List of practice Questions

While travelling for work from Dhaneri (3100) to Marwada (3197) along the metalled road, Sahil crossed over a number of 'causeways'. Why are causeways present in the area shown on the map extract?

What is the difference in altitude between the highest point on the map extract and the contour height in grid square 3203?

What is the black horizontal line made between 98 and 99 northings called?

On the outline map of India provided: (i) Mark and name the fold mountain range of India.
(ii) Mark with an arrow and name the river also known as the 'Sorrow of Bihar'.
(iii) Shade and label the Gulf of Kutch.
(iv) Mark and label the Karakoram Pass.
(v) Mark and label an offshore oil field of India.
(vi) Shade and label the Laterite soil area in the northeastern part of India.
(vii) Mark and name the shared capital city of Punjab and Haryana.
(viii) Mark and label the Western Ghats.
(ix) Shade and label the river Krishna.
(x) Shade and label an area of dense population.

Mawsynram, the rainiest place in the world, gets the rain from:

If \( \tan A = \cot B \), prove that \( A + B = 90^\circ \).

What is 3r in grid square 3501?

Identify one relief feature found in the grid square 3796.

The area shown on the map extract has seasonal streams, but in 3903 a large perennial water source can be seen. What may be the reason for the presence of this large perennial source of water?

Find the L.C.M of 17, 23, and 29.

The cost of fencing a circular field at the rate of Rs. 24 per meter is Rs. 5280. The field is ploughed at the rate of Rs. 0.50 per m². Find the cost of ploughing the field. (Take \( \pi = \frac{22}{7} \))

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

Prove that the lengths of tangents drawn from an external point to a circle are equal and they subtend equal angles at the center.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the center.

Evaluate $-5 \cos^2 60^\circ + 4 \sec^2 30^\circ - \tan 45^\circ$

If \(\cot \theta = \frac{7}{8}\), then evaluate \[ \frac{(1 + \sin \theta)(1 - \sin \theta)}{(1 + \cos \theta)(1 - \cos \theta)} \]

Two coins are tossed simultaneously. What is the probability of getting (i) at least one head (ii) no head?

For what value of k, $x-3y=7$ and $kx+6y=5$ will have no solution?

Find the quadratic polynomial whose sum and product of zeros are 6 and -2 respectively.

Find the value of $p(x) = x^2 + x + 1$ when $x = -1$.

In the given figure, the angle of elevation of the top of a tower AC from a point B on the ground is $60^\circ$. If the height of the tower is 20m, find the distance of the point from the foot of the tower.

A die is thrown once. Find the probability of getting (i) a prime number (ii) an odd number.

If the 3rd and the 9th terms of an AP are 4 and -8 respectively, which term of this AP is zero?

Find the area of the triangle whose vertices, taken in order are (-4, -2), (-3, -5) \& (3, -2).

Reena wants to become a teacher in a preschool. Suggest two educational qualifications that would help her in this context.