25 sq.cm
Area of required figure = 25 × 10 = 250 sq.cm.
18. ABCD and PQRS are two squares of same dimensions find the area of shaded part. [2014]
(A) 49 cm (B) 49 cm2 (C) 196 cm2 (D) 196 cm
Ans: C
19. Which of the following options shows distributive property of multiplication over addition? [2015]
(A) 4 + (5 × 8) = (4 + 5) × (4 + 8) (B) 4 × (5 + 8) = (4 × 5) + (4 × 8)
(C) 4 × (5 × 8) = (4 × 5) × 8 (D) (8 + 5) + 4 = 8 + (5 + 4)
Ans: B
20. Using distributive property, 258 × 1008 =? [2016]
(A) 258 + 1000 + 8 (B) 258 × 1000 + 258 × 8
(C) 258 × 1000 + 8 (D) 1000 + 8 × 258
Ans: B
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21. Which of the following three-dimensional shapes has 1 rectangular face and 4 triangular faces? [2012]
(A) Rectangular pyramid (B) Triangular pyramid
(C) Rectangular prism (D) Triangular prism
Ans: A
Solution: Rectangular pyramid is a three-dimensional shape which has one rectangular face and 4
triangular faces.
22. Which of the following figures has/have at least one line of symmetry? [2013]
(A) I and II (B) I and III (C) II and III (D) I, II and III
Ans: B
23. If 7
9 of a number is 63, then
1
3 of the number is ______. [2014]
(A) 21 (B) 27 (C) 49 (D) 42
Ans: B
24. Which of the following pair of numbers is co-prime? [2015]
(A) (17, 15) (B) (10, 16) (C) (20, 24) (D) (31, 62)
Ans: A
25. Which situation is best represented by the integer -12? [2016]
(A) The length of curtains is increased by 12 inches.
(B) The price of petrol is reduced by ₹ 12.
(C) The size of picture is enlarged by 12 per cent.
(D) The temperature rises by 12° C.
Ans: B
26. Siddharth is ordering these-decimals 0.40, 0.350, 0.200, 0.03.
Which number line shows these decimals in the correct order (Number lines are not drawn to scale). [2012]
Ans: C
27. What must be added to the product of 24
7 and 3 to make21
5
14? [2013]
(A) 139
12 (B) 12
9
14 (C) 13
9
14 (D) 15
11
14
Ans: C
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Solution: The required number be X,
The given expression will be, {2(4/7) * 3} + x = 21(5/14)
=> {(18/7) * 3} + x = (299/14)
=> (54/7) + x = 299/14
=> x = (299/14) – (54/7) => x = (299 – 108)/14
=> x = 191/14 => {13(9/14)}
28. Priya had ₹ 50. After buying 5 identical pens, she has ₹ y left.
The cost of 1 pen in terms of y is _______. [2014]
(A) ₹ (50−𝑦
5) (B) ₹ (50 −
𝑦
5) (C) ₹ (50 – 5y) (D) ₹ (
50𝑦
5)
Ans: A
29. How many of the given numbers are NOT divisible by 11? [2015]
(A) 4 (B) 7 (C) 6 (D) 5
Ans: C
30. Find the area of the following figure (not drawn to scale) by splitting them into rectangles and squares.
[2016]
(A) 14 sq. cm (B) 15 sq. cm (C) 17 sq. cm (D) 16 sq. cm
Ans: D
31. Represent the following expression algebraically. [2012]
A number x, decreased by the sum of 2x and 5
(A) (2x + 5) – x (B) x – (2x + 5) (C) x – 2x + 5 (D) (x – 2x) – 5
Ans: B
32. 2
3 Of the books in a box are English books,
1
4 are Math’s books and the rest are Science books.
What fraction of the books are Science books? [2013]
(A) 2
3−
1
4 (B)
2
3×
1
4 (C) 1 − (
2
3+
1
4) (D) 1 − (
2
3−
1
4)
Ans: C
Solution: Let the total number of books be 1,
Hence number of science books will be = 1 – {(2/3) + (1⁄4)}
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33. The given square PQRS is made up of 4 smaller squares.
