1. O is the circumcenter of the isosceles ΔABC. Given that AB = AC = 10 cm and BC = 12 cm. The radius of the circle is

(A) 6.25 cm

(B) 6.205 cm

(C) 6.125 cm

(D) 3.125 cm

2 2/3 of 2.1 is how much less than 0.2% of 800?

(A) 0.2

(B) 1.46

(C) 14.6

(D) 158.6

3. A certain amount is divided among A, B and C in the ratio of 3:7:6 respectively. If the difference between share of A and B is Rs. 2700, what is C’s share?

(A) Rs. 4050

(B) Rs. 4000

(C) Rs. 4100

(D) Rs. 4500

4. A 3 lit mixture contains two liquid wine and water in which 13% water is present. In the above mixture, another 3 lit mixture which has 8% water, is added and ¼ lit water also added separately then what is the percent age of water.

(A) 17.08%

(B) 14.08%

(C) 16.08%

(D) 12.08%

5. A bank offers 10% compound interest per year. A cus tomer deposits Rs. 3600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is.

(A) Rs 1116

(B) Rs 2232

(C) Rs 558

(D) Rs 279

**Direction (6-9):** In the Bar-graph data is given about some students who appeared in final exam. Study the data carefully and answer the related questions. Full marks in Math, Science and social science is 100,75 and 150 respectively.

6. What is respective ratio of average obtained marks in Math and science of all students together?

(A) 2 : 3

(B) 1 : 2

(C) 2 : 1

(D) None of these

7. Total marks obtained by B is what percent more/less than that of D?

(A) 3%

(B) 4%

(C) 4.34%

(D) 5.67%

8. What is average obtained marks of all students together in science?

(A) 40

(B) 50

(C) 48

(D) 60

9. What is difference between total obtained of A and C?

(A) 10

(B) 15

(C) 30

(D) 40

10. Tanya gave 20% in charity from her salary, and then 20% from the remaining she gave to her friend as loan. She is left now with 6400. What is the salary of Tanya?

(A) 12000

(B) 10000

(C) 10200

(D) 11000

__Solutions:__

**Ans.1(A)**

AB= AC = 10 cm.

AD ⊥ BC

BD = DC = 6 cm.

AD^{2} = AB^{2} – BD^{2}

= 100 – 36 = 64

AD = 8 cm

In triangle OCD

OC^{2} = OD^{2} + DC^{2}

r^{2} = (8 – r)^{2 } + 36

r^{2} = 64 + r^{2 }– 16r + 36

16r = 100

r = 100/16 =6.25

**Ans.2(A)** Required value = 1.6 – 1.4 = 0.2

**Ans.3(A)** 7x – 3x = 2700

4x = 2700

x = 675

C’s Share = 675 × 6 = Rs. 4050

**Ans.4(B)** Water in 1st = 3 ×13/100 = 0.39 lit

Water in 2nd = 3 × 8/100 = 0.24 lit

Additional = 0.25 lit

Total : 0.39 + 0.24 + 0.25 = 0.88 lit

Total of water = 0.88/(3+3+0.25)=0.88/6.25 × 100 = 14.08%

**Ans.5(A)** Compound Interest on 3600 deposited on 1st Jan at the end of the year at 10% per half year

= 360 + 360 +36

Compound Interest on 3600 deposited on 1st Jul at the end of the year at 10% per half year

= 360

Total Compound interest = 1080 + 36 = 1116

Note:

Here interest rate is given on half yearly basis not annually. So we will take rate of interest as it is i.e. 10% while calculating

**Ans.6(D)** Required ratio =

100×((45+70+75+80+90)/500)

75((60+80+40+60+80)/500)

Since obtaing marks given in graph is in percentage

= 4 × 360 : 3 × 320 = 3:2

**Ans.7(C)** Total marks of B =

**Ans.8(C)**

**Ans.9(B)**

**Ans.10(B)**Let the whole money be = 100 x

20% of 100x = 20x

After given to charity, Tanya had

= 100x – 20x = 80x

The money given to her friend= 20% of 80x = 16x

Remaining money

= 100x – (20x + 16x) = 64x

A.T.Q

64x = 6400

x = 100

Thus the whole money = 100x = 10000