On seeing the below display board outside Pearl Stationary Shop, Chetan enters the shop to buy the following items:

The shopkeeper handed over the bill to Chetan saying that he has given further discount of 2% on total bill. Chetan became so happy hearing about the discount that he did not check the bill until he reached home. He later found out that though shopkeeper has given 2% discount as promised, he had also mischarged uniform 18% GST on all the items.

(a) Calculate :

(i) total selling price of all the items as per the offers displayed on the board.

(ii) total amount to be paid by Chetan including GST with correct rates.

(iii) actual amount charged by the shopkeeper.

(b) Did the shopkeeper overcharge Chetan? Justify your answer

Using remainder and factor theorem, show that (2x + 3) is a factor of the polynomial 2x² + 11x + 12. Hence, factorise it completely. What must be multiplied to the given polynomial so that x² + 3x - 4 is a factor of the resulting polynomial? Also, write the resulting polynomial.

Given the equations of two straight lines, L1 and L2 are x - y = 1 and x + y = 5 respectively. If L1 and L2 intersects at point Q (3, 2). Find :

(a) the equation of line L3 which is parallel to L1 and has y-intercept 3.

(b) the value of k, if the line L3 meets the line L2 at a point P (k, 4).

(c) the coordinate of R and the ratio PQ : QR, if line L2 meets x-axis at point R.

In the figure given below (not drawn to scale), AD ∥ GE ∥ BC, DE = 18 cm, EC = 3 cm, AD = 35 cm. Find :

(a) AF : FC

(b) length of EF

(c) area(trapezium ADEF) : area(Δ EFC)

(d) BC ∶ GF