What is the ratio of the area of the shaded part to the area of the unshaded part? [2014]
(A) 2:3 (B) 1:3 (C) 1:4 (D) 3:1
Ans: B
34. Read the statements given below and identify the correct option. [2015]
(i) Every diameter of a circle is also a chord.
(ii) Every chord of a circle is also a diameter.
(iii) The centre of a circle is always in its interior.
(i) (ii) (iii)
(A) False True False
(B) True False True
(C) True False False
(D) True True False
Ans: B
35. Match the fractions given in Column I with the shaded portion of figure in Column II. [2016]
Column I Column II
(i) 6
4 (p)
(ii) 6
10 (q)
(iii) 6
6 (r)
(iv) 6
16 (s)
(i) (ii) (iii) (iv)
(A) (r) (q) (s) (p)
(B) (s) (p) (r) (q)
(C) (r) (s) (p) (q)
(D) (q) (p) (s) (r)
Ans: A
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36. A prime number can best be described as _____. [2012]
(A) A number with exactly 2 factors (B) Always an odd number
(C) A number with more than 2 different factors (D) Always an even number
Ans: A
Solution: A prime number has two and only two factors those are 1 and the number itself.
37. Priya drove from town P to town Q. She took 14 hours 35 minutes for the journey.
The clock shows the time she arrived at Town Q in the afternoon.
When did she set off from Town P? [2013]
(A) 2:10 am (B) 4:45 pm (C) 4:45 am (D) 2:45am
Ans: A
Solution: Arrival time = 4:45 PM
Travel time = 14hrs 35min
Hence time of start of journey will be 4:45PM – 14hrs 35min
which is = 2:10 AM
38. The given table shows the temperature of a country for 7 consecutive hours. [2014]
Hour 1 2 3 4 5 6 7
Temperature (°C) -6 15 -2 23 12 0 -4
Calculate the difference between the highest and the lowest temperature of the country over the 7-hour
period.
(A) 17 ³C (B) 29 °C (C) 21 °C (D) 25 °C
Ans: B
39. Which of the following hands of the clock shows 3
4 of a revolution? [2015]
Ans: D
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40. How many of the following figures are symmetrical? [2016]
(A) 9 (B) 10 (C) 3 (D) None of these
Ans: D
41. Which of the following shows a reflection of the figure (X) across the RS? [2012]
Ans: B
42. A hot air balloon was 150 feet in the air. The distances it moved down and up, in feet, is shown in this list
-40, 150, -80
How high in the air is the hot air balloon after moving these distances? [2012]
(A) -420feet (B) -180 feet (C) 180 feet (D) 420 feet
Ans: C
Solution: 150 – 40 + 150 – 80 = 180 feet
43. The ratio of the volume of water in Bottle P to the volume of water in Bottle Q is 3:4.
Rajeev drank 40 mL of the water from Bottle P and the ratio then became 13:20.
How much water was there in bottle P at first? [2013]
(A) 60 mL (B) 80 mL (C) 300 mL (D) 400 mL
Ans: C
Solution: Ratio of the volume of water in bottle P and Q = 3:4 = 4
40 ml of water drank in bottle P,
Then Required ratio of volume of water in bottle P and Q = (3x – 40): 4 = 13:20
Therefore x = 100
Volume of water in bottle P = 3 × 100 = 300ml.
