CBSE Class 10 Maths (Standard) 2026 — Paper 30/4/1

If the quadratic equation $9x^2+8kx+16=0$ has real and equal roots, then the value of $k$ is

It is given that $△ABC\sim △EDF$. Which of the following is not true ?

The $n^{\text{th}}$ term of an A.P. is $\sqrt{2}n+1$. Its common difference is :

If $PQ$ and $PR$ are tangents to the circle with centre $O$ and radius $4$ cm such that $\angle QPR=90^{\circ }$, then the length $OP$ is :

Observe the graph of polynomial $p(x)$. Number of zeroes of $p(x)$ is

In the given figure, $DE\parallel BC$. If $\frac{AD}{DB}=\frac{1}{3}$ and $AC=6$ cm, then length $AE$ is

In the given figure, a circle is centred at $(1,2)$. The diameter of the circle is

The value of $k$ for which the system of linear equations $\frac{x}{2}+\frac{y}{3}=5$ and $2x+ky=7$ is inconsistent, is

A circle is divided into $16$ identical sectors. If the radius of the circle is $7$ cm, the area of each sector is

Two different dice are rolled together. The probability that both the obtained numbers are less than $4$, is

When $\sin A=\frac{1}{3}$, the value of $\cot A$ is

$\frac{1+{\tan }^{2}A}{1+{\cot }^{2}A}$ equals to :

Three tennis balls are just packed in a cylindrical jar. If radius of each ball is $r$, volume of air inside the jar is

$PQ$ is tangent to a circle with centre $O$. If $\angle POR=65^{\circ }$, then $m\angle PTR$ is

The distance between the points $(a\cos \theta +b\sin \theta ,0)$ and $(0,a\sin \theta -b\cos \theta )$ is

An ice-cream cone of radius $r$ and height $h$ is completely filled by two spherical scoops of ice-cream. If the radius of each spherical scoop is $\frac{r}{2}$, then $h:2r$ equals :

Arc $PQ$ subtends an angle $\theta$ at the centre of the circle with radius $6.3$ cm. If arc $PQ=11$ cm, then the value of $\theta$ is

Mean and Median of a frequency distribution are $43$ and $40$ respectively. The value of mode is

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

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

Verify that roots of the quadratic equation $(p-q)x^2+(q-r)x+(r-p)=0$ are equal when $q+r=2p$.

$D$ is a point on the side $BC$ of $△ABC$ such that $\angle CAB=\angle CDA$. Show that $C{A}^2=CB\times CD$.

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

Evaluate : $\frac{3{\cos }^{2}30^{\circ }-6{\mathrm{cosec}}^{2}30^{\circ }}{{\tan }^{2}60^{\circ }}$

Prove that $2+3\sqrt{5}$ is an irrational number, given that $\sqrt{5}$ is an irrational number.

If the HCF of $210$ and $55$ is expressed as $210\times 5+55m$, then find the value of $m$.

$\alpha$ and $\beta$ are the zeroes of the polynomial $5x^2-16x-10$. Find the value of $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$.

In a class test, Veer scored $6$ more than twice as many marks as Kevin scored. If one of them had scored $4$ more marks, their total score would have been $40$. Find the marks obtained by Veer and Kevin.

Solve the linear equations $3x+y=14$ and $y=2$ graphically.

Chord $AB$ of a circle with centre $O$ and radius $21$ mm subtends an angle of $120^{\circ }$ at the centre. Find the perimeter of the shaded region. (Use $\sqrt{3}=1.73$)

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

To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted by semi-cylinder as shown in the figure. Find the area of the cloth required to make this shed, if dimensions of the cuboid are $14\text{ m}\times 25\text{ m}\times 16\text{ m}$.

The internal and external radii of a hollow hemisphere are $5\sqrt{2}$ cm and $10$ cm respectively. A cone of height $5\sqrt{7}$ cm and radius $5\sqrt{2}$ cm is surmounted on the hemisphere as shown in the figure. Find the total surface area of the object in terms of $\pi$. (Use $\sqrt{2}=1.4$)

Find the greatest number less than $10,000$ which is exactly divisible by $48$, $60$ and $65$.

A person on tour has $\text{₹}5400$ for his expenses. If he extends his tour by $5$ days, he has to cut down his daily expenses by $\text{₹}180$. Find the original duration of the tour and daily expense.

The total cost of a certain piece of cloth was ₹$2100$. During special sale time, the shopkeeper offered $2$ m extra cloth for free, thus reducing the price of cloth per metre by ₹$120$. What was the original per metre price of the cloth and its length?

A kite is flying at a height of $60$ m above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as $30^{\circ }$. From the bottom of the same building, the angle of elevation of kite is $45^{\circ }$. Find the length of the string and height of roof from the ground. (Use $\sqrt{3}=1.73$)

The median of the following data is $50$ and the sum of all frequencies is $90$. Find the values of $p$ and $q$.

Find the mean and mode of the following distribution :

Carom board is a very popular game. The board is a square of side length $65$ cm. It has circular pockets in each corner. Ansh strikes a disc, kept at position $P$ with a striker. The disc hits the boundary of the board at $R$ and goes straight to pocket at corner $C$. It is given that $PS=9$ cm, $PQ=35$ cm, $BR=x$, $\angle PRQ=\alpha$ and $\angle CRB=\theta$. Based on the above information, answer the following questions :

'Kolam' is a decorative art which is made with rice flour in South Indian States. It is drawn on grid pattern of dots. One such art work is shown below. Observe the given figure carefully. There are $4$ dots in first square, $8$ dots in second square, $12$ dots in third square and so on. Based on the above, answer the following questions :

Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below : Point A : $(-4,2)$ Rajasthan High Court Point B : $(4,-4)$ Birla Mandir Point C : $(4,3)$ Heera Bagh Point D : $(-5,-2)$ Amar Jawan Jyoti Based on the above, answer the following questions :