GSEB Class 10 Mathematics Standard Question Paper March 2026

Given that HCF (306, 657) is $2\mathrm{m} - 1$, $m =$

If two zeros of cubic polynomial $ax^3 + bx^2 + cx + d$ are 0 then the third zero will be

The lines are ______ for a pair of linear equation $3x + 2y - 4 = 0$ and $2x + 4y - 12 = 0$.

The value of $k$ for quadratic equation $kx(x - 2) + 6 = 0$ is ______ if it has two equal roots.

The missing term in following A.P. is ______. 2, □, 26.

For two triangles, $\Delta ABC$ and $\Delta PQR$, if $\frac{AB}{QR} = \frac{BC}{PQ} = \frac{AC}{PR}$ then $\Delta ABC \sim \_______$.

If $AB$ is a diameter of a circle whose centre is $(2, -3)$ and $B$ is $(1, 4)$ then coordinates of point $A$ are ______.

$(1 + \tan \theta + \sec \theta)(1 + \cot \theta - \cosec \theta) = \_______.$

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that PQ = 12 cm, length OQ = ____ cm.

A tangent to a circle intersects it in ____ point(s).

If the radius of a sector is doubled and angle of the sector is kept unchanged. Then area of new sector will be ____ times the area of original sector.

If a lemon is cut into four equal parts then the total surface area of one part will be ____.

For a frequency distribution, if $n = 51$, $l = 145$, $cf = 11$, $f = 18$ and $h = 5$ then median = ____.

The probability of an event can be $1\frac{3}{4}$.

A linear equation in two variable has infinite solutions.

If quadratic equation $6x^{2} + bx - 6 = 0$ has opposite roots then $b = 6$.

The distance of a point having coordinates $(\cos \theta, \sin \theta)$ from origin is 1, where $0^{\circ} < \theta < 90^{\circ}$.

If the radius of a cylinder is increased by 10% and its height is increased by 20% then what will be the increase in its volume in terms of percentage.

What is the combined mean of prime and composite numbers amongst first $n$ natural numbers.

Find the LCM of 12, 15 and 21.

Find the discriminant of the quadratic equation $3x^{2} - 2x + \frac{1}{3} = 0$.

Match the following: Table - 1 : | | A | B | | --- | --- | --- | | 21) | $\alpha^{2} + \beta^{2}$ | (a) $\left(-\frac{b^{2}}{c^{2}}\right)$ | | 22) | $\left(\frac{1}{\alpha} + \frac{1}{\beta}\right)^{2}$ | (b) $\frac{b^{2} - 2ac}{a^{2}}$ | | | | (c) $\frac{b^{2}}{c^{2}}$ |

Match the following: Table - 2 : | | A | B | | --- | --- | --- | | 23) | $\tan A$ | (a) $\frac{1}{\sqrt{1 - \sin^{2} A}}$ | | 24) | $\sec A$ | (b) $\sqrt{1 - \sin^{2} A}$ | | | | (c) $\frac{\sin A}{\sqrt{1 - \sin^{2} A}}$ |

There is a circular path around a sports field. Tashi takes 18 minutes to cover one round of the field, while Heer takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Solve the following pair of linear equation. $$ \begin{array}{l} \sqrt{2}x + \sqrt{3}y = 0 \\ \sqrt{3}x - \sqrt{8}y = 0 \\ \end{array} $$

Find the roots of the quadratic equation $3x^{2} - 2\sqrt{6}x + 2 = 0$.

Represent the following situation in the form of quadratic equation: ‘A train travels a distance of $480\mathrm{km}$ at a uniform speed. If the speed had been $8\mathrm{km/hr}$ less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.’

How many three digit numbers are divisible by 7?

If $\cot \theta = \frac{7}{8}$, evaluate $\frac{(1 + \sin \theta)(1 - \sin \theta)}{(1 + \cos \theta)(1 - \cos \theta)}$.

Prove the following identity, where the angles involved are acute angles for which the expressions are defined $\frac{\sin\theta - 2\sin^3\theta}{2\cos^3\theta - \cos\theta} = \tan \theta$.

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80^{\circ}$, then find $\angle POA$.

Define the following: i) Tangent to a circle ii) Secant of a circle

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $1\,\mathrm{cm}$ and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

The table below shows the daily expenditure on food of 25 households in a locality. | Daily expenditure (in ₹) | 100-150 | 150-200 | 200-250 | 250-300 | 300-350 | | --- | --- | --- | --- | --- | --- | | Number of households | 4 | 5 | 12 | 2 | 2 | Find the mean daily expenditure on food by a suitable method.

The following table shows the age of the patients admitted in a hospital during a year. | Age (in years) | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 | | --- | --- | --- | --- | --- | --- | --- | | Number of patients | 6 | 11 | 21 | 23 | 14 | 5 | Find the mode of the data given above.

A piggy bank contains hundred 50p coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin i) Will be a 50p coin? ii) Will not be a ₹5 coin?

Suppose we throw a die once. i) What is the probability of getting a number greater than 4? ii) What is the probability of getting a number less than or equal to 4?

Find the zeros of the quadratic polynomial $x^2 - 4x - 437$ and verify the relationship between the zeros and the coefficients.

Find a quadratic polynomial if sum and product of its zeros are $-\frac{1}{4}$ and $\frac{1}{4}$ respectively.

In an A.P., given $a_n = 4$, $d = 2$, $S_n = -14$, find $n$ and $a$.

For what value of $n$, are the $n^{\text{th}}$ terms of two A.P.s: 63, 65, 67, ... and 3, 10, 17, ... equal?

Find a relation between $x$ and $y$ such that the points $(x, y)$ is equidistant from the point $(3, 6)$ and $(-3, 4)$.

PQ is a chord of length $8\,\mathrm{cm}$ of a circle of radius $5\,\mathrm{cm}$. The tangents at P and Q intersect at a point T (see fig.). Find the length TP.

How many tangents to a given circle can be drawn from a point lying. i) Outside the circle ii) In the circle iii) On the circle

Prove that - The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Answer the following questions: i) How many tangents can a circle have? ii) How many parallel tangents at the most can a circle have? iii) What is common point of a tangent to a circle and the circle called?

To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle $80^{\circ}$ to a distance of $16.5\mathrm{km}$. Find the area of the sea over which the ships are warned. (Use $\pi = 3.14$)

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Jay wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise write all possible outcomes. Calculate the probability that Jay will win the game. Also find the probability of getting at least 2 heads.

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Find the present ages of Aftab and his daughter.

If AD and PM are medians of $\Delta ABC$ and $\Delta PQR$, respectively where $$\Delta ABC - \Delta PQR$$, prove that $$\frac{AB}{PQ} = \frac{AD}{PM}$$.

i) State basic proportionality theorem. ii) All ______ triangles are similar (isosceles, equilateral) iii) State SAS condition for similarity of two triangles. iv) Define similar triangles.

State and prove Thales theorem (Basic proportionality theorem).

i) Two polygons of the same number of sides are similar if their corresponding angles are _____. (equal, proportional) ii) All squares are _____. (similar, congruent) iii) State AAA condition for similarity of two triangles. iv) State whether given statement is True or False. "All congruent figures are similar but all similar figures need not be congruent."

The angles of depression of the top and the bottom of an 8 m tall building from the top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the multi-storeyed building and the distance between the two buildings.

Explain the following terms: i) Angle of elevation. ii) Angle of depression. iii) Line of sight. iv) Horizontal level.

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm. [Take π = 3.14]

The decorative block shown in given figure is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge $5\mathrm{cm}$, and the hemisphere fixed on the top has a diameter of $4.2\mathrm{cm}$. Find the total surface area of the block. $\left(\text{Take } \pi = \frac{22}{7}\right)$

Write the formula for the following: i) Volume of cuboid. ii) Curved surface area of hemisphere. iii) Volume of cone. iv) Total surface area of cylinder.

The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table: | Length (in mm) | Number of leaves | | --- | --- | | 118-126 | 3 | | 127-135 | 5 | | 136-144 | 9 | | 145-153 | 12 | | 154-162 | 5 | | 163-171 | 4 | | 172-180 | 2 | Find the median length of the leaves.