List of top Mathematics Questions

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:
  1. given a = 5, d = 3, an = 50, find n and Sn
  2. given a = 7, a13 = 35, find d and S13.
  3. given a12 = 37, d = 3, find a and S12.
  4. given a3 = 15, S10 = 125, find d and a10.
  5. given d = 5, S9 = 75, find a and a9.
  6. given a = 2, d = 8, Sn = 90, find n and an .
  7. given a = 8, an = 62, Sn = 210, find n and d.
  8. given an = 4, d = 2, Sn = –14, find n and a.
  9. given a = 3, n = 8, S = 192, find d.
  10. 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:
Two dice, one blue and one grey, are thrown at the same time.
(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?
Suppose you drop a die at random on the rectangular region

A child has a die whose six faces shows the letters as given below:

A child has a die whose six faces shows the letters as given below:
The die is thrown once. What is the probability of getting (i) A? (ii) D?

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears 
(i) a two-digit number 
(ii) a perfect square number 
(iii) a number divisible by 5.
Is it possible to design a rectangular park of perimeter 80 m and area 400 \(m^2\) ? If so, find its length and breadth.
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆PQR (see the given figure). Show that ∆ABC ∼ ∆PQR.

A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid. [Use \(\pi =\frac{22 }{7}\)]
In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ∆ABD ∼ ∆ECF
an isosceles triangle ABC with AB = AC
CD and GH are respectively the bisectors of ΔACB and ΔEGF, such that D and H lie on sides AB and FE of ΔABC and ΔEFG respectively. If ΔABC ~ ΔFEG, show that:
(i) \(\frac{CD}{GH}=\frac{AC}{FG}\)
(ii) ΔDCB~ΔHGE
(iii) ΔDCA~ΔHGF
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 \(m^2\)? If so, find its length and breadth.
In the following figure, ABC and AMP are two right triangles, right-angled at B and M, respectively. Prove that: 
ABC and AMP are two right triangles
(i) ΔABC ~ ΔAMP 
(ii) \(\frac{CA}{PA}=\frac{BC}{MP}\)

Find the values of k for each of the following quadratic equations, so that they have two equal roots. 
(i) \(2x^2 + kx + 3 = 0\) (ii) \(kx (x – 2) + 6 = 0\)