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#1 Class 12 Physics Electric Charges and Fields 2024 Mcq 1M

A thin plastic rod is bent into a circular ring of radius $R$. It is uniformly charged with linear charge density $\lambda$. What is the magnitude of the electric field at its centre?

A. $\dfrac{\lambda}{2\varepsilon_0 R}$

B. Zero

C. $\dfrac{\lambda}{4\pi\varepsilon_0 R}$

D. $\dfrac{\lambda}{4\varepsilon_0 R}$

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#2 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...

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#3 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 c...

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#4 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 ...

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#5 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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#6 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...

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#7 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° respec...

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#8 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 li...

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#9 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 ver...

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#10 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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#11 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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#12 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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#13 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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#14 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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#15 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 t...

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#16 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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#17 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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#18 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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#19 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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#20 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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