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#1 Class 10 Mensuration Areas Related to Circles 2025 Short 6M UP BOARD
In the figure, two concentric circles of radii 14 cm and 7 cm have centre O, with arcs AB and CD, and $\angle AOB = 30^\circ$. Find the area of the shaded portion (the region between the two arcs).
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#2 Class 10 Mensuration Surface Areas and Volumes 2025 Short 6M UP BOARD
A maximum sphere is made by peeling a wooden cube of side 14 cm. Find the volume of the peeled wood.
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#3 Class 10 Algebra Arithmetic Progressions 2025 Short 4M UP BOARD
Find the A.P. whose third term is 16 and whose seventh term is 12 more than the fifth term.
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#4 Class 10 Algebra Quadratic Equations 2025 Short 4M UP BOARD
Solve the following equation: $9x^2 - 3x - 2 = 0$
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#5 Class 10 Algebra Pair of Linear Equations in Two Variables 2025 Short 4M UP BOARD
By adding 1 to the numerator and denominator of a fraction, it becomes $\dfrac{4}{5}$. If 5 is subtracted from the numerator and denominator, then the value of the fraction becomes $\dfrac{1}{2}$. Find the fraction.
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#6 Class 10 Geometry Triangles 2025 Long 4M UP BOARD
The sides of a triangle are respectively 3 cm, 6 cm and 8 cm, and the sides of another triangle are 4.5 cm, 9 cm and 12 cm respectively. Prove that these triangles will be similar.
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#7 Class 10 Statistics and Probability Statistics 2025 Short 4M UP BOARD
Find the mode from the following table: Class-interval 0–10 10–20 20–30 30–40 40–50 Frequency 6 11 18 21 15
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#8 Class 10 Number Systems Real Numbers 2025 Short 2M UP BOARD
Find the LCM of the numbers 120 and 315.
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#9 Class 10 Number Systems Real Numbers 2025 Long 2M UP BOARD
Prove that $3\sqrt{2}$ is an irrational number.
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#10 Class 10 Statistics and Probability Statistics 2025 Short 2M UP BOARD
Find the median from the following frequency distribution: Class-interval 0–10 10–20 20–30 30–40 40–50 Frequency 7 9 19 15 7
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#11 Class 10 Trigonometry Introduction to Trigonometry 2025 Long 2M UP BOARD
Prove that: $\left(\dfrac{1 - \tan A}{1 - \cot A}\right)^2 = \tan^2 A$
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#12 Class 10 Coordinate Geometry Coordinate Geometry 2025 Short 2M UP BOARD
Find the ratio in which the line segment joining the points $(-3, 10)$ and $(6, -8)$ is divided by the point $(-1, 6)$.
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#13 Class 10 Statistics and Probability Statistics 2025 Mcq 1M UP BOARD
The median class of the following table will be: Class-interval 0–10 10–20 20–30 30–40 40–50 Frequency 6 8 10 9 12
A. 10–20
B. 20–30
C. 30–40
D. 40–50
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#14 Class 10 Statistics and Probability Statistics 2025 Mcq 1M UP BOARD
The mean from the following table will be: Class-interval 0–4 4–8 8–12 12–16 16–20 Frequency 4 6 6 5 4
A. 8.32
B. 8.76
C. 9.84
D. 10.36
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#15 Class 10 Algebra Quadratic Equations 2025 Mcq 1M UP BOARD
The discriminant of the quadratic equation $3x^2 - 4x + \dfrac{4}{3} = 0$ will be:
A. 0
B. 1
C. 2
D. 4
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#16 Class 10 Algebra Polynomials 2025 Mcq 1M UP BOARD
The product of the zeroes of the quadratic polynomial $p(x) = 4x^2 - 4x - 1$ will be:
A. –1
B. $-\dfrac{1}{4}$
C. $\dfrac{1}{4}$
D. 1
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#17 Class 10 Mensuration Surface Areas and Volumes 2025 Mcq 1M UP BOARD
The surface area of a sphere is $452\dfrac{4}{7}$ cm$^2$. Its radius will be:
A. 6 cm
B. 9 cm
C. 12 cm
D. 15 cm
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#18 Class 10 Mensuration Areas Related to Circles 2025 Mcq 1M UP BOARD
An arc of a circle of radius 7 cm subtends an angle of $60^\circ$ at the centre. The area of the sector will be:
A. $\dfrac{77}{4}$ cm$^2$
B. $\dfrac{77}{3}$ cm$^2$
C. $\dfrac{77}{2}$ cm$^2$
D. 77 cm$^2$
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#19 Class 10 Trigonometry Introduction to Trigonometry 2025 Mcq 1M UP BOARD
The value of $\dfrac{1 + \tan^2 A}{1 + \cot^2 A}$ will be:
A. $\sec^2 A$
B. –1
C. $\cot^2 A$
D. $\tan^2 A$
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#20 Class 10 Geometry Circles 2025 Mcq 1M UP BOARD
The point of contact of a tangent to a circle is joined to the centre. The angle between the tangent and the radius at the point of contact will be:
A. $90^\circ$
B. $60^\circ$
C. $45^\circ$
D. $30^\circ$
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