List of top Questions asked in UP Board X

Find the coordinates of the point which divides the line segment joining the points A(-1, 7) and B(4, -3) in the ratio 2 : 3.
If $\sin \theta - \cos \theta = 0$ then the value of $\sin^4 \theta + \cos^4 \theta$ will be
The length of tangent from a point Q to a circle is 24 cm and the distance of Q from the centre of circle is 25 cm. Then radius of the circle will be
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°, then $\angle POA$ will be
Area of the sector of an angle $\theta^\circ$ of a circle with radius $r$ will be
The diameter of a solid pipe is 4 cm whose length is 20 cm. Then the volume of the metal used in the pipe will be
Total surface area of a solid hemisphere with radius $r$ will be
10th term of the sequence $\sqrt{2}, 2\sqrt{2}, 3\sqrt{2}, \dots$ will be
If in $\triangle ABC$ and $\triangle DEF$, $\dfrac{AB}{DE} = \dfrac{BC}{FD}$, then they will be similar if
The perimeter of a triangle whose vertices are (0, 4), (0, 0), and (3, 0) will be
If $3 \tan A = 4$ then the value of $\sec A$ will be
If $\tan \alpha + \cot \alpha = 5$, then the value of $\tan^2 \alpha + \cot^2 \alpha$ will be
If $\sin \theta = \csc \theta$ and $0 \leq \theta \leq \dfrac{\pi}{2}$, then the value of $\theta$ will be
The angle of elevation of the top of a tower from the top of a house whose height is 15 m is \(30^\circ\). Also, the angle of elevation of the top of the tower from the ground of the same house is \(60^\circ\). Find the height of the tower and the distance of the tower from the house.
Both the ends of a metallic solid cylinder are semi-spherical. Its total height is 19 cm and the diameter of the cylinder is 7 cm. Find the weight of the solid if the weight of \(1 \, \text{cm}^3\) of the metal is \(4.5 \, \text{g}\).
A chord of a circle of radius 15 cm subtends an angle of \(60^\circ\) at the centre of the circle. Find the area of the corresponding minor segment. \((\pi = 3.14, \, \sqrt{3} = 1.73)\)
Rational number will be
The shape of the graph of a quadratic equation $y = ax^2 + bx + c$, $a \neq 0$, will be
In the system of equations $\dfrac{x}{a} = \dfrac{y}{b}$, $ax + by = a^2 + b^2$, value of y will be
If the equation $x^2 - 4x + a = 0$ has no real roots, then
If the sum of first \(m\) terms of an A.P. is \(n\) and the sum of first \(n\) terms of the A.P. is \(m\), then find the sum of \((m+n)\) terms.
Prove that the angle between the tangents drawn from an external point to a circle is supplementary to the angle formed by the line segment joining the points of contact at the centre of the circle.
In what ratio does the point \((-4, 6)\) divide the line segment joining the points \(A(-6, 10)\) and \(B(3, -8)\)?
Find the roots of the quadratic equation \(3x^2 - 2\sqrt{6}x + 2 = 0\).
The distance between the two points (2, 3) and (4, 1) will be