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1,589 Questions
CBSE
#1 Class Class 10 Mathematics Circles 2026 Long 4M
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 OAB is fenced along line segments OA, AP, PB and BO where P is a point on the outer circle.
(i) Find m∠AOP.
(ii) Prove that ΔOAP ≅ ΔOBP.
(iii)(a) Find the length of fencing required to protect the statue. (Take √3 = 1.73)
OR
(iii)(b) Find the area of quadrilateral OAPB. (Take √3 = 1.73)
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CBSE
#2 Class Class 10 Mathematics Surface Areas and Volumes 2026 Long 4M
There are many varieties of mushrooms available in the world. One such mushroom 'Amanita muscaria' has an upper part like a red cap (hemispherical) and a lower part like a white stem (cylindrical). The hemispherical cap's radius = 3 cm and the cylindrical stem is 2 cm high with diameter 1.4 cm. Considering the mushroom a solid object, answer the following questions:
(i) What is the total height of a mushroom?
(ii) Find the volume of the stem.
(iii)(a) Determine the volume of 7 such mushrooms.
OR
(iii)(b) Find the total surface area of 7 such mushrooms.
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CBSE
#3 Class Class 10 Mathematics Pair of Linear Equations in Two Variables 2026 Long 4M
Seema daily goes to a park to exercise on machines available there. When Seema spent 15 minutes on exercise bicycle and 30 minutes on double cross walker, she received a message of burning 435 calories on her fitness watch. When she spent 30 minutes on exercise bicycle and 40 minutes on double cross walker, she received a message of burning 690 calories. To find the number of calories burned per minute on each machine, answer the following:
(i) Represent the above situation in terms of a pair of linear equations in two variables.
(ii) Show that the equations have a unique solution.
(iii)(a) Solve both equations to find the values of the variables using the elimination method.
OR
(iii)(b) Solve both equations to find the values of the variables using the substitution method.
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CBSE
#4 Class Class 10 Mathematics Statistics 2026 Long 5M
Find mean and mode of the following data:
Class: 10-20, 20-30, 30-40, 40-50, 50-60, 60-70, 70-80
Frequency: 5, 4, 10, 13, 12, 10, 6
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CBSE
#5 Class Class 10 Mathematics Quadratic Equations 2026 Long 5M
(a) ABCD is a rectangle of dimensions 80 cm × 60 cm. Another rectangle PQRS is drawn inside ABCD leaving space of equal width x cm along the edges of ABCD. If area PQRS is half of the area ABCD, then find the value of x.
OR
(b) A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/h more, it would have taken 30 minutes less for the same journey. Find the original speed of the train.
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CBSE
#6 Class Class 10 Mathematics Some Applications of Trigonometry 2026 Long 5M
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles and the distance of the point from the poles.
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CBSE
#7 Class Class 10 Mathematics Triangles 2026 Long 5M
(a) In the given figure, ΔABC is right angled triangle with ∠A = 90°. AD is perpendicular to BC.
Prove that: (i) ΔDBA ~ ΔDAC (ii) DA² = DB × DC (iii) Find the area of ΔABC when DB = 9 cm and DC = 16 cm.
OR
(b) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
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CBSE
#8 Class Class 10 Mathematics Polynomials 2026 Short 3M
(a) If α, β are zeroes of the polynomial $p(x)=5x^2-7x-3$, then form a quadratic polynomial whose zeroes are $\frac{2}{\alpha}$ and $\frac{2}{\beta}$.
OR
(b) Find the zeroes of the polynomial $p(x)=3x^2+7x-20$ and verify the relationship between its zeroes and the coefficients.
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CBSE
#9 Class Class 10 Mathematics Areas Related to Circles 2026 Short 3M
Chord AB of a circle subtends an angle of 120° at the centre O of the circle. Find the length of arc AB, if radius of the circle is 21 cm.
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CBSE
#10 Class Class 10 Mathematics Introduction to Trigonometry 2026 Short 3M
Prove that $\sqrt{\frac{1-\sin A}{1+\sin A}}=\frac{1}{\sec A+\tan A}$
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CBSE
#11 Class Class 10 Mathematics Arithmetic Progressions 2026 Short 3M
(a) In an A.P., it is given that a = 2, d = 8 and Sn = 90. Find the value of n.
OR
(b) How many 4-digit numbers are divisible by 7?
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CBSE
#12 Class Class 10 Mathematics Coordinate Geometry 2026 Short 3M
Points P(6, 0), Q(2, 8) and R(–2, 4) are vertices of ΔPQR. It is given that MN || QR such that PM/MQ = 1/3. Using distance formula and ratio formula, show that MN/QR = 1/4.
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CBSE
#13 Class Class 10 Mathematics Triangles 2026 Short 2M
In the given figure, AB || DC. If OB = 3OD and CD = 1.8 cm, then find the length AB.
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CBSE
#14 Class Class 10 Mathematics Probability 2026 Short 2M
(a) Find the probability that a number selected at random from the numbers 30, 31, 32, 33, ....., 60 is (i) a prime number (ii) a multiple of 6.
OR
(b) Slips of letters of the word 'BACKGROUND' are put in a bowl and thoroughly mixed. One slip is picked up at random. Find the probability that picked up slip's letter is (i) a vowel (ii) present in the word 'BALL'.
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CBSE
#15 Class Class 10 Mathematics Coordinate Geometry 2026 Short 2M
If A(a, 0), B(1, 1) and C(0, b) form a triangle, right angled at B when joined, then establish a relation between a and b.
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CBSE
#16 Class Class 10 Mathematics Real Numbers 2026 Short 2M
Find the H.C.F. and L.C.M. of 1530 and 2040.
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CBSE
#17 Class Class 10 Mathematics Introduction to Trigonometry 2026 Short 2M
(a) If sec A = √2 and tan B = √3, then find the value of 2 sin A cos B.
OR
(b) Evaluate: (4cos³60° + cosec 30°) / tan²30°
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CBSE
#18 Class Class 10 Mathematics Statistics 2026 Long 1M
Assertion (A): Median of a data is the value of N/2, where N represents sum of all frequencies.
Reason (R): Median divides the whole distribution in two equal parts.
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CBSE
#19 Class Class 10 Mathematics Introduction to Trigonometry 2026 Long 1M
Assertion (A): For an acute angle θ, cos θ is always less than 1.
Reason (R): In a right-angled triangle, hypotenuse is the longest side and cos θ = Base/Hypotenuse.
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CBSE
#20 Class Class 10 Mathematics Probability 2026 Mcq 1M
A bag contains some red and some white balls. If the probability of getting a red ball is 2/7, then the probability of getting a white ball is:
A. 1/14
B. 5/7
C. 1/7
D. 2/7
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