Bihar Board Class 10 Mathematics Question Paper 2025 PDF (Code 110 Set-J) is available for download here. The Mathematics exam was conducted on February 18, 2025 in the Morning Shift from 9:30 AM to 12:15 PM and in the Evening Shift from 2:00 PM to 5:15 PM. The total marks for the theory paper are 100. Students reported the paper to be easy to moderate.
Bihar Board Class 10 Mathematics Question Paper 2025 (Code 110 Set-J) with Solutions
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From an external point \( P \), two tangents \( PA \) and \( PB \) are drawn on a circle. If \( PA = 8 \) cm, then \( PB = \)
If \( PA \) and \( PB \) are the tangents drawn from an external point \( P \) to a circle with center \( O \), and \( \angle APB = 80^\circ \), then \( \angle POA = \)
What is the angle between the tangent drawn at any point of a circle and the radius passing through the point of contact?
The ratio of the radii of two circles is \(3:4\); then the ratio of their areas is:
The area of the sector of a circle of radius 42 cm and central angle \(30^\circ\) is:
The ratio of the circumferences of two circles is \(5:7\); then the ratio of their radii is:
\(7\sec^2 A - 7\tan^2 A = \ ?\)
If \(x = a \cos \theta\) and \(y = b \sin \theta\), then \(b^2x^2 + a^2y^2 = \ ?\)
The angle of elevation of the top of a tower at a distance of \(10\) m from its base is \(60^\circ\). The height of the tower is:
A kite is at a height of \(30\) m from the earth and its string makes an angle of \(60^\circ\) with the earth. Then the length of the string is:
The length of the class intervals of the classes, \( 2 - 5, 5 - 8, 8 - 11, \dots \), is:
If the mean of four consecutive odd numbers is 6, then the largest number is:
The mean of the first 6 even natural numbers is:
\[ 1 + \cot^2 \theta = \]
The mode of 8, 7, 9, 9, 3, 9, 5, 4, 5, 7, 5 is:
If \( P(E) = 0.02 \), then \( P(E') \) is equal to:
Two dice are thrown at the same time. What is the probability that the difference of the numbers appearing on top is zero?
The probability of getting heads on both the coins in throwing two coins is:
A month is selected at random in a year. The probability of it being June or September is:
The probability of getting a number 4 or 5 in throwing a die is:
The ratio of the volumes of two spheres is 64:125. Then the ratio of their surface areas is:
The radii of two cylinders are in the ratio 4:5 and their heights are in the ratio 6:7. Then the ratio of their volumes is:
What is the total surface area of a hemisphere of radius \( R \)?
If the curved surface area of a cone is \( 880 \, cm^2 \) and its radius is 14 cm, then its slant height is:
If the length of the diagonal of a cube is \( \frac{2}{\sqrt{3}} \) cm, then the length of its edge is:
If the edge of a cube is doubled, then the total surface area will become how many times of the previous total surface area?
The ratio of the total surface area of a sphere and that of a hemisphere having the same radius is:
If the curved surface area of a hemisphere is \( 1232 \, cm^2 \) and its radius is 14 cm, then its slant height is:
If \( \cos^2 \theta + \sin^2 \theta = 1 \), then the value of \( \sin^2 \theta + \cos^4 \theta \) is:
\[ \frac{1 + \tan^2 A}{1 + \cot^2 A} = \]
If \( A(0,1) \), \( B(0,5) \), and \( C(3,4) \) are the vertices of triangle \( \triangle ABC \), then the area of triangle \( \triangle ABC \) is:
\[ \tan 10^\circ \cdot \tan 23^\circ \cdot \tan 80^\circ \cdot \tan 67^\circ = \]
If the ratio of areas of two similar triangles is 100:144, then the ratio of their corresponding sides is:
A line which intersects a circle in two distinct points is called:
The corresponding sides of two similar triangles are in the ratio 4:9. What will be the ratio of the areas of these triangles?
In \( \triangle ABC \sim \triangle DEF \), BC = 3 cm, EF = 4 cm. If the area of \( \triangle ABC \) is 54 cm², then the area of \( \triangle DEF \) is:
In \( \triangle ABC \) where \( \angle A = 90^\circ \), \( BC = 13 \, cm \), \( AB = 12 \, cm \), then the value of \( AC \) is:
In \( \triangle DEF \sim \triangle PQR \), it is given that \( \angle D = \angle L \), \( \angle R = \angle E \), then which of the following is correct?
In \( \triangle ABC \sim \triangle DEF \), it is given that \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{DF} \) and \( \angle A = 40^\circ \), \( \angle B = 80^\circ \), then the measure of \( \angle F \) is:
The number of common tangents of two intersecting circles is:
If the 5th term of an A.P. is 11 and the common difference is 2, what is its first term?
The sum of an A.P. with \(n\) terms is \(n^2 + 2n + 1\), then its 6th term is:
Which of the following is in an A.P.?
Which of the following is not in an A.P.?
