Solved maths problems — page 6
1518 problems, newest first. Browse by chapter at NCERT solutions by class.
- हिंदी में जवाब दो: A shopkeeper buys 12 dozen eggs. 15 eggs break during transport, and he sells the rest at ₹6 per egg. How much money does he collect?
दुकानदार कुल ₹774 इकट्ठा करता है।
- A shopkeeper buys 12 dozen eggs. 15 eggs break during transport, and he sells the rest at ₹6 per egg. How much money does he collect?
The shopkeeper collects ₹774.
- हिंदी में जवाब दो: Observe the pattern: 1 = 1, 1 + 3 = 4, 1 + 3 + 5 = 9. Using this pattern, find the sum of the first 8 odd numbers and explain why the pattern
पहली 8 विषम संख्याओं का योग 64 है। यह पैटर्न इसलिए काम करता है क्योंकि पहली n विषम संख्याओं का योग n² के बराबर होता है, जिसे अंकगणितीय प्रगति के योग के सूत्र का
- Observe the pattern: 1 = 1, 1 + 3 = 4, 1 + 3 + 5 = 9. Using this pattern, find the sum of the first 8 odd numbers and explain why the pattern works.
The sum of the first 8 odd numbers is 64. The pattern works because the sum of consecutive odd numbers forms perfect squares, which can be visualized geometrica
- हिंदी में जवाब दो: The marks of 10 students are 22, 35, 35, 40, 22, 50, 35, 45, 40 and 22. Find the mode and the range of the data.
The mode of the data is 22 and 35. The range of the data is 28.
- हिंदी में जवाब दो: A number is such that when you double it and add 7, you get 33. Form an equation and find the number.
The number is 13.
- हिंदी में जवाब दो: A matchstick pattern uses 4 sticks for 1 square, 7 sticks for 2 squares joined in a row, and 10 sticks for 3 squares. Write a rule for the nu
The rule for the number of sticks needed to make n squares is 3n + 1.
- हिंदी में जवाब दो: Among the capital letters H, N, S, T and Z, which have (a) a vertical line of symmetry, and (b) rotational symmetry of order 2?
(a) Vertical line of symmetry: H, T (b) Rotational symmetry of order 2: H, N, S, Z
- हिंदी में जवाब दो: How many lines of symmetry does a regular hexagon have? Describe where they lie.
A regular hexagon has 6 lines of symmetry. Three lines pass through opposite vertices, and three lines pass through the midpoints of opposite sides.
- हिंदी में जवाब दो: Classify each of the following angles as acute, right, obtuse, straight or reflex: 45°, 90°, 135°, 180° and 200°.
The classifications are as follows: 45^° is an acute angle, 90^° is a right angle, 135^° is an obtuse angle, 180^° is a straight angle, and 200^° is a reflex an
- हिंदी में जवाब दो: Draw a line segment AB of length 7 cm and mark a point P on it such that AP = 3 cm. What is the length of PB? If Q is the midpoint of AB, fin
PB की लंबाई 4 सेमी है और PQ की लंबाई 0.5 सेमी है।
- हिंदी में जवाब दो: A square of side 8 cm has a smaller square of side 3 cm cut out from one corner. Sketch the resulting shape and find the area of the remainin
The area of the remaining figure is 55 cm².
- हिंदी में जवाब दो: A rectangular garden is 45 m long and 30 m wide. A person walks around it 4 times. What total distance does the person cover?
व्यक्ति द्वारा तय की गई कुल दूरी 600 मीटर है।
- हिंदी में जवाब दो: If 8 pens cost ₹96, what is the cost of 15 such pens?
15 पेनों की कीमत ₹180 होगी।
- हिंदी में जवाब दो: A ribbon of length 12.5 m is cut into pieces each of length 0.75 m. How many complete pieces can be cut, and what length of ribbon remains?
16 पूर्ण टुकड़े काटे जा सकते हैं और 0.5 मीटर रिबन शेष रहेगा।
- हिंदी में जवाब दो: Arrange in ascending order: 0.6, 0.06, 0.66, 0.606 and 0.066.
