List of practice Questions

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

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:

(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) \(kx (x – 2) + 6 = 0\)

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ΔABE ~ ΔCFB.

In the following figure, altitudes AD and CE of ΔABC intersect each other at the point P.Show that: