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#1 Class 10 Mathematics Probability 2026 Short 3M CBSE

Two different dice are thrown together. Find the probability that the numbers obtained have : (i) even sum, (ii) even product.

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#2 Class 10 Mathematics Coordinate Geometry 2026 Short 3M CBSE

The three vertices of a rhombus PQRS are P(2, – 3), Q(6, 5) and R(– 2, 1). Find the coordinates of the fourth vertex S and coordinates of the point where both the diagonals PR and QS intersect.

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

Find the area of the segment AYB shown in the figure, if the radius of the circle is 21 cm and $\angle$ AOB = $120^\circ$. $\left[\text{Use } \pi = \dfrac{22}{7}\right]$ (Figure : O is the centre, A and B are on the c...

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#4 Class 10 Mathematics Probability 2026 Short 3M CBSE

Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is 5, and (ii) difference of the numbers on the two dice is 3.

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

Find the area of the sector of a circle of radius 42 cm and of central angle $30^\circ$. Also, find the area of the corresponding major sector. $\left[\text{Use } \pi = \dfrac{22}{7}\right]$

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#6 Class 10 Mathematics Circles 2026 Short 3M CBSE

(a) Prove that the lengths of tangents drawn from an external point to a circle are equal. OR (b) Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that $\angle$ PTQ = 2 $\angl...

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#7 Class 10 Mathematics Introduction to Trigonometry 2026 Short 3M CBSE

(a) Prove that : $$\dfrac{\sec^3\theta}{\sec^2\theta - 1} + \dfrac{\operatorname{cosec}^3\theta}{\operatorname{cosec}^2\theta - 1} = \sec\theta \cdot \operatorname{cosec}\theta\,(\sec\theta + \operatorname{cosec}\thet...

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#8 Class 10 Mathematics Coordinate Geometry 2026 Short 3M CBSE

Find the coordinates of the points of trisection of the line segment joining the points A(– 1, 4) and B(– 3, – 2).

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#9 Class 10 Mathematics Real Numbers 2026 Short 3M CBSE

Prove that $\sqrt{5}$ is an irrational number.

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#10 Class 10 Mathematics Introduction to Trigonometry 2026 Short 2M CBSE

(a) If $\tan A = \dfrac{4}{3}$, find $\sin A$ and $\cos A$. OR (b) Express $\cos A$ and $\tan A$ in terms of $\sin A$.

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#11 Class 10 Mathematics Coordinate Geometry 2026 Short 2M CBSE

If the distance between the points (4, p) and (1, 0) is 5, what is the value of p ?

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#12 Class 10 Mathematics Polynomials 2026 Short 2M CBSE

Find the value of $p$, for which one zero of the quadratic polynomial $px^2 - 14x + 8$ is 6 times the other.

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#13 Class 10 Mathematics Introduction to Trigonometry 2026 Short 2M CBSE

(a) Evaluate : $\dfrac{5\cos^2 60^\circ + 4\sec^2 30^\circ - \tan^2 45^\circ}{\sin^2 30^\circ + \cos^2 30^\circ}$ OR (b) Prove that : $1 + \dfrac{\cot^2\alpha}{1 + \operatorname{cosec}\alpha} = \operatorname{cosec}\al...

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#14 Class 10 Mathematics Circles 2026 Short 2M CBSE

In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic. (Figure : PQ and PR are tangents touching the circle at Q and R respectively, drawn from external...

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#15 Class 10 Mathematics Introduction to Trigonometry 2026 Short 2M CBSE

(a) If $\tan\theta + \dfrac{1}{\tan\theta} = 2$, find the value of $\tan^2\theta + \dfrac{1}{\tan^2\theta}$. OR (b) Prove that : $\sqrt{\dfrac{1-\sin\theta}{1+\sin\theta}} = \sec\theta - \tan\theta$

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#16 Class 10 Mathematics Coordinate Geometry 2026 Short 2M CBSE

If the points A(4, 5), B(m, 6), C(4, 3) and D(1, n) taken in this order are the vertices of a parallelogram ABCD, then find the values of m and n.

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#17 Class 10 Mathematics Triangles 2026 Short 2M CBSE

(a) In the given figure, $\triangle$ AHK $\sim$ $\triangle$ ABC. If AK = 10 cm, BC = 3$\cdot$5 cm and HK = 7 cm, find the length of AC. OR (b) In the given figure, XY $\parallel$ QR, $\dfrac{PQ}{XQ} = \dfrac{7}{3}$ an...

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#18 Class 10 Mathematics Polynomials 2026 Short 2M CBSE

If $\alpha,\ \beta$ are the zeroes of the quadratic polynomial $px^2 + qx + r$, then find the value of $\alpha^3\beta + \beta^3\alpha$.

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#19 Class 10 Mathematics Statistics 2026 Long 1M CBSE

Assertion (A) : The mean of first 'n' natural numbers is $\dfrac{n-1}{2}$. Reason (R) : The sum of first 'n' natural numbers is $\dfrac{n(n+1)}{2}$.

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#20 Class 10 Mathematics Surface Areas and Volumes 2026 Long 1M CBSE

Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 cm$^2$. Reason (R) : The surface area of a cuboid of dimensions $l \times b \times h$ is $(lb + bh + hl)$.

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