List of practice Questions

If business fails, then the creditors can recover their dues not only from the business assets, but also from the personal assets of the proprietor. Which feature of sole proprietorship is applied here?
Earthquake comes under which type of risk?
Seema and Daya are two sisters who sell their domestic T.V. set at a profit. This is a/an...
The Board of Directors of a joint stock company is elected by...
Sales promotion is important from the point of view of manufacturers because it...
Sudha Publishing House was a Private Limited Company. The publishing business was growing by leaps and bounds. The demand was huge. It required huge investment to set up its branches and printing base all over the country. The board members were thinking to offer shares to the public to meet investment requirements.
On the basis of above case, answer the following questions
The vertices of a quadrilateral ABCD are A(6, – 2), B(9, 2), C(5, – 1) and D(2, – 5). Prove that ABCD is a rhombus, and not a square.
Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube.
The interior of a building is in the form of a cylinder of base radius 12 m and height 3×5 m surmounted by a cone of equal base and slant height 14 m. Find the internal curved surface area of the building.
$ABCD$ is a trapezium with $AB \parallel DC$. $AC$ and $BD$ intersect at $E$. If $\triangle AED \sim \triangle BEC$, then prove that $AD = BC$.
Solve for $x$: \[ \frac{4}{x} - \frac{5}{2x + 3} = 3. \]
The sum of two numbers is 18, and the sum of their reciprocals is $\frac{1}{4}$. Find the numbers.
Calculate the mean of the following data :
Class :4 – 67 – 910 – 1213 – 15
Frequency :54910
Prove that: \[ \frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta \]
From an external point $P$, two tangents $PA$ and $PB$ are drawn to a circle with centre $O$. At a point $E$ on the circle, a tangent is drawn which intersects $PA$ and $PB$ at $C$ and $D$ respectively. If $PA = 10$ cm, find the perimeter of $\triangle PCD$.
A circle is inscribed in a right-angled triangle ABC, right-angled at B. If BC = 7 cm and AB = 24 cm, find the radius of the circle
The monthly incomes of A and B are in the ratio 8 : 7 and their expenditures are in the ratio 19 : 16. If each saves Rs 2500 per month, find the monthly income of each
Find the zeroes of the polynomial $f(t) = t^2 + 4\sqrt{3}t - 15$ and verify the relationship between the zeroes and the coefficients of the polynomial.
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = 6x^2 + 11x - 10$, find the value of $\frac{\alpha}{\beta} + \frac{\beta}{\alpha}$.
Prove that $\sqrt{3}$ is an irrational number.
A horse, a cow and a goat are tied, each by ropes of length 14 m, at the corners A, B and C respectively, of a grassy triangular field ABC with sides of lengths 35 m, 40 m and 50 m. Find the total area of grass field that can be grazed by them
If $\sin A = \frac{3}{5}$ and $\cos B = \frac{12}{13}$, then find the value of $(\tan A + \tan B)$.
If $\tan \theta + \sec \theta = m$, then prove that $\sec \theta = \frac{m^2 + 1}{2m}$.
If a hexagon ABCDEF circumscribes a circle, prove that AB + CD + EF = BC + DE + FA.
If $\triangle ABC \sim \triangle DEF$ and $AB = 4$ cm, $DE = 6$ cm, $EF = 9$ cm, and $FD = 12$ cm, find the perimeter of $\triangle ABC$.