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44. Find the value of CXVI + XIII + VI + CCLXV – XVI. [2014]
(A) CD (B) CCCLXXXIV (C) CCCLXXXV (D) M
Ans: B
45. The given figure has _______ edges and _______ vertices. [2015]
(A) 12, 8 (B) 14, 8 (C) 9, 7 (D) 15, 10
Ans: D
46. The diagram below shows a framed picture. Find the area of the picture. [2016]
(A) 48 cm2 (B) 39 cm2 (C) 92 cm2 (D) 120 cm2
Ans: A
47. Evaluate 121
3− 9
3
5+ 8.4 ÷ 0.02 [2012]
(A) 81.83 (B) 420.73 (C) 422.73 (D) 42.273
Ans: C
Solution: 37/3 - 48/5 + 8.4/0.02 = 41/5 + 420 = 2.73 + 420 = 422.73
48. Machine P can shred 12 sheets of paper in 15 seconds. Machine Q can shred 18 sheets of paper in 20
seconds. Which machine can shred more sheets of paper in one minute and by how many more? [2013]
(A) Machine P, 6 sheets (B) Machine Q, 6 sheets
(C) Machine P, 8 sheets (D) Machine Q, 8 sheets
Ans: B
Solution: Accd. To question,
Machine P sheds 12 sheets in 15secs,
Hence P sheds 48 sheets in 60 secs (or 1 min)
Again, Machine Q sheds 18 sheets in 20 secs
Hence Q sheds 54 sheets in 60 secs (or 1 min)
Therefore Q sheds 6more sheets in 1 min.
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49. Find the missing number. [2014]
143
4× 4
1
2− 3
1
4× 4
1
2+ 11
1
2× 5
1
2= ? - 4
(A) 323
8 (B) 111 (C) 115 (D) 119
Ans: D
50. Evaluate: [2015]
– 1 + 55 – (– 1) – (– 82) + (– 3)
(A) 161 (B) – 161 (C) 158 (D) – 158
Ans: A
51. Which sign will show correct comparison between the given expressions? [2016]
(-3) – 74 + (-42) + (-82) (-12) + (-43) – (-57) + 1.
(A) > (B) < (C) = (D) Can’t be determined
Ans: B
52. Find the area of the given figure, (Figure not drawn to scale) [2012]
(A) 12.5 cm2 (B) 42.5 cm2 (C) 32.5 cm2 (D) 10 cm2
Ans: C
Solution: Let put a line on the right to get a full rectangle as shown below
Now the required area = Total Area – Area of DEFG
= 15 × 2.5 – 5 × 1 = 32.5 sq. cm.
53. Fill in the blanks: [2013]
Every natural number has a ______ except and has a ________.
(A) Successor 0, predecessor (B) Successor, 1, predecessor
(C) Predecessor, 0, successor (D) Predecessor, 1, successor
Ans: D
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54. Estimate the following by rounding off each number to nearest hundreds. 78203 – 16407 [2014]
(A) 61700 (B) 62000 (C) 61800 (D) 61500
Ans: C
55. Arrange the shaded fractions of the following figures in ascending order. [2015]
(A) s, q, r, p (B) p, r, s, q (C) s, p, q, r (D) p, r, q, s
Ans: D
56. The number of collinear points in the given figure are [2016]
(A) 10 (B) 18 (C) 15 (D) 12
Ans: A
57. Which word describes the boxed number? [2012]
x = y
(A) Coefficient (B) Equation (C) Term (D) Variable
Ans: A
58. Which of the following diagrams correctly describes the factors of 15 and 12? [2013]
Ans: C
Solution: Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 15 = 1, 3, 5, 15
59. When we multiply a whole number and the multiplicative identity of whole numbers, then we get __. [2014]
(A) The number itself (B) The multiplicative identity
(C) 0 (D) Negative of that number
Ans: A
8
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60. 0 is the ______ identity for whole numbers, whereas 1 is the _____ identity for whole numbers. [2015]
(A) Additive, Multiplicative (B) Multiplicative, Additive
(C) Commutative, Additive (D) Positive, Not-defined
Ans: A
61. A polygon has prime under of sides. If number of sides is equal to the sum of the two least consecutive
primes. The number of diagonals of the polygon is [2016]
(A) 4 (B) 5 (C) 7 (D) 10
Ans: B
62. Fill in blank: [2012]
A number for which sum of all its factors is equal to _______. The number is called perfect number.
(A) Twice (B) Thrice (C) Four times (D) Square
Ans: A
Solution: 6 is a perfect number as the sum if its factors those are 1, 2, 3, 6 is 12 which is twice of 6.