आरोही क्रम में संख्याएँ हैं: 0.06, 0.066, 0.6, 0.606, 0.66.
- हिंदी में जवाब दो: A recipe needs 3/4 cup of sugar for one cake. How many cups of sugar are needed to bake 5 such cakes?
3(3)/(4) cups of sugar
- हिंदी में जवाब दो: Rohan ate 2/7 of a pizza and his sister ate 3/14 of the same pizza. What fraction of the pizza is left?
पिज़्ज़ा का (1)/(2) हिस्सा बचा है।
- हिंदी में जवाब दो: The temperature at a hill station was 5 °C at noon. It fell by 3 °C every hour for the next 4 hours. What was the temperature after 4 hours?
The temperature after 4 hours was -7 °C.
- हिंदी में जवाब दो: Explain why the sum of any three consecutive whole numbers is always divisible by 3. Illustrate your reasoning with two examples.
The sum of any three consecutive whole numbers is always divisible by 3 because their sum can be expressed as 3(n+1), which is a multiple of 3. For example, 4+5
- हिंदी में जवाब दो: Two bells ring at intervals of 18 minutes and 24 minutes respectively. If they ring together at 9:00 a.m., at what time will they next ring t
The bells will next ring together at 10:12 a.m.
- Two bells ring at intervals of 18 minutes and 24 minutes respectively. If they ring together at 9:00 a.m., at what time will they next ring together?
The bells will next ring together at 10:12 a.m.
- हिंदी में जवाब दो: A milk vendor pours milk into bottles of 250 mL each. If he has 47 litres of milk, how many bottles can he completely fill, and how much milk
The milk vendor can completely fill 188 bottles, and 0 mL of milk is left over.
- हिंदी में जवाब दो: Write the greatest and the smallest 6-digit numbers that can be formed using the digits 4, 0, 7, 2, 9 and 1 exactly once. Then find the diffe
The greatest 6-digit number is 974210, the smallest 6-digit number is 102479, and their difference is 871731.
- हिंदी में जवाब दो: A stadium has 48,750 seats. During a concert 3/5 of the seats were filled in the first hour, and another 6,200 people entered in the second h
13,300 सीटें दूसरे घंटे के बाद खाली रह गईं।
- A card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability that it is (a) a king, (b) a red card, and (c) a face card.
The probability of drawing (a) a King is (1)/(13), (b) a red card is (1)/(2), and (c) a face card is (3)/(13).
- Find the roots of the equation 2x² - 5x + 3 = 0 by factorisation.
The roots of the equation are x = 1 and x = (3)/(2).
- Prove that the square root of 3 is irrational.
√3 is irrational.
- In triangles ABC and PQR, AB/RQ = BC/QP = CA/PR, with angle A = 80 degrees and angle B = 60 degrees. Find angle P.
P = 40^°
- Using a suitable identity, evaluate (102)³.
(102)³ = 1,061,208
- A shopkeeper buys a book for Rs 120 and sells it for Rs 150. Find the profit percent.
The profit percent is 25%.
- Prove that the sum of two odd numbers is always even
The sum of two odd numbers is always an even number.
- 5X+12Y=1280. If X=5 what is the value of Y?
Y = (1255)/(12)
- 1. Solve for x: 4x - 6 = 18 2. Calculate the area of a rectangle with a length of 12 cm and a width of 4 cm. 3. If cos(x) = 0.5, what is the value of x in degre
The length of side b is 18.
- If tan θ =1 and θ is acute find the value of sin θ + cosθ
The value of sin θ + cos θ is √2.
- 1. A pair of fair dice is thrown. If the two numbers appearing are different, find the probability p that: (a) the sum is 6; (b) an ace appears; (c) the sum is
The probability that all three students selected are boys is (11)/(28).
- Find the mean of 4, 8, 15, 16, 23, 42
The mean of the given numbers is 18.
- Find the circumference of a circle with radius 7 cm. Use pi = 22/7
The circumference of the circle is 44 cm.
- A train travels 240 km in 3 hours. What is its average speed in km per hour?
