List of practice Questions

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
(i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)
(ii) (–3, 5), (3, 1), (0, 3), (–1, – 4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)

Choose the correct choice in the following and justify: \(30^{th}\) term of the AP: \(10, 7, 4,.....\) is

In a classroom, 4 friends are seated at points A, B, C and D. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using the distance formula, find which of them is correct.

In \(ΔABC\) right angled at B, AB = 24 cm, BC = 7 m. Determine
(i) sin A, cos A
(ii) sin C, cos C

A circus artist is climbing a \(20\, m\) long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is \(30 °\).

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear

Find the area of a quadrant of a circle whose circumference is 22cm.

Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.

Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B ?

A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter o the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm³. Check whether she is correct, taking the above as the inside measurements, and \(\pi = 3.14.\)

Find the distance between the following pairs of points :
(i) (2, 3), (4, 1)
(ii) (– 5, 7), (– 1, 3)
(iii) (a, b), (– a, – b)

In an AP:

given a = 5, d = 3, an = 50, find n and S_n
given a = 7, a₁₃ = 35, find d and S₁₃.
given a₁₂ = 37, d = 3, find a and S₁₂.
given a₃ = 15, S₁₀ = 125, find d and a₁₀.
given d = 5, S₉ = 75, find a and a₉.
given a = 2, d = 8, S_n = 90, find n and a_n .
given a = 8, a_n = 62, S_n = 210, find n and d.
given a_n = 4, d = 2, S_n = –14, find n and a.
given a = 3, n = 8, S = 192, find d.
given l = 28, S = 144, and there are total 9 terms. Find a.

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm. [Use \(\pi=\frac{22}{ 7} \)]

If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC ~ ΔPQR, proves that \(\frac{AB}{PQ}=\frac{AD}{PM}\)

A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that ΔABC∼ΔPQR

D is a point on the side BC of a triangle ABC such that \(\angle\)ADC = \(\angle\)BAC. Show that CA²=CB.CD

Which of the following arguments are correct and which are not correct? Give reasons for your answer.
(i) If two coins are tossed simultaneously there are three possible outcomes - - two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is \(\frac{1}{3}\).
(ii) If a die is thrown, there are two possible outcomes - - an odd number or an even number. Therefore, the probability of getting an odd number is \(\frac{1}{2}\)

A die is thrown twice. What is the probability that
(i) 5 will not come up either time?
(ii) 5 will come up at least once?
[Hint: Throwing a die twice and throwing two dice simultaneously are treated as the same experiment].

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Two dice, one blue and one grey, are thrown at the same time.
(i) Write down all the possible outcomes and complete the following table:

(ii) A student argues that 'there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability \(\frac{1}{11}\)

A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that
(i) She will buy it.
(ii) She will not buy it.

Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?