- Sainik School 2024 Entrance Exam for Class 6 Students
- Sainik School Question Paper 2024 for Class 6
- Sainik School 2024 Question Paper Class 6, Sainik School Entrance Exam 2024, Class 6 Sainik School Paper, AISSEE 2024 Class 6, Sainik School MCQ, Sainik School Exam Preparation
Instructions: Each question has four options. There is only one correct answer to each question. Choose the MOST APPROPRIATE option and darken/blacken the corresponding circle on the OMR Answer Sheet.
Section - "B": MATHEMATICS
026. Which of the following is the correct representation using Roman Numerals of the number 199?
(1) ICC
(2) CLXXXXIX
(3) CXCIX
(4) ICCCD
Answer. (3) CXCIX
Roman numeral values:
C = 100
XC = 90
IX = 9
So,
199 = 100 + 90 + 9 = CXCIX
027. A number written using Roman Numerals ( XXI-XV)-VI+MCLXXIII is equal to
(1) MCLXXIII
(2) MCLXVII
(3) MCL
(4) MCXLIII
Answer.(1) MCLXXIII
First convert Roman numerals into numbers:
M=1000
C=100
L=50
XXI = 21
MCLXXIII = 1173
Now, calculate step by step:
(21 − 15) − 6 + 1173
= 6 − 6 + 1173
= 0 + 1173
= 1173
1173 in Roman numerals = MCLXXIII
028. Harish drives his car at a speed of 45 km/h. How much time ( in minutes) will be take to drive 12 km?
(1) 9
(2) 12
(3) 16
(4) 20
Answer. (3) 16
Time = Distance ÷ Speed
Time = 12 ÷ 45 hours
= 4/15 hours
Convert hours into minutes:
(4/15) × 60 = 16 minutes
029. Raman covers a distance of 24 km in 40 minutes. If he increases his speed by 4 km/hour, the how much time (in minutes) will be take to cover the same distance?
(1) 28
(2) 32
(3) 36
(4) 38
Answer. (3) 36
First, we need to find the original speed:
40 minutes = 2/3 hour
Speed = Distance ÷ Time
= 24 ÷ (2/3)
= 36 km/hour
New speed = 36 + 4 = 40 km/hour
Now calculate the new time:
Time=Distance/speed
Time = 24 ÷ 40 = 3/5 hour
Convert into minutes:
(3/5) × 60 = 36 minutes
030. Amrita went to a market for purchasing stationery items for her son. She carried rupees 500 with her. She paid rupees 135.50 for the notebooks, rupees 30.5 for pens, rupees 3.75 for erasers, rupees 48 for a box of colours, and rupees 142 for a Geometry box. How much money is left with her?
(1) 132.25
(2) 142
(3) 140.25
(4) 145.75
Answer. (3) 140.25
Explanation of the questions as follows:
Total money = ₹500
Expenses:
Notebooks = ₹135.50
Pens= ₹ 30.5
Erasers= ₹ 3.75
Colours = ₹48
Geometry box = ₹142
Total spent = 135.50 + 30.5+ 3.75+ 48 + 142
= ₹359.75
Money left = 500 − 359.75
= ₹140.25
031. If the average of numbers 12, 15, 19, k, and (k+5) is 13, then the value of k is:
(1) 3
(2) 5
(3) 7
(4) 13.5
Answer. (3) 7
Average = (Sum of observations) ÷ (Number of observations)
Given average = 13 and total numbers = 5
So, total sum = 13 × 5 = 65
Now add the numbers:
12 + 15 + 19 + k + (k + 5)
= 51 + 2k
Set up the equation:
51 + 2k = 65
2k = 14
k = 7
032. The average weight of five friends weighing 48 kg, 50 kg, 53 kg, 55 kg, and 49 kg is:
(1) 50 kg
(2) 51 kg
(3) 52 kg
(4) 53 kg
Answer. (2) 51 kg
Sum of weights = 48 + 50 + 53 + 55 + 49 = 255 kg
Average = 255 ÷ 5 = 51 kg
033. Read the given statements and choose the correct option:
Statement I: Two distinct lines can intersect is more than one point.
Statement-II: More than two lines can pass through one point.
(1) Only statement I is true
(2) Only statement II is true
(3) Both the statements are true
(4) Both the statements are false
Answer. (2) Only statement II is true
Statement I: Two distinct lines can intersect in more than one point.
This is false — two distinct lines can intersect at only one point.
Statement II: More than two lines can pass through one point.
This is true — many lines can pass through a single point.
034. If x=30 and y =120, then value of 16(x/y +5) +1 is:
(1) 85
(2) 84
(3) 21
(4) 117
Answer. (1) 85
First, evaluate inside the bracket:
(x / y + 1) = (30 / 120 + 1) = 21/4
Now,
16*21/4= 84
84 +1 = 85
035. Joseph borrowed INR 25,000 on simple interest at the rate of 6 % per annum for 4 years. How much did he pay at the end of 4 years?
(1) 30000
(2) 31000
(3) 31800
(4) 31920
Answer. (2) 31000
Simple Interest (SI) = (P × R × T) ÷ 100
P = 25,000
R = 6%
T = 4 years
SI = (25,000 × 6 × 4) ÷ 100
= 6,000
Total amount = Principal + Interest
= 25,000 + 6,000
= ₹31,000
036. In how many years will a sum of INR 1,800 become INR 2,610 on simple interest at the rate of 9% per annum?
(1) 4
(2) 5
(3) 6
(4) 9/2
Answer. (2) 5
Amount (A) = ₹2,610
Principal (P) = ₹1,800
Simple Interest (SI) = A − P
SI = 2,610 − 1,800 = ₹810
Using SI formula:
Simple interest P*R*T/100
810=1800*9*T/100
T=5
037. The perimeter of the given figure is:
(1) 32 cm
(2) 40 cm
(3) 48 cm
(4) 52 cm
Answer. (3) 48 cm
The given figure is a cross-shaped figure made of straight line segments. To find the perimeter, we add only the outer boundary lengths (internal lines are not counted).
Total perimeter = Sum of all outer sides = 48 cm
038. Pinky runs around a square field of side 50 m and takes 6 rounds. Shruti runs around a rectangular field of length 160 m and breadth 120 m and takes 2 rounds. Who covers more distance and how much more ( in m)?
(1) Shruti, 80 m
(2) Pinky, 80 m
(3) Shruti, 65 m
(4) Pinky, 40 m
Answer. (2) Pinky, 80 m
Pinky:
Perimeter of square = 4*L=4 × 50 = 200 m
Distance covered = 200 × 6 = 1200 m
Shruti:
Perimeter of rectangle = 2(L+W)= 2(160 + 120) = 560 m
Distance covered = 560 × 2 = 1120 m
Difference:
1200 − 1120 = 80 m
Pinky covers more distance of 80 m.
039. The sum of the greatest 4-digit number and the smallest 3-digit number is:
(1) 10000
(2) 10110
(3) 10099
(4) 10999
Answer. (3) 10099
Greatest 4-digit number = 9999
Smallest 3-digit number = 100
Sum = 9999 + 100 = 10099
040. The difference between the greatest and the smallest 5-digit numbers formed using digits 0,2,5,3, and 1, is:
(1) 45555
(2) 44444
(3) 43205
(4) 42975
Answer. (4) 42975
Greatest number: Arrange digits in descending order
→ 5 3 2 1 0 = 53210
Smallest number: Smallest non-zero digit first
→ 1 0 2 3 5 = 10235
Difference = 53210 − 10235 = 42975
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