Using the digits 5, 0, 3 and 8 exactly once, form the greatest and the smallest possible 4-digit numbers. What is the difference between them?
Explanation: Greatest number (no leading zero, digits descending) = 8530. Smallest number (smallest non-zero digit first, then remaining digits ascending) = 3058. Difference = 8530 − 3058 = 5472.
Find the sum of the successor of 99,999 and the predecessor of 1,00,000.
Explanation: Successor of 99,999 = 1,00,000. Predecessor of 1,00,000 = 99,999. Sum = 1,00,000 + 99,999 = 1,99,999.
What is the Roman numeral representation of 1749?
Explanation: 1749 = 1000 + 700 + 40 + 9 = M + DCC + XL + IX = MDCCXLIX.
How many prime numbers are there between 1 and 30 (inclusive)?
Explanation: The primes between 1 and 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 — a total of 10 primes.
Find the HCF of 48 and 60.
Explanation: 48 = 2⁴ × 3, and 60 = 2² × 3 × 5. The common factors are 2² and 3, so HCF = 4 × 3 = 12.
Find the LCM of 12 and 18.
Explanation: 12 = 2² × 3, and 18 = 2 × 3². LCM takes the highest powers: 2² × 3² = 36.
Which of the following numbers is divisible by 9?
Explanation: A number is divisible by 9 if the sum of its digits is divisible by 9. For 4536: 4+5+3+6 = 18, which is divisible by 9. The digit sums of the other options (14, 16, 16) are not divisible by 9.
How many factors does the number 36 have?
Explanation: 36 = 2² × 3². The number of factors = (2+1) × (2+1) = 9. (These are 1, 2, 3, 4, 6, 9, 12, 18, 36.)
Which of the following pairs of numbers is co-prime (HCF = 1)?
Explanation: HCF(15,18) = 3, HCF(8,9) = 1, HCF(12,16) = 4, HCF(20,25) = 5. Only 8 and 9 share no common factor other than 1.
Look at the pattern: 2, 6, 12, 20, 30, __. What is the next number?
Explanation: Each term equals n × (n+1): 1×2=2, 2×3=6, 3×4=12, 4×5=20, 5×6=30, so the next term is 6×7 = 42. (Equivalently, the differences 4, 6, 8, 10 increase by 2, so the next difference is 12: 30 + 12 = 42.)
Which of the following fractions is the greatest?
Explanation: Converting all to twelfths: 3/4 = 9/12, 5/8 = 7.5/12, 7/12 = 7/12, 2/3 = 8/12. The greatest value is 9/12 = 3/4.
Add: 2/3 + 3/5
Explanation: LCM of 3 and 5 is 15. 2/3 = 10/15 and 3/5 = 9/15. Adding: 10/15 + 9/15 = 19/15 (which equals 1 4/15).
A water tank holds 60 litres. If 2/5 of the tank is filled with water, how many litres of water are in the tank?
Explanation: 2/5 of 60 = (2 × 60) ÷ 5 = 120 ÷ 5 = 24 litres.
Find the sum: 45.68 + 12.375
Explanation: Aligning the decimal points: 45.680 + 12.375 = 58.055.
Express 7/8 as a decimal.
Explanation: 7 ÷ 8 = 0.875.
Find the missing number: 3/7 = __/28
Explanation: 28 ÷ 7 = 4, so multiply the numerator by 4 as well: 3 × 4 = 12. Hence 3/7 = 12/28.
A pizza is cut into 8 equal slices. Ravi eats 3/8 of the pizza and Sam eats 2/8 of it. What fraction of the pizza is left?
Explanation: Together they eat 3/8 + 2/8 = 5/8 of the pizza. The fraction left = 1 − 5/8 = 3/8.
Which of these decimal numbers is the smallest?
Explanation: Comparing place by place: 0.099 has a 0 in the tenths place while the others have 4 or 5, making 0.099 the smallest.
Reduce 84/126 to its lowest terms.
Explanation: HCF of 84 and 126 is 42. Dividing both by 42: 84 ÷ 42 = 2, and 126 ÷ 42 = 3. So 84/126 = 2/3.
Convert 5 3/7 into an improper fraction.
Explanation: (5 × 7 + 3)/7 = (35 + 3)/7 = 38/7.
Which is the smallest integer among −8, 3, −12 and 0?
Explanation: On the number line, the integer farthest to the left is the smallest. −12 lies to the left of −8, 0 and 3, so it is the smallest.
The temperature at 6 a.m. was −6°C. By noon it had risen by 15°C. What was the temperature at noon?
Explanation: A rise means we add: −6 + 15 = 9°C.
A submarine was at a depth of −250 m. It rose to a depth of −90 m. By how many metres did it rise?
Explanation: Rise = New position − Old position = −90 − (−250) = −90 + 250 = 160 m.
Find the difference: 9 − (−17)
Explanation: Subtracting a negative number is the same as adding: 9 − (−17) = 9 + 17 = 26.
Solve for x: 3x + 7 = 25
Explanation: 3x + 7 = 25 → 3x = 18 → x = 6.
If x = 4, find the value of 2x² − 3x + 1.
Explanation: 2(4)² − 3(4) + 1 = 2(16) − 12 + 1 = 32 − 12 + 1 = 21.
The nth term of a sequence is given by 3n + 2. What is the 10th term?
