Directions (Q. 1-6): For the two given equations I and II.
Give answer:
(1) If p is greater than q.
(2) If p is smaller than q.
(3) If p is equal to q.
(4) If p is either equal to or greater than q.
(5) If p is either equal to or smaller than q.
1.
I. 6p^2+5p+1=0
II. 20q^2+9q=-1
2.
I. 3p^2+2p-1=0
II. 2q^2+7q+6=0
3.
I. 3p^2+15p=-18
II. q^2+7q+12=0
4.
I. p=√4/√9
II. 9q^2-12q+4=0
5.
I. p^2+13p+42=0
II. q^2=36
6.
I. p=10
II. q=√100
Directions (Q. 7-10): Study following graph carefully and answer the questions given below:
7. What is the average income earned by all the companies together?
(1) Rs. 34,50,00,000/-
(2) Rs. 33,50,00,000/-
(3) Rs. 33,50,000/-
(4) Rs. 3,45,00,00/-
(5) None of these
8. Expenditure incurred by Company C is approximately what per cent to the expenditure incurred by company B?
(1) 41%
(2) 57%
(3) 62%
(4) 51%
(5) 65%
9. What is the approximate difference between the percent profit earned by Company A and that by Company D?
(1) 5%
(2) 20%
(3) 35%
(4) 15%
(5) 25%
10. What is the total expenditure incurred by all the companies together?
(1) Rs. 1,37,50,000/-
(2) Rs. 1,37,50,00,000/-
(3) Rs. 13,75,00,00,000/-
(4) Rs. 13,75,000/-
(5) None of these
Answers with explanations:
1►Ans:(2);
I. 6p^2+5p+1=0
(3p+1)(2p+1)=0
p=-1/3,-1/2
II. 20q^2+9q+1=0
(4q+1)(5q+1)=0
q=-1/4,-1/5
∴p<q
2►Ans:(1)I. 3p^2+2p-1=0
(3p-1)(p+1)=0
p=1/3,-1
II. 2q^2+7q+6=0
(2q+3)(q+2)=0
q=-3/2,-2
3►Ans:(4)
I. 3p^2+15p+18=0
(3p+6)(p+3)=0
p=-2,-3
II. q^2+7q+12=0
(q+4)(q+3)=0
q=-3,-4
∴p≥q
4►Ans:(3)
I. p=√4/√9=2/3
II. 9q^2-12q+4=0
(3q-2)^2=0
q=2/3
∴p=q
5►Ans:(5)I. p^2+13p+42=0
(p+7)(p+6)=0
p=-6,-7
II. q^2=36
q=±6
∴p≤q
6►Ans:(3)
I. p=10
II. q=10
p=q
7►Ans:(4); Required average income=(3.5+3.25+2.5+4.25+3.75)/5=17.25/5=Rs.3.45 crore =Rs.3,45,00,000/-
8►Ans:(2); Required percentage=2/3.5×100≈57%
=55.55-21.42≈35%
10►Ans:(5); Total expenditure=2.25+3.5+2+3.5+2.5=Rs. 13.75 crore=Rs. 13,75,00,000/-
