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#1 Class 10 Mensuration Surface Areas and Volumes 2025 Short 6M UP BOARD
A spherical glass vessel has a cylindrical neck 8 cm long and 2 cm in diameter, and the diameter of the spherical part is 8.5 cm. Find the volume of water that can be filled in it. (Use $\pi = 3.14$)
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#2 Class 10 Mensuration Surface Areas and Volumes 2025 Short 6M UP BOARD
A toy is in the form of a hemisphere surmounting on a cone whose radius is 3.5 cm. If the total height of the toy is 15.5 cm, find its total surface area and volume.
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#3 Class 10 Trigonometry Introduction to Trigonometry 2025 Long 6M UP BOARD
Prove that: $\dfrac{\sin A - \cos A + 1}{\sin A + \cos A - 1} = \dfrac{1}{\sec A - \tan A}$
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#4 Class 10 Trigonometry Some Applications of Trigonometry 2025 Short 6M UP BOARD
The shadow of a tower, when the angle of elevation of the sun is $30^\circ$, is found to be 50 metres longer than when the angle of elevation was $60^\circ$ on the plane ground. Find the height of the tower.
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#5 Class 10 Statistics and Probability Probability 2025 Short 4M UP BOARD
A bag contains 5 black, 7 red and 3 white balls. A ball is drawn at random. Find the probability that the ball drawn is: (i) red    (ii) black    (iii) not black
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#6 Class 10 Statistics and Probability Statistics 2025 Short 4M UP BOARD
Find the unknown frequency $p$ if the median of the given frequency distribution is 24: Class interval 0–10 10–20 20–30 30–40 40–50 Frequency 5 25 25 $p$ 7
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#7 Class 10 Algebra Quadratic Equations 2025 Short 4M UP BOARD
If the roots of the equation $x^2 + 2(m - 1)x + (m + 5) = 0$ are real and equal, find the value of $m$.
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#8 Class 10 Geometry Triangles 2025 Long 4M UP BOARD
Prove that a straight line drawn parallel to one side of a triangle, intersecting the other two sides at two distinct points, divides those sides in the same ratio.
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#9 Class 10 Geometry Circles 2025 Short 4M UP BOARD
The radii of two concentric circles are 3 cm and 5 cm. Find the length of the chord of the larger circle which touches the smaller circle.
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#10 Class 10 Statistics and Probability Statistics 2025 Short 2M UP BOARD
Find the mean of the following frequency table: Class-interval 0–6 6–12 12–18 18–24 24–30 Frequency 5 9 10 12 4
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#11 Class 10 Trigonometry Introduction to Trigonometry 2025 Long 2M UP BOARD
Prove that: $\dfrac{1 + \sec\theta}{\sec\theta} = \dfrac{\sin^2\theta}{1 - \cos\theta}$
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#12 Class 10 Coordinate Geometry Coordinate Geometry 2025 Short 2M UP BOARD
Find the value of $x$ for which the distance between the points $(x, 2)$ and $(6, 5)$ is 5 units.
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#13 Class 10 Coordinate Geometry Coordinate Geometry 2025 Short 2M UP BOARD
Find the coordinates of the point which divides the line segment joining the points $A(3, 4)$ and $B(-2, -1)$ in the ratio $3 : 2$.
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#14 Class 10 Mensuration Areas Related to Circles 2025 Short 2M UP BOARD
Find the length of an arc of a circle of radius 14 cm which subtends an angle of $30^\circ$ at the centre.
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#15 Class 10 Algebra Quadratic Equations 2025 Mcq 1M UP BOARD
The area of a rectangular field is 30 m$^2$. If its length is 1 m greater than its breadth $x$, then the quadratic equation to find them will be:
A. $x^2 + x + 30 = 0$
B. $x^2 - x + 30 = 0$
C. $x^2 + x - 30 = 0$
D. $x^2 - x - 30 = 0$
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#16 Class 10 Statistics and Probability Statistics 2025 Mcq 1M UP BOARD
The modal class of the following table will be: Class interval 0–5 5–10 10–15 15–20 20–25 Frequency 5 8 12 10 7
A. 5–10
B. 15–20
C. 20–25
D. 10–15
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#17 Class 10 Statistics and Probability Statistics 2025 Mcq 1M UP BOARD
The mean and median of a frequency distribution are 26.1 and 25.8 respectively. The value of mode for the distribution will be:
A. 24.2
B. 25.1
C. 25.2
D. 26.4
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#18 Class 10 Trigonometry Introduction to Trigonometry 2025 Mcq 1M UP BOARD
The value of $(\sec A + \tan A)(1 - \sin A)$ will be:
A. $\sec A$
B. $\sin A$
C. $\operatorname{cosec} A$
D. $\cos A$
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#19 Class 10 Trigonometry Introduction to Trigonometry 2025 Mcq 1M UP BOARD
If $\tan 2A = 1$, where $2A$ is an acute angle, the value of $A$ will be:
A. $36^\circ$
B. $22\dfrac{1}{2}^\circ$
C. $38^\circ$
D. $45^\circ$
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#20 Class 10 Trigonometry Introduction to Trigonometry 2025 Mcq 1M UP BOARD
The value of $\cos 0^\circ$ will be:
A. 1
B. 0
C. 2
D. –1
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