CBSE Class 10 Maths (Basic) 2026 — Paper 430(B)

The product of the H.C.F. and L.C.M. of two numbers $50$ and $20$ is:

If $\alpha$ and $\beta$ are two zeroes of the quadratic polynomial $p(x)=x^2-11x+30$, then $\frac{1}{\alpha }+\frac{1}{\beta }$ is equal to:

The value of $k$ for which the pair of linear equations $kx-3y=5$, $4x-6y=10$ has infinitely many solutions, is:

If $x=\sqrt{3}$ is a solution of the equation $a{x}^2+\sqrt{3}x-12=0$, then

The $n^{\text{th}}$ term of an A.P. is $3n+2$. The common difference is:

The fourth vertex $D$ of a parallelogram $ABCD$ whose three vertices are $A(-4,1)$, $B(4,5)$ and $C(6,1)$ is:

The ratio in which the $x$-axis divides the line segment joining the points $A(-8,4)$ and $B(-6,-2)$ is:

If two tangents inclined at an angle of $60^{\circ }$ are drawn from an external point to a circle of radius $6$ cm, then the length of each tangent is:

If in two triangles $ABC$ and $DEF$, $\frac{AB}{EF}=\frac{BC}{DE}=\frac{CA}{DF}$; then

In $△ABC$, $P$ is a point on $AB$ and $Q$ is a point on $AC$ such that $PQ\parallel BC$. If $AP:PB=3:2$, then $PQ:BC$ is equal to:

In two concentric circles with centre $O$, the radius of the outer circle is $25$ cm. Chord $PQ$ of the outer circle is tangent to the inner circle at $R$. If $PQ=14$ cm, then the radius of the inner circle is:

If $\cos A=\frac{3}{5}$, then the value of $\tan A$ is:

If $\sin \theta =\frac{\sqrt{3}}{2}$, then the value of $2\sqrt{3}\cdot \cos \frac{\theta }{2}$ is:

The area (in ${\text{cm}}^2$) of a sector of a circle of radius $14$ cm cut off by an arc of length $22$ cm is:

The minute hand of a clock is $21$ cm long. The distance covered by the tip of the minute hand from $2:10$ pm to $2:25$ pm is:

Volumes of two spheres are in the ratio $64:27$. The ratio of their surface areas is:

A card is drawn from a packet of $50$ identical cards numbered from $1$ to $50$. The probability of drawing a number which is a perfect square, is :

The probability of getting a sum of $7$, when two dice are thrown simultaneously, is :

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

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

Find the smallest $5$-digit number exactly divisible by $24$ and $36$.

Find the zeroes of the polynomial $p(x)=15x^2-19x+6$.

If one zero of the polynomial $p(x)=(k-1)x^2-(4k+1)x+10$ is $5$, find the value of $k$.

The sum of first $n$ terms of an A.P. is given by $S_n=4n^2-n$. Find the $25^{\text{th}}$ term of this A.P.

Prove that: $\frac{\sin A}{1+\cos A}+\frac{1+\cos A}{\sin A}=2\text{cosec}A$.

If $\sin (A+2B)=\frac{\sqrt{3}}{2}$ and $\cos (A+4B)=0$, $A>B$, find $A$ and $B$.

Solve the following pair of linear equations: $31x+43y-117=0$; $43x+31y=105$.

When $1$ is subtracted from the numerator and $2$ is added to the denominator of a fraction, it becomes $\frac{1}{2}$. When $7$ is subtracted from the numerator and $2$ is subtracted from the denominator, the fraction becomes $\frac{1}{3}$. Find the fraction.

$S$ is any point on the side $QR$ of a $△PQR$ such that $\angle PSR=\angle QPR$. Prove that $\frac{QR}{RP}=\frac{RP}{RS}$.

A circle touches the side $BC$ of a $△ABC$ at $P$ and also touches the sides $AB$ and $AC$ produced at $Q$ and $R$ respectively. Prove that $AR=\frac{1}{2}(\text{perimeter of }△ABC)$.

If $\cos \theta +\sin \theta =\sqrt{2}\cos \theta$, then prove that $\cos \theta -\sin \theta =\sqrt{2}\sin \theta$.

A chord $PQ$ of a circle of diameter $28$ cm subtends an angle of $90^{\circ }$ at the centre $O$. Find the area of the sector $OPCQ$, where $C$ is a point on minor arc $PQ$. Also, find the area of segment $PCQ$.

Solve for $x$: $\frac{x-2}{x-3}+\frac{x-4}{x-5}=\frac{10}{3}$; $x\ne 3,5$.

A motor boat, whose speed in still water is $20$ km/h, takes $1$ hour more to go $48$ km upstream than to return downstream to the same point. Find the speed of the stream.

Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

The angle of elevation of the top of a tower as observed from a point in a horizontal plane through the foot of the tower is $30^{\circ }$. When the observer moves towards the tower a distance of $100$ m, he finds the angle of elevation of the top to be $60^{\circ }$. Find the height of the tower and the distance of first position from the tower.

Two pillars of equal heights stand on either side of a roadway $150$ m wide. From a point on the roadway between the pillars, the angles of elevation of the top of the pillars are $60^{\circ }$ and $30^{\circ }$ respectively. Find the height of the pillars and the position of the point from the pillars.

Find the mean and the mode for the following frequency distribution :

The best athlete of your school wants to participate in a $300$ m race in a state championship. Presently he can run that distance in $60$ seconds but is confident that with each day of practice it will take him $3$ seconds less than the previous day. So, first day he will take $60$ seconds, $2^{\text{nd}}$ day $57$ seconds, third day $54$ seconds and so on, to complete the race. He wants to do it in $30$ seconds. Based on the above, answer the following questions :

In the school garden, Arun (A), Babu (B), Chandra (C) and Daya (D) planted flower plants of Sunflower, Rose, Champa and Jasmine respectively at point $A(2,8)$, $B(7,8)$, $C(9,3)$ and $D(2,3)$ respectively. Based on the above, answer the following questions:

In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with each of diameter $8$ cm and height $7$ cm, and the other hemispherical with each of diameter $14$ cm. Based on the above, answer the following questions: