GSEB Class 10 Mathematics Basic Question Paper March 2026
The latest GSEB STD 10 Mathematics Basic March 2026 board paper is available in Gujarati and English medium. Download and practice the most current paper pattern.
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Category / Board
GSEB
Level / Std
Std 10
Subject
Mathematics (Basic)
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The graphs of equations $2x + 3y = 9$ and ______ represent coincident lines.
If discriminant of quadratic equation $3x^{2} - 4x + P = 0$ is 112, then $P = \_$.
$2k+1, 13, 5k-3$ are three consecutive terms of an A.P. then $k = \underline{\hspace{2cm}}$.
The distance of the point $(-3, 5)$ from the origin is $\underline{\hspace{2cm}}$.
$\sin^2 30^\circ = \underline{\hspace{2cm}}$.
For a grouped data $m - \overline{x} = 2$ and $m + \overline{x} = 12$, then $z = \underline{\hspace{2cm}}$.
$\sqrt{7}$ is $\underline{\hspace{2cm}}$ number. (rational, irrational, whole)
Product of zeroes of $P(x) = x^2 - 5x + 6$ is $\underline{\hspace{2cm}}$. (6, 5, -6)
A balanced die is tossed once. The probability of getting 1 on it is $\underline{\hspace{2cm}}$. $\left(\frac{1}{6}, \frac{1}{4}, \frac{3}{4}\right)$
If $\sin\theta = \cos\theta$, then $\tan\theta = \underline{\hspace{2cm}}$. $\left(\sqrt{2}, 1, \frac{1}{\sqrt{2}}\right)$
______ tangents can be drawn from the point lying in the exterior of the circle. (2, 1, 0)
The modal class of the following frequency distribution is ______. | Class | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | | --- | --- | --- | --- | --- | --- | | Frequency | 25 | 5 | 16 | 8 | 35 | (60 - 70, 40 - 50, 80 - 90)
H.C.F. (6, 72) = 6.
(A) The question is for normal students. As per given fig., $y = P(x)$. The graph has 1 zero.
(B) The question is only for blind students. There are at most 2 zeroes for any cubic polynomial.
Pair of linear equations $x - y = 8$ and $3x - 3y = 16$ are consistent.
The probability of an event which is sure to occur is 1.
Find the sum of the first 50 positive integer.
1275
PQRS is a cyclic quadrilateral $\angle P : \angle R = 2 : 3$. Find $\angle R$.
108ยฐ
Aniket gets 20 marks out of 25 marks in unit test. What will be the probability of getting 20 marks.
$\frac{20}{25} = \frac{4}{5}$
Find the median of the given data. 3, 5, 1, 4, 5
4
Match the pairs: | A | B | | --- | --- | | 21) Curved surface area of a cone | (a) $\pi r^2 h$ | | 22) Volume of cylinder | (b) $\frac{\pi r^2 h}{3}$ | | | (c) $\pi r l$ |
| Column A | Column B |
|---|
Match the pairs: | A | B | | --- | --- | | 23) Circumference of a circle | (a) $\frac{\theta}{360^\circ}$ | | Diameter of a circle | | | 24) Area of minor sector | (b) $\frac{\pi r^2 \theta}{360^\circ}$ | | Area of a circle | (c) $\pi$ |
| Column A | Column B |
|---|
Find the zeroes of the quadratic polynomial $4x^{2} - 4x + 1$.
Find a quadratic polynomial whose sum and product of its zeroes are $\sqrt{2}$ and $\frac{1}{3}$ respectively.
Find the roots of the quadratic equation $100x^{2} - 20x + 1 = 0$ by factorisation.
Find the $34^{\text{th}}$ term of the AP: 7, 13, 19,...
Find the sum of the first 22 terms of the AP: 8, 3, -2,...
Find the distance between the points (3, 2) and (2, 3) using distance formula.
Find the coordinates of the midpoint of the points (4, -3) and (-3, 4).
If $\sin A = \frac{3}{4}$, calculate $\cos A$ and $\tan A$.
If $\tan (A + B) = \sqrt{3}$ and $\tan (A - B) = \frac{1}{\sqrt{3}}$; $0^{\text{b}} < A + B \leq 90^{\text{o}}$; $A > B$, find $A$ and $B$.