The sum of first 20 terms of the A.P. \( 1, 4, 7, 10, \dots \) is:
Which of the following values is equal to 1?
\[ \cos^2 A(1 + \tan^2 A) = \]
\[ \tan 30^\circ = \]
\[ \cos 60^\circ = \]
\[ \sin^2 90^\circ - \tan^2 45^\circ = \]
The distance between the points \( (8 \sin 60^\circ, 0) \) and \( (0, 8 \cos 60^\circ) \) is:
If \( O(0, 0) \) be the origin and the coordinates of point \( P \) are \( (x, y) \), then the distance \( OP \) is:
The distance of the point \( (12, 14) \) from the \( y \)-axis is:
The ordinate of the point \( (-6, -8) \) is:
In which quadrant does the point \( (3, -4) \) lie?
Which of the following points lies in the second quadrant?
The co-ordinates of the mid-point of the line segment joining the points \( (4, -4) \) and \( (-4, 4) \) are:
The mid-point of the line segment \( AB \) is \( (2, 4) \) and the co-ordinates of point \( A \) are \( (5, 7) \), then the co-ordinates of point \( B \) are:
The co-ordinates of the ends of a diameter of a circle are \( (10, -6) \) and \( (-6, 10) \). Then the co-ordinates of the center of the circle are:
The co-ordinates of the vertices of a triangle are \( (4, 6) \), \( (0, 4) \), and \( (5, 5) \). Then the co-ordinates of the centroid of the triangle are:
Which of the following fractions has terminating decimal expansion?
In the form of \( \frac{p}{2^n \times 5^m} \), \( 0.505 \) can be written as:
If in division algorithm \( a = bq + r \), \( b = 4 \), \( q = 5 \), and \( r = 1 \), then what is the value of \( a \)?
The zeroes of the polynomial \( 2x^2 - 4x - 6 \) are:
The degree of the polynomial \( (x^3 + x^2 + 2x + 1)(x^2 + 2x + 1) \) is:
Which of the following is not a polynomial?
Which of the following quadratic polynomials has zeroes 2 and -2?
If \( \alpha \) and \( \beta \) are the zeroes of the polynomial \( x^2 + 7x + 10 \), then the value of \( \alpha \beta \) is:
\[ \left( \sin 30^\circ + \cos 30^\circ \right) - \left( \sin 60^\circ + \cos 60^\circ \right) = \]
If one zero of the quadratic polynomial \( (k - 1)x^2 + kx + 1 \) is -4, then the value of \( k \) is:
For what value of \( k \), the roots of the quadratic equation \( kx^2 - 6x + 1 = 0 \) are real and equal?
If one of the zeroes of the polynomial \( p(x) \) is 2, then which of the following is a factor of \( p(x) \)?
If \( \alpha \) and \( \beta \) are the zeroes of the polynomial \( x^2 + ax + b \), then the value of \( \alpha \beta \) is:
Which of the following is a quadratic equation?
Which of the following is not a quadratic equation?
The discriminant of the quadratic equation \( 2x^2 - 7x + 6 = 0 \) is:
Which of the following points lies on the graph of \( x - 2 = 0 \)?
If \( P + 1 \), \( 2P + 1 \), \( 4P - 1 \) are in A.P., then the value of \( P \) is:
The common difference of arithmetic progression \( 1, 5, 9, \dots \) is:
Which term of the A.P. \( 5, 8, 11, 14, \dots \) is 38?
\( \sin(90^\circ - A) = \)
If \( \alpha = \beta = 60^\circ \) then the value of \( \cos(\alpha - \beta) \) is:
If \( \theta = 45^\circ \) then the value of \( \sin \theta + \cos \theta \) is:
If \( A = 30^\circ \) then the value of \( \frac{2 \tan A}{1 - \tan^2 A} \) is:
If \( \tan \theta = \frac{12}{5} \), then the value of \( \sin \theta \) is:
\[ \frac{\cos 59^\circ \cdot \tan 80^\circ}{\sin 31^\circ \cdot \cot 10^\circ} = \]
If \( \tan 25^\circ \times \tan 65^\circ = \sin A \), then the value of \( A \) is:
If \( \cos \theta = x \), then \( \tan \theta = \):
\[ (1 - \cos^4 \theta) = \]
What is the form of a point lying on the \( y \)-axis?
Which of the following quadratic polynomials has zeros: 3 and -10?
