Mathematics Questions

Browse 1,240 Mathematics questions with expert-verified, step-by-step solutions — NCERT, exemplar and previous-year questions, organised by chapter.

Q1221 CBSE Board 2026

A group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are dropped. Rest of the cards are shuffled and one card is drawn at random. Assuming that the dropped cards were a queen of hearts, a ten of spades and an ace of clubs, answer the following questions :

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Q1222 CBSE Board 2026

'Kolam' is a decorative art which is made with rice flour in South Indian States. It is drawn on grid pattern of dots. One such art work is shown below. Observe the given figure carefully. There are $4$ dots in first square, $8$ dots in second square, $12$ dots in third square and so on. Based on the above, answer the following questions :

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Q1223 CBSE Board 2026

A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical bulb of diameter $7$ cm is latched with a very thin rod. (Ignore the rod while making calculations.) Dimensions of the cuboid are $24$ cm $\times$ $12$ cm $\times$ $17$ cm.
Cuboid of dimensions 24 cm x 12 cm x 17 cm with the spherical bulb at the centre of the front face.

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Q1224 CBSE Board 2026

A friend of yours wants to buy an electric car, for which he plans to take a loan from a bank and repay the total loan and interest, $₹ 5, 90, 000$ , by paying every month. He starts with a first instalment of $₹ 5, 000$ and increases the instalment by $₹ 500$ every month.

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Q1225 CBSE Board 2026

The Air Quality Index (AQI) is a scale from $0$ to $500$ that indicates air quality, with higher numbers signifying more pollution and greater health concerns. The Central Pollution Control Board's air quality standards map AQI ranges to categories (Good, Satisfactory, Moderate, Poor, Very Poor, Severe), as shown in the figure. Mansi collected the daily data of AQI of her city for a month and presented it as given below.

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Q1226 CBSE Board 2026

As a part of school project, Mishika and Sahaj created a bird-bath from the cylindrical log of wood by scooping out the hemispherical depression from one end of the cylinder as shown in the figure given below. Cylinder has a length $2$ m out of which $0.6$ m is in earth and the diameter is $1.4$ m. On the basis of the above information, answer the following questions :

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Q1227 CBSE Board 2026

Climate change and global warming are influencing storm behaviour, particularly in terms of intensity and rainfall. Strong winds and storms often cause uprooting and/or breaking of trees, which damage the vehicles standing underneath the trees. On a particular day, during a high intensity storm, a tree broke such that its broken part formed an angle of $3 0^{\circ}$ with the ground. The distance between the base of the tree to the point where the top touches the ground is found to be $10$ m. Based on the above information, answer the following questions :

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Q1228 CBSE Board 2026

Jigyasa is fly fishing in a stream sitting at the height of $3.1$ m above the surface of water. The fishing rod is $22$ m long and the fly at the end of the string resting on the surface of water is $5$ m away from the base of the platform on which Jigyasa is sitting. The fishing rod makes an angle of $4 5^{\circ}$ with the horizontal and the string which is fully taut makes an angle of $6 0^{\circ}$ with the horizontal as shown in the given figure. Based on the above information, answer the following questions : (Use $3 = 1.7$ )

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Q1229 CBSE Board 2026

A brooch is crafted from silver wire in the shape of a circle with a diameter of $35$ cm. The wire is also used to create $5$ diameters, dividing the circle into $10$ equal sectors as shown in figure. Based on the above information, answer the following questions :

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Q1230 CBSE Board 2026

On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik's cube and a strawberry ice-cream for you. Based on the information given above, answer the following questions :

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Q1231 CBSE Board 2026

In a circular museum hall of radius $14$ m, some statues are displayed. Statues are kept inside the inner concentric circle of radius $7$ m. One such statue lying in sector $O A B$ is fenced along line segments $O A$ , $A P$ , $P B$ and $B O$ , where $P$ is a point on the outer circle. Based on the above information, answer the following questions:
Concentric circles with the fenced region OAPB.

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Q1232 CBSE Board 2026

In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with each of diameter $8$ cm and height $7$ cm, and the other hemispherical with each of diameter $14$ cm. Based on the above, answer the following questions:

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Q1233 CBSE Board 2026

A model of Leafy Ball Fountain is made to be kept on the tabletop. Water gently cascades down the ball into a decorative cylindrical pool where it is recycled. The diameter of the spherical ball is $21$ cm. For the cylindrical pool, the outer diameter is $50$ cm and the inner diameter is $40$ cm. The height of the solid base is $14$ cm and the height of the water filled is $7$ cm. Observe the figure and answer the following questions:
Vertical section: sphere on a cylinder, water height 7 cm and solid base 14 cm

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Q1234 CBSE Board 2026

Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below : Point A : $(- 4, 2)$ Rajasthan High Court Point B : $(4, - 4)$ Birla Mandir Point C : $(4, 3)$ Heera Bagh Point D : $(- 5, - 2)$ Amar Jawan Jyoti Based on the above, answer the following questions :

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Q1235 CBSE Board 2026

Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, $A B$ is an elevated water tank and $C D$ is a nearby multistorey building. The building is $54$ metres away from the water tank. From a window ( $W$ ) of the building, the angle of elevation of top of the tank is $4 5^{\circ}$ and angle of depression of its foot is $3 0^{\circ}$ .

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Q1236 CBSE Board 2026

Raghav has a collection of balls of different colours. He has a total of $35$ balls in his basket, out of which seven are black and eight are yellow. Out of the remaining balls, some are white and the rest are red.

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Q1237 CBSE Board 2026

'Gilli Danda' is a very popular traditional game of India which is played with two wooden sticks — the larger one is called 'Danda' and the smaller one 'Gilli'. 'Danda' — It is cylindrical in shape with diameter $4$ cm and length $42$ cm. Gilli — It is cylindrical in the middle with identical conical ends of the same radius $1.5$ cm and length $2.8$ cm. The length of the cylindrical part is $7$ cm. Based on the above, answer the following questions:

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Q1238 CBSE Board 2026

A flagstaff, $7.32$ m long is fitted at the top of $10$ m tall building. The flagstaff is supported by the ropes which are tied to the point $P$ on the ground which is $x$ m away from the base of the building. It is given that $l_{1}$ is the length of rope from point $P$ to the base of the flagstaff and $l_{2}$ is the length of rope from point $P$ to the top of flagstaff. Rope $l_{1}$ makes an angle of $3 0^{\circ}$ with the horizontal and $θ$ be the angle which rope $l_{2}$ makes with the horizontal as shown in the figure. Based on the above information, answer the following questions : (Use $2 = 1.4$ and $3 = 1.732$ )

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Q1239 CBSE Board 2026

For a cricket tournament involving $8$ countries, a special trophy, as shown below, is designed. The height and diameter of the cylindrical part are $14$ cm and $6$ cm respectively and the diameter of the spherical ball on the top is $7$ cm. Based on the above information, answer the following questions :

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Q1240 CBSE Board 2026

A farmer has a semicircular field as shown in the figure given below : In segment $A C P A$ , he grows rice. In the triangular region $A P B$ , he grows vegetables. He allows his cows to graze in the segment $B D P B$ . The diameter of the semicircular field with centre $O$ is $120$ m, $∠ P A O = 3 0^{\circ}$ and $∠ P O B = 6 0^{\circ}$ . Based on the above information, answer the following questions :

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