63. Select the INCORRECT match. [2013]
(A) One pair of parallel side - Trapezium
(B) Parallelogram with 4 - Rectangle
right angles
(C) Parallelogram with 4 - Rhombus
sides of equal length
(D) A rhombus with 4 - Kite
right angles
Ans: D
64. Which of the following statements is incorrect? [2014]
(A) Two parallel line segments will always intersect.
(B) All equilateral triangles are isosceles.
(C) Measure of straight angle is twice that of right angle.
(D) The diameter of a circle is double of its radius.
Ans: A
65. Which of the following statements is definitely true, if PQRS is a parallelogram? [2015]
(A) PQ and SR are adjacent sides. (B) ∠P and SR are adjacent sides.
(C) SR ∥ PQ. (D) PR = RQ.
Ans: C
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66. Number of primes between 16 to 80 and 90 to 100 is [2016]
(A) 20 (B) 18 (C) 17 (D) 16
Ans: C
67. Solve the following Roman numerals. LIX + XXXVI + IX + XC – LX [2012]
(A) CXXXVI (B) CXXXLIV (C) CXXVII (D) CXXXIV
Ans: D
Solution: LIX + XXXVI + IX – LX = 59 + 36 + 9 + 90 – 60 = 134 = CXXXIV
68. Which of the following statements is correct? [2013]
(A) 14 tenths 4 thousandths = 0.144 (B) 2 tenths 13 hundredths = 0.213
(C) 4 hundredths 2 tenths = 0.024 (D) 7 tenths 14 hundredths = 0.87
Ans: A
Solution: 14 tenths 4 thousands = + = 1.4 + 0.004 = 1.404
69. Ali will be 6y years old in 6 years’ time. How old was Ali 4y years ago? [2014]
(A) 6y – 6 (B) 10y – 6 (C) 2y – 6 (D) 2y + 6
Ans: C
70. Solid P has _________ more faces than Solid Q. [2015]
(A) 4 (B) 3 (C) 2 (D) 5
Ans: B
71. Which three-dimensional figure has 5 faces. 8 edges and 5 vertices? [2016]
Ans: A
72. Find the lowest natural number which when divided by 112, 140 and 168 leaves a remainder 8 in each
case. [2012]
(A) 1440 (B) 1688 (C) 720 (D) 1672
Ans: B
Solution: LCM of 112, 140 and 168 = 1680
The required number is 1680 + 8 = 1688.
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73. The fractional number corresponding to the given number “9 tens + 5 ones + 3 tenths + 7 hundredths” is
__________. [2013]
(A) 9437
100 (B)
9537
100 (C)
9000
100 (D)
9637
100
Ans: B
74. Express the given expression in the standard form. 0.0001289 – 0.0000000274 × 1293 + 0.0000419032
[2014]
(A) 1.35375 × 10-2 (B) 1.53357 × 10-4 (C) 1.35375 × 104 (D) 1.35375 × 10-4
Ans: D
75. Find X. [2015]
16.7 + 12.38 – X = 10.09
(A) 17.89 (B) 18.99 (C) 16.98 (D) 20.09
Ans: B
76. If the sum of two angles is equal to an obtuse angle, then which of the following is not possible? [2016]
(A) One obtuse and one angle (B) One right angle and one acute angle
(C) Two acute angles (D) Two right angles
Ans: D
77. By joining any two points on the circumference of a circle, we obtain a _______. [2012]
(A) Diameter (B) Chord (C) Radius (D) Circumference
Ans: B
Solution: Chord is the line segment joins two points on the circumference of a circle.
78. Prateek, Divyanshu and Manish jog daily in the morning around a rectangular park.
They take 3 minutes, 10 minutes and 5 minutes respectively to take one complete round. In one morning,
all of them start at the same time from the same point and jog in the same direction for an hour. [2014]
(a) After how many minutes will all three of them meet again?
(b) How many times will they meet together during the 1 hour period?