(A) The question is for normal students. A circus artist is climbing a $20\mathrm{m}$ long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with ground level is $30^{\circ}$ (see the fig.)
(B) The questions are only for blind students. Define: (i) Angle of Elevation (ii) Angle of Depression
Find the volume of copper rod with diameter 14 cm and length 8 cm.
The radius and the height of a cone is 7 cm and 24 cm respectively. Find the total surface area of a cone.
If for any frequency distribution $l = 3, f_1 = 8, f_0 = 7, f_2 = 2$ and $h = 2$. Then find the mode.
Solve the following pair of linear equations by any suitable method. $$ \begin{array}{l} s - t = 3 \\ 2s + 3t = 36 \end{array} \quad \begin{array}{l} t = 6, s = 9 \\ 3, 6 \\ x, 6 \\ 6 \\ 9 \\ \end{array} $$
The ratio of incomes of two persons is $9:7$ and the ratio of their expenditures is $4:3$. If each of them manages to save $2,000$ per month, find their monthly incomes. $$ \begin{array}{l} 0c = 2000 \\ y = -4000 \end{array} $$
How many multiples of 4 lie between 10 and 250?
Determine if the points (1, 5), (2, 3), (-2, -11) are collinear. $$ \begin{array}{l} \text{not} \\ 18(600) \\ 10000 \\ \phantom{0000} 0000 \end{array} $$
In what ratio does the point $(-4, 6)$ divide the line segment joining the points A$(-6, 10)$ and B$(3, -8)$?
(A) The question is for normal students. Prove the lengths of tangents drawn from an external point to a circle are equal.
(B) The questions are only for blind students. Answer the following questions : (i) How many tangent/s can be drawn at a point of the circle? (ii) How many maximum parallel tangents can a circle have? (iii) Define the secant of a circle.
(A) The question is for normal students. Two concentric circles are of radii 40 cm and 41 cm. Find the length of the chord of the larger circle with touches the smaller circle.
(B) The questions are only for blind students. Define : (i) Point of contact of a circle (ii) Tangent of a circle (iii) Length of tangent
A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data. | Number of cars | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Frequency | 7 | 14 | 13 | 12 | 20 | 11 | 15 | 8 |
One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting. (i) a queen of black colour (ii) not a face card. (iii) a diamond.
(A) The question is for normal students. State basic proportionality theorem and prove it.
(B) The questions are only for blind students. Fill in the blanks using the correct word given in brackets: (i) All ___ triangles are similar (isosceles, equilateral) (ii) All squares are ___ (similar, congruent) (iii) All right angled triangles are ___ (non similar, congruent) (iv) All circles are ___ (congruent, similar)
(A) The questions are for normal students. $\Delta ABC$ is given, $DE \parallel BC$. Answer the following questions from fig. (i) Find AD (ii) Find AB (iii) Find AC (iv) Which triangle is similar to $\Delta ADE$?
(B) The questions are only for blind students. State whether the following statements are true or false. (i) SSA (Side - Side - Angle) is one of the criteria for similarity of triangles. (ii) All rhombus are always similar. (iii) All circles are always similar. (iv) All the similar triangles are always congruent.
A train travels a distance of $480 \mathrm{~km}$ at a uniform speed. If the speed had been $8 \mathrm{~km/h}$ less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.
Find $51^{\mathrm{st}}$ term and sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using step-deviation. | Daily wages (in โน) | Number of workers | | --- | --- | | 500-520 | 12 | | 520-540 | 14 | | 540-560 | 8 | | 560-580 | 6 | | 580-600 | 10 |
The following table gives the distribution of the life time of 400 neon lamps: | Life time (in hours) | Number of lamps | | --- | --- | | 1500-2000 | 14 | | 2000-2500 | 56 | | 2500-3000 | 60 | | 3000-3500 | 86 | | 3500-4000 | 74 | | 4000-4500 | 62 | | 4500-5000 | 48 | Find the median life time of a lamp.
Two dice, one blue and one grey, are thrown at the same time. Find the probability of the numbers appearing on the top of two dice have. (i) sum of the numbers is 10. (ii) sum of the numbers is 12. (iii) sum of the numbers is less than or equal to 12. (iv) same numbers on the both dice.
