List of top Questions asked in BSE Manipur Class 10

The number of days within which the stock exchange is supposed to resolve dispute at their end is

Show that\( a^3 + b^3 + c^3 - 3abc = \dfrac{1}{2}(a+b+c)\left\{(a-b)^2 + (b-c)^2 + (c-a)^2\right\}\)

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height \(h\). At a point on the plane, the angle of elevation of the bottom of the flagstaff is \(\alpha\) and that of the top of the flagstaff is \(\beta\). Prove that the height of the tower is \(\dfrac{h\tan\alpha}{\tan\beta-\tan\alpha}\).
If three consecutive vertices of a parallelogram are \( A(1,-2) \), \( B(3,6) \) and \( C(5,10) \), find its fourth vertex.
Prove that \(x^n - y^n\) is divisible by \(x+y\) only when \(n\) is even.
A metallic sphere of radius \(9\) cm is melted and recast to form a cylinder of radius \(3\) cm. Find the curved surface area of the cylinder.
If \( \cos A = \dfrac{3}{5} \), calculate \( \sin A \) and \( \tan A \).
If \(x, y, z\) are real numbers, \(x \neq 0\), and \(xy = xz\), prove that \(y = z\).
Show that the square of an odd integer is of the form \( 8k + 1 \).
Find the area of the quadrilateral whose vertices are \( (1,1) \), \( (3,4) \), \( (5,-2) \) and \( (4,-7) \) taken in order.
Write down the formula to find the area of a triangle whose vertices are \((x_1,y_1)\), \((x_2,y_2)\) and \((x_3,y_3)\).
State and prove Basic Proportionality Theorem.
Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
Define mode of a frequency distribution.
Find the area of a circle whose radius is 7 cm.
The ratio of incomes of two persons is \(9:7\) and the ratio of their expenditures is \(4:3\). If each of them saves Rs. \(5000\) per month, find their monthly incomes.
Write the statement of Euclid's Division Lemma.
Prove that the area of a sector of sectorial angle \( \theta \) and radius \( r \) is \( \dfrac{\pi r^2 \theta}{360} \).
Write the full form of SCORES.
How many tangents can be drawn to a circle through a point lying outside the circle?
In a right triangle \( ABC \), right angled at \( B \), prove that \( \sin A = \cos (90^\circ - A) \) and \( \cos A = \sin (90^\circ - A) \).
Write down the quadratic equation whose roots are 2 and -3.
What is the first term of the quotient when \(2x^3 + x^2 - 3x + 5\) is divided by \(1 - 3x + x^2\)?
If $p(x)$ is a polynomial of degree $\geq 1$ and $a$ is any real number, then the remainder when $p(x)$ is divided by $x-a$ is
The remainder when \(4x^3 + 4x^2 + x - 4\) is divided by \(2x - 1\) is