Bihar Board Class 10 Mathematics Question Paper 2025 PDF (Code 110 Set-B) 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-B) with Solutions
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The distance between the points \( ( 8 \sin 60^\circ, 0 ) \) and \( ( 0, 8 \cos 60^\circ ) \) is
If \( O( 0, 0 ) \) is the origin and co-ordinates of the 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 line segment \( AB \) is \( (2, 4) \) and point \( A \) is \( (5, 7) \). Find the co-ordinates of point \( B \).
The co-ordinates of the ends of a diameter of a circle are \( (10, -6) \) and \( (-6, 10) \). Then the co-ordinates of the centre 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
If \( A(0, 1), B(0, 5) \) and \( C(3, 4) \) are the vertices of any triangle, then the area of triangle \( ABC \) is
\[ \tan 10^\circ \times \tan 23^\circ \times \tan 80^\circ \times \tan 67^\circ = \]
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 the triangles?
In \( \triangle ABC \sim \triangle DEF \), \( BC = 3 \, cm \), \( EF = 4 \, cm \). If the area of \( \triangle ABC \) is \( 54 \, cm^2 \), then the area of \( \triangle DEF \) is
In any \( \triangle ABC \), \( \angle A = 90^\circ \), \( BC = 13 \, cm \), \( AB = 12 \, cm \); 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 \( \triangle ABC \) and \( \triangle DEF \), \( AB = BC = CA = 40^\circ \), \( \angle B = 80^\circ \), then the measure of \( \angle F \) is
The number of common tangents of two intersecting circles is
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 centre at \( O \) 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° is
The ratio of the circumferences of two circles is \( 5 : 7 \); then the ratio of their radii is
\[ \sec^2 A - \tan^2 A = \]
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°. Then 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° with the earth. Then the length of the string is
For what value of \( k \), roots of the quadratic equation \( kx^2 - 6x + 1 = 0 \) are real and equal?
If one of the zeros of the polynomial \( p(x) \) is 2, then which of the following is a factor of \( p(x) \)?
If \( \alpha \) and \( \beta \) be the zeros of the polynomial \( cx^2 + ax + b \), 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 \( x = 2 \)?
If \( P + 1, 2P + 1, 4P - 1 \) are in A.P., then the value of \( P \) is
The common difference of the arithmetic progression \( 1, 5, 9, \dots \) is
Which term of the A.P. \( 5, 8, 11, 14, \dots \) is 38?
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 cm², then its radius is
If \( \cos \theta + \cos^2 \theta = 1 \), then the value of \( \sin^2 \theta + \sin^4 \theta \) is
\[ \frac{1 + \tan^2 A}{1 + \cot^2 A} \]
\[ \sin(90^\circ - A) = ? \]
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
\[ \frac{\cos 59^\circ \times \tan 80^\circ}{\sin 31^\circ \times \cot 10^\circ} \]
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 zeroes 3 and -10?
If the sum of zeroes of a quadratic polynomial is 3 and their product is -2, then that 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 is
How many solutions will \( x + 2y + 3 = 0, 3x + 6y + 9 = 0 \) have?
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 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 another root is
What is the nature of the roots of the quadratic equation \( 2x^2 - 6x + 3 = 0 \)?
The length of the class intervals of the classes, \( 2-5, 5-8, 8-11, \ldots \) is
If the mean of four consecutive odd numbers is 6, then the largest number is
The mean of first 6 even natural numbers is
\(1 + \cot^2 \theta =\)
The mode of \(8, 7, 9, 3, 9, 5, 4, 5, 7, 5\) 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
If the 5th term of an A.P. is 11 and common difference is 2, then 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 the first 20 terms of the A.P. \( 1, 4, 7, 10, \dots \) is
Which of the following values is equal to 1?
\( \cos^2 A(1 + \tan^2 A) = \)
\( \tan 30^\circ = \)
\( \cos 60^\circ = \)
\[ \sin^2 90^\circ - \tan^2 45^\circ = \]
Which of the following fractions has a terminating decimal expansion?
In the form of \( \frac{p}{2^n \times 5^m} \), 0.505 can be written as
If in division algorithm \( a = bq + r \) and \( b = 4 \), \( q = 5 \), 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
\[ (\sin 30^\circ + \cos 30^\circ) - (\sin 60^\circ + \cos 60^\circ) = \]
If one zero of the quadratic polynomial \( (k-1)x^2 + kx + 1 \) is -4, then the value of k is.
Find the co-ordinates 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 \( (-5, -1), (3, -5), (5, 2) \).
The diagonal of a cube is \( 9\sqrt{3} \) cm. Find the total surface area of the cube.
If \( \tan \theta = \frac{5}{12} \), then find the value of \( \sin \theta + \cos \theta \).
If \( \sin 3A = \cos(A - 26^\circ) \), where \( 3A \) 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.
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.
If \( E \) is a point on the extended part of the side \( AD \) of a parallelogram \( ABCD \), and \( BE \) intersects \( CD \) at \( F \), then prove that \( \triangle ABE \sim \triangle CFB \).
ABC is an isosceles right triangle with \( \angle C \) as the right angle. Prove that \( AB^2 = 2AC^2 \).
If \( E \) is a point on side \( CB \) produced of an isosceles triangle \( ABC \) with \( AB = AC \) and \( EF \perp AC \), then prove that \( \triangle ABD \sim \triangle ECF \).
Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Then prove that \( \triangle ABC \sim \triangle PQR \).
\( \triangle ABC \) and \( \triangle DEF \) are similar and their areas are 9 cm² and 64 cm² respectively. If \( DE = 5.1 \) cm, then find \( AB \).
Divide \( x^3 + 1 \) by \( x + 1 \).
Using Euclid's vision 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 also.
If the radius of 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 \( \tan 7^\circ \times \tan 60^\circ \times \tan 83^\circ = \sqrt{3} \).
Using the quadratic formula, find the roots of the equation \( 2x^2 - 2\sqrt{2}x + 1 = 0 \).
Find the sum of \( 3 + 11 + 19 + \dots + 67 \).
If 5th and 9th terms of an A.P. are 43 and 79 respectively, find the A.P.
Prove that \( \frac{1 + \cos \theta}{1 - \cos \theta} = \frac{1 + \cos \theta}{\sin \theta} \).
Prove that \( \tan 9^\circ \times \tan 27^\circ = \cot 63^\circ \times \cot 81^\circ \).
If \( \cos A = \frac{4}{5} \), then find the values of \( \cot A \) and \( \csc A \).
Find two consecutive positive integers, sum of whose squares is 365.
The difference of squares of two numbers is 180. The square of 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 \( \frac{PS}{PQ} = \frac{PT}{PR} \) and \( \angle PST = \angle PQR \), then prove that \( \triangle PQR \) is an isosceles triangle.
Prove that \( 5 - \sqrt{3} \) is an irrational number.
For what value of \( k \) the points \( (1, 1), (3, k), (-1, 4) \) are collinear?
Find such a point on the y-axis which is equidistant from the points \( (6, 5) \) and \( (-4, 3) \).
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 \( \frac{\sec \theta - \tan \theta}{\sec \theta + \tan \theta} = 1 + 2 \tan^2 \theta - 2 \sec \theta \cdot \tan \theta \).
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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