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#1 Class Class 10 Mathematics Introduction to Trigonometry 2026 Mcq 1M

If value of $\cot\theta$ is $\sqrt5$, then $\sin\theta$ equals:

A. 1/√6

B. √6

C. √5/6

D. 1/2

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#2 Class Class 10 Mathematics Triangles 2026 Mcq 1M

Which of the following statements is not always true?

A. Two circles are similar

B. Two isosceles right triangles are similar

C. Two rectangles are similar

D. Two equilateral triangles are similar

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#3 Class Class 10 Mathematics Circles 2026 Mcq 1M

PT is tangent to the circle with centre O and radius 5 cm. OP intersects the circle at Q. If PQ = x, then PT² equals:

A. x² + 5x

B. x² + 10x + 50

C. x² + 10x

D. x² - 25

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#4 Class Class 10 Mathematics Surface Areas and Volumes 2026 Mcq 1M

Two wooden solid hemispheres of same radii r are joined at a point (flat faces outward, forming an hourglass shape). The total surface area of the object is:

A. 4πr²

B. 6πr²

C. 3πr²

D. 5πr²

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#5 Class Class 10 Mathematics Quadratic Equations 2026 Mcq 1M

The value of k for which the equation $2kx^2-6x+3=0$ has real and equal roots, is:

A. 3/2

B. 1/2

C. -3/2

D. 2

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#6 Class Class 10 Mathematics Real Numbers 2026 Mcq 1M

If HCF (850, 325) is 25, then LCM (850, 325) is:

A. 442

B. 11050

C. 8450

D. 2210

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#7 Class Class 10 Mathematics Surface Areas and Volumes 2026 Long 4M

In a coffee shop, coffee is served in two types of cups. One type is cylindrical with each of diameter 8 cm and height 7 cm, while the other type is hemispherical with each of diameter 14 cm.
(i) What is the outer curved surface area of the cylindrical cup?
(ii) What is the inner surface area of the hemispherical cup?
(iii)(a) Find the difference of the capacities of the two cups.
OR
(iii)(b) Find the total volume of coffee in two cylindrical and one hemispherical cup.

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#8 Class Class 10 Mathematics Coordinate Geometry 2026 Long 4M

In the school garden, Arun (A), Babu (B), Chandra (C) and Daya (D) planted flower plants of Sunflower, Rose, Champa and Jasmine respectively at points A(2, 8), B(7, 8), C(9, 3) and D(2, 3) respectively.
(i) Find the distances AB and AD.
(ii) Find BC - CD.
(iii)(a) If Varun wants to plant his flower plant at a point M such that DM : MC = 3 : 2, find the coordinates of M.
OR
(iii)(b) If N divides the line segment AC in the ratio 2 : 3, find the coordinates of N.

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#9 Class Class 10 Mathematics Arithmetic Progressions 2026 Long 4M

The best athlete of your school wants to participate in a 300 m race in a state championship. Presently he can run that distance in 60 seconds but is confident that with each day of practice it will take him 3 seconds less than the previous day. So, first day he will take 60 seconds, 2nd day 57 seconds, third day 54 seconds and so on, to complete the race. He wants to do it in 30 seconds.
(i) Write the first five terms of time and show that it forms an A.P.
(ii) How much time will he take on the 6th day to complete the race?
(iii)(a) On which day will he be able to achieve his target of 30 seconds?
OR
(iii)(b) If he devotes more time in practice and that may take him 3.2 seconds less than the previous day in completing the race, then on which day will he be able to complete the race in 28 seconds?

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#10 Class Class 10 Mathematics Statistics 2026 Long 5M

Find the mean and the mode for the following frequency distribution:
Class: 30-35, 35-40, 40-45, 45-50, 50-55
Frequency: 3, 9, 7, 3, 2

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#11 Class Class 10 Mathematics Some Applications of Trigonometry 2026 Long 5M

(a) The angle of elevation of the top of a tower as observed from a point in a horizontal plane through the foot of the tower is 30°. When the observer moves towards the tower a distance of 100 m, he finds the angle of elevation of the top to be 60°. Find the height of the tower and the distance of the first position from the tower.
OR
(b) Two pillars of equal heights stand on either side of a roadway 150 m wide. From a point on the roadway between the pillars, the angles of elevation of the top of the pillars are 60° and 30° respectively. Find the height of the pillars and the position of the point from the pillars.

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#12 Class Class 10 Mathematics Triangles 2026 Long 5M

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio. (Basic Proportionality Theorem)

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#13 Class Class 10 Mathematics Triangles 2026 Long 5M

(a) Solve for x: (x-2)/(x-3) + (x-4)/(x-5) = 10/3 ; x ≠ 3, 5
OR
(b) A motor boat, whose speed in still water is 20 km/h, takes 1 hour more to go 48 km upstream than to return downstream to the same point. Find the speed of the stream.

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#14 Class Class 10 Mathematics Areas Related to Circles 2026 Short 3M

A chord PQ of a circle of diameter 28 cm subtends an angle of 90° at the centre O, where C is a point on minor arc PQ. Find the area of sector OPCQ and the area of segment PCQ.

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#15 Class Class 10 Mathematics Introduction to Trigonometry 2026 Short 3M

If cos θ + sin θ = √2 cos θ, then prove that cos θ - sin θ = √2 sin θ

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#16 Class Class 10 Mathematics Circles 2026 Short 3M

(a) A circle touches the side BC of a ΔABC at P and also touches the sides AB and AC produced at Q and R respectively. Prove that AR = (1/2)(perimeter of ΔABC).
OR
(b) Prove that the tangents drawn to a circle at the end points of a diameter are parallel to each other.

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#17 Class Class 10 Mathematics Triangles 2026 Short 3M

S is a point on the side QR of a ΔPQR such that ∠PSR = ∠QPR. Prove that QR/RP = RP/RS.

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#18 Class Class 10 Mathematics Pair of Linear Equations in Two Variables 2026 Short 3M

(a) Solve the following pair of linear equations: 31x + 43y - 117 = 0; 43x + 31y = 105
OR
(b) When 1 is subtracted from the numerator and 2 is added to the denominator of a fraction, it becomes 1/2. When 7 is subtracted from the numerator and 2 is subtracted from the denominator, the fraction becomes 1/3. Find the fraction.

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#19 Class Class 10 Mathematics Real Numbers 2026 Short 3M

Prove that √2 is an irrational number.

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#20 Class Class 10 Mathematics Probability 2026 Short 2M

All the red face cards are removed from a pack of 52 playing cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a: (i) red card (ii) a king or queen.

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