Explanation: Substitute n = 10: 3(10) + 2 = 30 + 2 = 32.
Rahul is x years old today. In 5 years he will be 18 years old. Find x.
Explanation: x + 5 = 18, so x = 18 − 5 = 13.
A shopkeeper loses ₹8 on every defective item sold. If 7 items turn out to be defective, what is the total loss, expressed as an integer?
Explanation: A loss of ₹8 per item is represented as −8. For 7 items: 7 × (−8) = −56.
An elevator starts at floor −2 (the second basement level) and goes up 9 floors. Which floor does it reach?
Explanation: Going up means adding: −2 + 9 = 7.
Three angles P, Q and R are shown below. Which one is an obtuse angle (an angle greater than 90° but less than 180°)?
Explanation: An obtuse angle measures more than 90° but less than 180°. Angle P (45°) is acute, Angle Q (90°) is a right angle, and Angle R (120°) fits the obtuse range.
In the triangle shown, two of the angles are 55° and 65°. Find the measure of the third angle.
Explanation: The angles of a triangle always add up to 180°. Third angle = 180° − (55° + 65°) = 180° − 120° = 60°.
Two angles are complementary (their sum is 90°). If one of the angles is 35°, what is the measure of the other angle?
Explanation: Complementary angles add up to 90°. The other angle = 90° − 35° = 55°.
Look at the triangle shown, with all three sides labelled. How would you classify this triangle?
Explanation: A triangle with all three sides equal (here, all sides are 5 cm) is called an equilateral triangle.
The sides of a triangle are 7 cm, 9 cm and 11 cm. Find its perimeter.
Explanation: Perimeter = sum of all sides = 7 + 9 + 11 = 27 cm.
The rectangle shown below is not a square. How many lines of symmetry does it have?
Explanation: A rectangle (with unequal side lengths) has exactly two lines of symmetry: one horizontal and one vertical, both passing through the midpoints of opposite sides.
Lines l and m are parallel and are cut by a transversal. One angle is marked 70° as shown. Find the corresponding angle marked with "?" on line m.
Explanation: When two parallel lines are cut by a transversal, corresponding angles are equal. So the marked angle on line m is also 70°.
Three angles of a quadrilateral are 80°, 95° and 60°. Find the fourth angle.
Explanation: The angles of a quadrilateral add up to 360°. Fourth angle = 360° − (80° + 95° + 60°) = 360° − 235° = 125°.
The radius of a circular garden is 21 m, as shown. Find its circumference. (Take π = 22/7.)
Explanation: Circumference = 2πr = 2 × 22/7 × 21 = 2 × 66 = 132 m.
What is the angle between the hour hand and the minute hand of the clock shown, at 4:20?
Explanation: The minute hand at 20 minutes points to 20 × 6° = 120° from 12. The hour hand at 4:20 has moved 4 × 30° + 20/60 × 30° = 120° + 10° = 130°. The angle between them = 130° − 120° = 10°.
A rectangular field is 45 m long and 30 m wide. Find the cost of fencing it at ₹15 per metre.
Explanation: Perimeter = 2 × (45 + 30) = 2 × 75 = 150 m. Cost = 150 × ₹15 = ₹2250.
The perimeter of a square is 64 cm. Find its area.
Explanation: Side = Perimeter ÷ 4 = 64 ÷ 4 = 16 cm. Area = side² = 16 × 16 = 256 cm².
A square garden of side 15 m has a 1.5 m wide path running all around, just inside its edge, as shown. Find the area of the path.
Explanation: Outer area = 15 × 15 = 225 m². The inner square has side 15 − 1.5 − 1.5 = 12 m, so inner area = 144 m². Path area = 225 − 144 = 81 m².
A triangle has a base of 16 cm and a height of 9 cm. Find its area.
Explanation: Area of a triangle = 1/2 × base × height = 1/2 × 16 × 9 = 72 cm².
A regular hexagon has each side measuring 8 cm. Find its perimeter.
Explanation: A regular hexagon has 6 equal sides. Perimeter = 6 × 8 = 48 cm.
A square of side 10 cm and a rectangle of dimensions 14 cm × 6 cm are shown below. Both shapes have the same perimeter (40 cm). Which shape has the larger area?
Explanation: Square area = 10 × 10 = 100 cm². Rectangle area = 14 × 6 = 84 cm². Among all rectangles with a fixed perimeter, the square always has the maximum area.
Express the ratio 45 : 60 in its simplest form.
Explanation: The HCF of 45 and 60 is 15. Dividing both terms by 15: 45 ÷ 15 = 3 and 60 ÷ 15 = 4, giving the ratio 3 : 4.
In a class of 40 students, 25% are girls. How many students are boys?
Explanation: Number of girls = 25% of 40 = 10. Number of boys = 40 − 10 = 30.
The bar graph below shows the number of fruits sold by a shopkeeper in a day. How many more apples were sold than mangoes?
Explanation: Apples sold = 40, Mangoes sold = 20. Difference = 40 − 20 = 20.
The average of 5 numbers is 18. If one number is removed, the average of the remaining 4 numbers becomes 16. What is the removed number?
Explanation: Sum of 5 numbers = 5 × 18 = 90. Sum of remaining 4 numbers = 4 × 16 = 64. Removed number = 90 − 64 = 26.