List of practice Questions

A die is thrown once, the probability of getting an even number will be:

If $\tan \theta = \tfrac{3}{4}$, then the value of $\cos \theta$ will be:
 

The length of a rectangular field is 9 m more than the twice of its width. If the area of the field is $810 \, m^2$, find the length and width of the field.
Prove that \(\displaystyle \frac{\sin\theta-\cos\theta+1}{\sin\theta+\cos\theta-1}=\sec\theta+\tan\theta\).
A cubical block of side $14\,$cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid. (Use $\pi=3.14$)
Find the ratio in which Y-axis divides the line segment joining the points $(5,-6)$ and $(-1,-4)$.
Prove that \[ \sqrt{\frac{1-\cos\theta}{1+\cos\theta}} = \csc\theta - \cot\theta \]
A chord of a circle of radius 14 cm subtends an angle of $120^\circ$ at the centre. Find the area of the corresponding segment of the circle.
One card is drawn from a well-shuffled pack of 52 cards, find the probability of getting:
(i) A king of red colour
(ii) A face card
Find the zeroes of the quadratic polynomial $x^2-5$ and verify the relationship between the zeroes and the coefficients.
The zeroes of quadratic polynomial $6x^2 - 7x - 3$ will be:
The $LCM$ of the numbers 12, 15 and 21 will be:
The distance between the points $(2,3)$ and $(4,1)$ will be:
The angle of a sector of a circle with radius of 6 cm is $60^\circ$. The area of the sector will be:
A solid is made by joining corresponding faces of two cubes each of side 10 cm. The surface area of the resulting cuboid will be:
Which of the following cannot be the probability of any event?
The value of $\cos 60^\circ$ is:
What was the astrologer's prediction about the Tiger King's death?
Answer any one of the following questions in about 80 words:
(a) How is the study of Antarctica useful to us?
Write the central idea of the poem "My Mother at Sixty-Six."
Describe the environment of Antarctica.
What was the third level? Where was it situated?
What was the meaning of garbage for children? What did they find in it?
What did the instructor do to train Douglas?
On what ground did the English owners of indigo plantation demand compensation from the sharecroppers?