The average speed of the train is 80 km/hour.
- Find the value of sin 30 degrees + cos 60 degrees
The value of sin 30^(°) + cos 60^(°) is 1.
- Solve the quadratic equation x² - 5x + 6 = 0
The solutions to the quadratic equation x² - 5x + 6 = 0 are x=3 and x=2.
- Determine if the vertices A(3, 1), B(6, 4), C(8, 2), and D(5, -1) form a specific quadrilateral (like a rectangle, rhombus, or square), and find its perimeter.
The given vertices form a rectangle, and its perimeter is 10√2 units.
- In ABC, a line DE is drawn parallel to the base BC, intersecting side AB at point D and side AC at point E.If AD = x, DB = x - 2, AE = x + 2, and EC = x - 1, fi
The value of x is 4 and the total length of side AB is 6.
- If 9 workers can build a brick wall in 20 days, how many workers will be required to build the exact same wall in 12 days?
15 workers will be required to build the exact same wall in 12 days.
- A car travels 228 km in 3 hours. How far will it travel in 7 hours if it maintains the same speed?
The car will travel 532 km in 7 hours.
- A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his
The distance the boy walked towards the building is 19√3 m (approximately 32.91 m).
- In a right-angled triangle △ ABC, the right angle is at B. If AB = 24 cm and BC = 7 cm, find the values of sin A, cos A, sin C, and cos C.
sin A = (7)/(25), cos A = (24)/(25), sin C = (24)/(25), cos C = (7)/(25)
- what does a square + b square
The expression a² + b² represents the sum of the square of 'a' and the square of 'b'. It is a fundamental algebraic expression often seen in the Pythagorean the
- Express each number as a product of its prime factors: (i) 140
140 = 2² × 5 × 7
- Differentiate the following w.r.t. x. (i) cos^-1(sin x) (ii) tan^-1(sin x / (1 + cos x)) (iii) sin^-1(2^(x+1) / (1 + 4^x))
(i) (-cos x)/(|cos x|) (or -1 if cos x > 0, 1 if cos x < 0) (ii) (1)/(2) (iii) (2^(x+1) ln 2)/(1 + 4^x)
- One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be (i) a diamond (ii) n
(i) The probability of drawing a diamond is (1)/(4). (ii) The probability of not drawing an ace is (12)/(13). (iii) The probability of drawing a black card is (
- A coin is tossed three times, consider the following events. A: 'No head appears', B: 'Exactly one head appears' and C: 'Atleast two heads appear'. Do they form
Yes, the events A, B, and C form a set of mutually exclusive and exhaustive events.
- Find the equation of the hyperbola where foci are (0, +-6) and the length of the latus rectum is 36.
The equation of the hyperbola is y²198 - 54√13 - x²-162 + 54√13 = 1.
- Graph the line y = 2x - 3
The graph of the line y = 2x - 3 is a straight line passing through the points (0, -3) and (1, -1).
- Find the equation of the hyperbola where foci are (0, ± 12) and the length of the latus rectum is 36
The equation of the hyperbola is (y²)/(36) - (x²)/(108) = 1.
- A vertical tower stands on a horizontal plane. From a point on the ground 22 meters away from the base of the tower, the angle of elevation to the top of the to
The height of the tower is (22√3)/(3) meters.
- STEP-BY-STEP DERIVATION 1 Identify the given information and unknown. Distance from tower base = 18 m Angle of elevation = 30^° Height of tower = h =? 2 Choose
The height of the tower is 6√3 m.
- A vertical tower stands on a horizontal plane. From a point on the ground 18 meters away from the base of the tower, the angle of elevation to the top of the to
The height of the tower is 6√3 meters.
- A vertical tower stands on a horizontal plane. From a point on the ground 17 meters away from the base of the tower, the angle of elevation to the top of the to
The height of the tower is (17√3)/(3) meters.
- Chalkboard Explanation Video Step-by-step Derivation 1 Identify the given information and unknown Distance from base = 15 m Angle of elevation = 60^° Height of
The height of the tower is 15√3 m.