The total expenses of a trip for certain number of people is ₹ 18,000. If three more people join them, then the share of each reduces by ₹ 3,000. Take x to be the original number of people, form a quadratic equation in x and solve it to find the value of x.

Using ruler and compass only construct ∠ABC = 60°, AB = 6 cm and BC = 5 cm.

(a) construct the locus of all points which are equidistant from AB and BC.

(b) construct the locus of all points equidistant from A and B.

(c) mark the point which satisfies both the conditions (a) and (b) as P.

Hence, construct a circle with center P and passing through A and B.

Each of the letter of the word "HOUSEWARMING" is written on cards and put in a bag. If a card is drawn at random from the bag after shuffling, what is the probability that the letter on the card is :

(a) a vowel

(b) one of the letters of the word SEWING

(c) not a letter from the word WEAR

Use graph sheet for this question. Take 2 cm = 1 unit along the axes.

(a) Plot A(1, 2), B(1, 1) and C(2, 1)

(b) Reflect A, B and C about y-axis and name them as A', B' and C'.

(c) Reflect A, B, C, A', B' and C' about x-axis and name them as A'', B'', C'', A''', B''' and C''' respectively.

(d) Join A, B, C, C'', B'', A'', A''', B''', C''', C', B' , A' and A to make it a closed figure.