(a) (b)
20 minutes 3 times
25 minutes 2 times
30 minutes 2 times
60 minutes 1 time
Ans: C
79. The H. C. F. of 252, 324 and 594 is ______. [2015]
(A) 36 (B) 18 (C) 12 (D) 6
Ans: B
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80. Latika, Garima and Sanchi draw 3 cards each from 9 cards numbered from 1 to 9. [2016]
Latika: L, Garima: G, Sanchi: S
L: The product of my numbers is 48.
G: The sum of my numbers is 15.
S: The product of my numbers is 63.
What is the largest number in the cards of Sanchi?
(A) 8 (B) 7 (C) 9 (D) 6
Ans: C
81. Which of the following shows a symmetric figure? [2012]
Ans: B
82. Which of the following numbers is divisible by 11? [2014]
(A) 1011011 (B) 1111111 (C) 22222222 (D) 3333333
Ans: C
83. Rohit’s teacher asked him to tell the correct answer after performing the steps given below. [2015]
Round off 43, 98 and 250 to nearest tens.
After rounding off, add them
Round off the sum to the nearest hundreds.
Then, the correct answer is _______.
(A) 300 (B) 400 (C) 350 (D) 480
Ans: B
84. Find the greatest number from the options that will divide 1025, 1299 and 1575 leaving remainders 5, 7
and 11 respectively. [2016]
(A) 70 (B) 78 (C) 68 (D) 98
Ans: C
85. Which of the following fractions is smaller than5
9? [2012]
(A) 1
4 (B)
11
13 (C)
5
7 (D)
6
7
Ans: A
86. 35% of a number is 189. What is 25% of the number? [2014]
(A) 315 (B) 135 (C) 540 (D) 125
Ans: B
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87. Which of the following figures have maximum shaded area? [2015]
(A) (i) (B) (ii) (C) (iii) (D) Can’t be determined
Ans: B
88. Select the CORRECT statement. [2016]
(A) 1592 rounded off to nearest tens is 1600.
(B) 7532 rounded off to nearest thousands is 7500.
(C) 245 rounded off to nearest hundreds is 240.
(D) 214653 rounded off to nearest ten thousands is 210000.
Ans: D
89. Express 12 sec as a percentage of 3 mins 20 sec. [2012]
(A) 6% (B) 3.75% (C) 62% (D) 37.5%
Ans: A
Solution: 12 / 200 × 100 = 6%
90. If P and Q represent the prime digits, then find the value of P and Q respectively. [2014]
P P 5
× Q Q
2 Q 2 5
+2 Q 2 5 0
2 5 5 7 5
(A) 3, 3 (B) 7, 5 (C) 1, 5 (D) 7, 3
Ans: D
91. Number name for 900800700 in Indian system is _______. [2015]
(A) Ninety crores, eight lakhs and seven hundreds
(B) Nine crores, eight lakhs and seven hundreds
(C) Ninety crores, eighty lakhs and seven hundreds
(D) Ninety crores, eight lakhs and seven
Ans: A
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92. In an activity class, students were asked to make a circular rangoli. Trishu, Sidak, Mini and Kavleen made
rangolis having different diameters as 17
20 inches,
5
6 inches and
7
10 inches, respectively.
Who among them made the smallest one? [2016]
(A) Kavleen (B) Trishu (C) Mini (D) Sidak
Ans: A
93. Which of the following figures satisfy the given conditions? [2014]
Figure (i) Faces: 4 Figure (ii) Faces: 5
Edges: 6 Edges: 9
Vertices: 4 Vertices: 6
Ans: C
94. The charges in a resort are shown below. [2015]
Entrance Fee ₹ 40 per car
Monday to Friday ₹ 15.50 per passenger
Saturday and Sunday ₹ 22.50 per passenger
Parking charges ₹ 10.60 per half hour
Mr.Mohit drove to the resort with his wife and three children on Sunday at 1 : 30 p.m.
They left the resort at 8 p.m. How much did Mr. Mohit and his family have to pay in all?
(A) ₹ 250.30 (B) ₹ 300.90 (C) ₹ 267. 80 (D) ₹ 290.30
Ans: D
95. Which of the following will not represent zero? [2016]
(A) 1
0 (B) 0 × 9 (C)
0
2 (D)
3−3
2
Ans: A