A box contains 3 blue, 2 white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be. (i) white? (ii) blue? (iii) red? (iv) green?
Official Answer Key
All answers and explanations are shown below.
The graphs of equations $2x + 3y = 9$ and ______ represent coincident lines.
If discriminant of quadratic equation $3x^{2} - 4x + P = 0$ is 112, then $P = \_$.
$2k+1, 13, 5k-3$ are three consecutive terms of an A.P. then $k = \underline{\hspace{2cm}}$.
The distance of the point $(-3, 5)$ from the origin is $\underline{\hspace{2cm}}$.
$\sin^2 30^\circ = \underline{\hspace{2cm}}$.
For a grouped data $m - \overline{x} = 2$ and $m + \overline{x} = 12$, then $z = \underline{\hspace{2cm}}$.
$\sqrt{7}$ is $\underline{\hspace{2cm}}$ number. (rational, irrational, whole)
Product of zeroes of $P(x) = x^2 - 5x + 6$ is $\underline{\hspace{2cm}}$. (6, 5, -6)
A balanced die is tossed once. The probability of getting 1 on it is $\underline{\hspace{2cm}}$. $\left(\frac{1}{6}, \frac{1}{4}, \frac{3}{4}\right)$
If $\sin\theta = \cos\theta$, then $\tan\theta = \underline{\hspace{2cm}}$. $\left(\sqrt{2}, 1, \frac{1}{\sqrt{2}}\right)$
______ tangents can be drawn from the point lying in the exterior of the circle. (2, 1, 0)
The modal class of the following frequency distribution is ______. | Class | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | | --- | --- | --- | --- | --- | --- | | Frequency | 25 | 5 | 16 | 8 | 35 | (60 - 70, 40 - 50, 80 - 90)
H.C.F. (6, 72) = 6.
(A) The question is for normal students. As per given fig., $y = P(x)$. The graph has 1 zero.
(B) The question is only for blind students. There are at most 2 zeroes for any cubic polynomial.
Pair of linear equations $x - y = 8$ and $3x - 3y = 16$ are consistent.
The probability of an event which is sure to occur is 1.
Find the sum of the first 50 positive integer.
1275
PQRS is a cyclic quadrilateral $\angle P : \angle R = 2 : 3$. Find $\angle R$.
108ยฐ
Aniket gets 20 marks out of 25 marks in unit test. What will be the probability of getting 20 marks.
$\frac{20}{25} = \frac{4}{5}$
Find the median of the given data. 3, 5, 1, 4, 5
4
Match the pairs: | A | B | | --- | --- | | 21) Curved surface area of a cone | (a) $\pi r^2 h$ | | 22) Volume of cylinder | (b) $\frac{\pi r^2 h}{3}$ | | | (c) $\pi r l$ |
| Column A | Column B |
|---|
Match the pairs: | A | B | | --- | --- | | 23) Circumference of a circle | (a) $\frac{\theta}{360^\circ}$ | | Diameter of a circle | | | 24) Area of minor sector | (b) $\frac{\pi r^2 \theta}{360^\circ}$ | | Area of a circle | (c) $\pi$ |
| Column A | Column B |
|---|
Find the zeroes of the quadratic polynomial $4x^{2} - 4x + 1$.
Find a quadratic polynomial whose sum and product of its zeroes are $\sqrt{2}$ and $\frac{1}{3}$ respectively.
Find the roots of the quadratic equation $100x^{2} - 20x + 1 = 0$ by factorisation.
Find the $34^{\text{th}}$ term of the AP: 7, 13, 19,...
Find the sum of the first 22 terms of the AP: 8, 3, -2,...
Find the distance between the points (3, 2) and (2, 3) using distance formula.
Find the coordinates of the midpoint of the points (4, -3) and (-3, 4).
If $\sin A = \frac{3}{4}$, calculate $\cos A$ and $\tan A$.
If $\tan (A + B) = \sqrt{3}$ and $\tan (A - B) = \frac{1}{\sqrt{3}}$; $0^{\text{b}} < A + B \leq 90^{\text{o}}$; $A > B$, find $A$ and $B$.
(A) The question is for normal students. A circus artist is climbing a $20\mathrm{m}$ long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with ground level is $30^{\circ}$ (see the fig.)
