CBSE Class 10 Maths (Standard) 2026 — Paper 30/2/1

The LCM of $960$ and $240$ is :

The natural number $1$ is :

For any natural number $n$, $5^n$ ends with the digit :

The graph of $y=f(x)$ is given. The number of distinct zeroes of $y=f(x)$ is :

If $\alpha$ and $\beta$ are two zeroes of a polynomial $f(x)=p{x}^2-2x+3p$ and $\alpha +\beta =\alpha \beta$, then value of $p$ is :

If the pair of linear equations : $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ is consistent and dependent, then

Which of the following sequence is not an A.P. ?

In triangles $ABC$ and $PQR$, $\angle A=\angle Q$ and $\angle B=\angle R$, then $AB:AC$ is equal to :

The distance of the point $A(4a,3a)$ from the x-axis is :

If $\cos A=\frac{4}{5}$, then the value of $\tan A$ is :

If $2\sin A=1$, then the value of $\tan A+\cot A$ is :

From a point on the ground, which is $60$ m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be $45^{\circ }$. The height (in metres) of the tower is :

In the given figure, $PA$ and $PB$ are tangents to a circle centred at $O$. If $\angle OAB=15^{\circ }$, then $\angle APB$ equals :

In the given figure, PA and PB are tangents to a circle centred at O. If $\angle AOB=130^{\circ }$, then $\angle APB$ is equal to :

Area of a segment of a circle of radius $r$ and central angle $60^{\circ }$ is :

A hemispherical bowl is made of steel of thickness $1$ cm. The outer radius of the bowl is $6$ cm. The volume of steel used (in ${\text{cm}}^3$) is :

The mean and median of a frequency distribution are $43$ and $43.4$ respectively. The mode of the distribution is :

The probability for a randomly selected number out of $1,2,3,4,\dots ,25$ to be a composite number is :

In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option :

A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.

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

In the given figure, $△AHK\sim △ABC$. If $AK=10$ cm, $BC=3.5$ cm and $HK=7$ cm, find the length of $AC$.

In the given figure, $XY\parallel QR$, $\frac{PQ}{XQ}=\frac{7}{3}$ and $PR=6.3$ cm. Find the length of $YR$.

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 $n$.

If $\tan \theta +\frac{1}{\tan \theta }=2$, find the value of ${\tan }^2\theta +\frac{1}{{\tan }^2\theta }$.

Prove that : $\sqrt{\frac{1-\sin \theta }{1+\sin \theta }}=\sec \theta -\tan \theta$

In the given figure, $O$ is the centre of the circle. $PQ$ and $PR$ are tangents. Show that the quadrilateral $PQOR$ is cyclic.

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

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

Prove that : $\frac{{\sec }^3\theta }{{\sec }^2\theta -1}+\frac{{\mathrm{cosec}}^3\theta }{{\mathrm{cosec}}^2\theta -1}=\sec \theta \cdot \mathrm{cosec}\theta (\sec \theta +\mathrm{cosec}\theta )$

If $\frac{\sec \alpha }{\mathrm{cosec}\beta }=p$ and $\frac{\tan \alpha }{\mathrm{cosec}\beta }=q$, then prove that $(p^2-q^2){\sec }^2\alpha =p^2$.

Prove that the lengths of tangents drawn from an external point to a circle are equal.

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that $\angle PTQ=2\angle OPQ$.

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. $\left[\text{Use }\pi =\frac{22}{7}\right]$

Aarush bought $2$ pencils and $3$ chocolates for ₹ $11$ and Tanish bought $1$ pencil and $2$ chocolates for ₹ $7$ from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of $1$ pencil and $1$ chocolate, graphically.

A person on a tour has ₹ $4,200$ for expenses. If he extends his tour for $3$ days, he has to cut down his daily expenses by ₹ $70$. Find the original duration of the tour.

The area of a right-angled triangle is $600{\text{cm}}^2$. If the base of the triangle exceeds the altitude by $10$ cm, find all the three dimensions of the triangle.

As shown in the given figure, a girl of height $90$ cm is walking away from the base of a lamp post at a speed of $1.2$ m/s. If the lamp is $3.6$ m above the ground, find the length of her shadow after $4$ seconds.

An SBI health insurance agent found the following data for distribution of ages of $100$ policy holders. The health insurance policies are given to persons of age $15$ years and onwards, but less than $60$ years. Find the modal age and median age of the policy holders.

Case Study - 1 Your elder brother wants to buy a car and plans to take a loan from a bank for his car. He repays his total loan of ₹ $1,18,000$ by paying every month, starting with the first instalment of ₹ $1,000$ and he increases the instalment by ₹ $100$ every month. Based on the information given above, answer the following questions :

Tejas is standing at the top of a building and observes a car at an angle of depression of $30^{\circ }$ as it approaches the base of the building at a uniform speed. $6$ seconds later, the angle of depression increases to $60^{\circ }$, and at that moment, the car is $25$ m away from the building. Based on the information given above, answer the following questions :

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 :