If the sum of zeros of a quadratic polynomial is 3 and their product is -2, then the quadratic polynomial is:
If \( p(x) = x^4 - 2x^3 + 17x^2 - 4x + 30 \) and \( q(x) = x + 2 \), then the degree of the quotient when \( p(x) \) is divided by \( q(x) \) is:
How many solutions will the system of equations have: \[ x + 2y + 3 = 0, \quad 3x + 6y + 9 = 0 \]
If the graphs of two linear equations are parallel, then the number of solutions will be:
The pair of linear equations \( 5x - 4y + 8 = 0 \) and \( 7x + 6y - 9 = 0 \) is:
If \( \alpha \) and \( \beta \) are the roots of the quadratic equation \( 3x^2 - 5x + 2 = 0 \), then the value of \( \alpha^2 + \beta^2 \) is:
If one root of the quadratic equation \( 2x^2 - 7x - p = 0 \) is 2, then the value of \( p \) is:
If one root of the quadratic equation \( 2x^2 - x - 6 = 0 \) is \( -\frac{3}{2} \), then its other root is:
What is the nature of the roots of the quadratic equation \( 2x^2 - 6x + 3 = 0 \)?
Prove that \[ \frac{1 + \cos \theta}{1 - \cos \theta} = \frac{1 + \cos \theta}{\sin \theta} \]
Prove that \[ \tan 9^\circ \cdot \tan 27^\circ = \cot 63^\circ \cdot \cot 81^\circ \]
If \( \cos A = \frac{4}{5} \), then find the values of \( \cot A \) and \( \csc A \).
Find two consecutive positive integers, the sum of whose squares is 365.
The difference of squares of two numbers is 180. The smaller number is 8 times the larger number. Write the equation for this statement.
In a triangle \( PQR \), two points \( S \) and \( T \) are on the sides \( PQ \) and \( PR \) respectively such that \[ \frac{PS}{SQ} = \frac{PT}{TR} \quad and \quad \angle PST = \angle PQR, \]
then prove that \( \triangle PQR \) is an isosceles triangle.
If the radius of the base of a cone is \( 7 \) cm and its height is \( 24 \) cm, then find its curved surface area.
The length of the minute hand for a clock is \( 7 \) cm. Find the area swept by it in 40 minutes.
Prove that \( \tan 7^\circ \cdot \tan 60^\circ \cdot \tan 83^\circ = \sqrt{3} \).
Prove that \( 5 - \sqrt{3} \) is an irrational number.
For what value of \( k \), points \( (1, 1) \), \( (3, k) \), and \( (1, 4) \) are collinear?
Find such a point on the \( y \)-axis which is equidistant from the points \( (6, 5) \) and \( (-4, 3) \).
A ladder 7 m long makes an angle of 30° with the wall. Find the height of the point on the wall where the ladder touches the wall.
Prove that \( AB = 2AC \).
ABC is an isosceles right triangle with \( \angle C = 90^\circ \). Prove that \( AB^2 = 2AC^2 \).
Using quadratic formula, find the roots of the equation \( 2x^2 - 2\sqrt{2}x + 1 = 0 \).
Find the sum of \( 3 + 11 + 19 + \dots \) up to the nth term.
If the 5th and 9th terms of an A.P. are 43 and 79 respectively, find the A.P.
Divide \( x^3 - 1 \) by \( x + 1 \).
Using Euclid's division algorithm, find the H.C.F. of 504 and 1188.
Find the discriminant of the quadratic equation \( 2x^2 + 5x - 3 = 0 \) and find the nature of the roots.
Find the co-ordinate of the point which divides the line segment joining the points \( (-1, 7) \) and \( (4, -3) \) in the ratio \( 2 : 3 \) internally.
Find the area of the triangle whose vertices are \( (-5, -1) \), \( (3, -5) \), and \( (5, 2) \).
The diagonal of a cube is \( 9\sqrt{3} \) cm. Find the total surface area of the cube.
If \( \sin \theta = \frac{5}{12} \), find \( \cos \theta \).
If \( \sin 3A = \cos (A - 26^\circ) \) and \( 3A \) is an acute angle, then find the value of \( A \).
The sum of two numbers is 50 and one number is \( \frac{7}{3} \) times the other; then find the numbers.
In \( \triangle ABC \), \( AB = AC \) and \( \angle ABC = 90^\circ \). If \( CB = 8 \) and \( AB = 10 \), find \( AC \).
If \( \triangle ABC \) is an isosceles triangle, and \( \triangle AD \) is an altitude, prove that \( \triangle ABD \sim \triangle AEC \).
In \( \triangle ABC \) and \( \triangle DEF \), the areas are 9 cm\(^2\) and 64 cm\(^2\) respectively. If \( DE = 5 \) cm, then find \( AB \).
Draw the graphs of the pair of linear equations \( x + 3y - 6 = 0 \) and \( 2x - 3y - 12 = 0 \) and solve them.
If one angle of a triangle is equal to one angle of the other triangle and the sides included between these angles are proportional, then prove that the triangles are similar.
A two-digit number is four times the sum of its digits and twice the product of its digits. Find the number.
Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure both parts.
Prove that \( \frac{\sec \theta - \tan \theta}{\sec \theta + \tan \theta} = 1 + 2\tan^2 \theta - 2\sec^2 \theta \cdot \tan \theta \).
The radii of two circles are 19 cm and 9 cm, respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
Find the mean of the following distribution:
The slant height of a frustum of a cone is 4 cm and the perimeters (circumferences) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.
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