(B) The questions are only for blind students. Define: (i) Angle of Elevation (ii) Angle of Depression
Find the volume of copper rod with diameter 14 cm and length 8 cm.
The radius and the height of a cone is 7 cm and 24 cm respectively. Find the total surface area of a cone.
If for any frequency distribution $l = 3, f_1 = 8, f_0 = 7, f_2 = 2$ and $h = 2$. Then find the mode.
Solve the following pair of linear equations by any suitable method. $$ \begin{array}{l} s - t = 3 \\ 2s + 3t = 36 \end{array} \quad \begin{array}{l} t = 6, s = 9 \\ 3, 6 \\ x, 6 \\ 6 \\ 9 \\ \end{array} $$
The ratio of incomes of two persons is $9:7$ and the ratio of their expenditures is $4:3$. If each of them manages to save $2,000$ per month, find their monthly incomes. $$ \begin{array}{l} 0c = 2000 \\ y = -4000 \end{array} $$
How many multiples of 4 lie between 10 and 250?
Determine if the points (1, 5), (2, 3), (-2, -11) are collinear. $$ \begin{array}{l} \text{not} \\ 18(600) \\ 10000 \\ \phantom{0000} 0000 \end{array} $$
In what ratio does the point $(-4, 6)$ divide the line segment joining the points A$(-6, 10)$ and B$(3, -8)$?
(A) The question is for normal students. Prove the lengths of tangents drawn from an external point to a circle are equal.
(B) The questions are only for blind students. Answer the following questions : (i) How many tangent/s can be drawn at a point of the circle? (ii) How many maximum parallel tangents can a circle have? (iii) Define the secant of a circle.
(A) The question is for normal students. Two concentric circles are of radii 40 cm and 41 cm. Find the length of the chord of the larger circle with touches the smaller circle.
(B) The questions are only for blind students. Define : (i) Point of contact of a circle (ii) Tangent of a circle (iii) Length of tangent
A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data. | Number of cars | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Frequency | 7 | 14 | 13 | 12 | 20 | 11 | 15 | 8 |
One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting. (i) a queen of black colour (ii) not a face card. (iii) a diamond.
(A) The question is for normal students. State basic proportionality theorem and prove it.
(B) The questions are only for blind students. Fill in the blanks using the correct word given in brackets: (i) All ___ triangles are similar (isosceles, equilateral) (ii) All squares are ___ (similar, congruent) (iii) All right angled triangles are ___ (non similar, congruent) (iv) All circles are ___ (congruent, similar)
(A) The questions are for normal students. $\Delta ABC$ is given, $DE \parallel BC$. Answer the following questions from fig. (i) Find AD (ii) Find AB (iii) Find AC (iv) Which triangle is similar to $\Delta ADE$?
(B) The questions are only for blind students. State whether the following statements are true or false. (i) SSA (Side - Side - Angle) is one of the criteria for similarity of triangles. (ii) All rhombus are always similar. (iii) All circles are always similar. (iv) All the similar triangles are always congruent.
A train travels a distance of $480 \mathrm{~km}$ at a uniform speed. If the speed had been $8 \mathrm{~km/h}$ less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.
Find $51^{\mathrm{st}}$ term and sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using step-deviation. | Daily wages (in โน) | Number of workers | | --- | --- | | 500-520 | 12 | | 520-540 | 14 | | 540-560 | 8 | | 560-580 | 6 | | 580-600 | 10 |
The following table gives the distribution of the life time of 400 neon lamps: | Life time (in hours) | Number of lamps | | --- | --- | | 1500-2000 | 14 | | 2000-2500 | 56 | | 2500-3000 | 60 | | 3000-3500 | 86 | | 3500-4000 | 74 | | 4000-4500 | 62 | | 4500-5000 | 48 | Find the median life time of a lamp.
Two dice, one blue and one grey, are thrown at the same time. Find the probability of the numbers appearing on the top of two dice have. (i) sum of the numbers is 10. (ii) sum of the numbers is 12. (iii) sum of the numbers is less than or equal to 12. (iv) same numbers on the both dice.
A box contains 3 blue, 2 white and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be. (i) white? (ii) blue? (iii) red? (iv) green?