1. A car travels 8 km in the first quarter of an hour, 6 km in the
second quarter and 16 km in the third quarter. The average speed of the car in
km per hour over the entire journey is

2. Find the sum to n terms of the series 10+84+734+….

3. The set of values of p for which the roots of the equation 3x

(A)30 (B)36 (C)40 (D)24

__Sol:__
This is a simple formula based one.

Total distance = 8+6+16 = 30 km

Total time taken = 3 quarters of an hour = ¾ hr

Average speed = total distance/ total time = 30/(3/4) = 40 kmph

Ans:

**C**2. Find the sum to n terms of the series 10+84+734+….

(A)9(9

^{n}+1)/10 + 1 (B) 9(9^{n}-1)/8 + 1 (C) 9(9^{n}-1)/8 + n (D) 9(9^{n}-1)/8 + n^{2}

__Sol:__
Check from the options by substituting n = 1,2…

For n=1, all options are right

For n=2, sum must be 10+84=94.

Only option D is correct for this and we can bank on that…

Ans: **D**

3. The set of values of p for which the roots of the equation 3x

^{2}+2x+p(p-1)=0 are of opposite sign is

**(A)(-∞,0) (B)(0,1) (C)(1,∞) (D)(0,∞)**

__Sol:__

**This is a question on quadratic equations funda.**

**For ax**

^{2}+bx+c=0,

**if the two roots are of different signs, their product must be –ve => c/a < 0**

**=> p(p-1)/3 < 0 => p(p-1) < 0 => 0 < p < 1**

**Ans:**

**B**

**4. What is the chance that a leap year, selected at random, will contain 53 Saturdays?**

**(A)2/7 (B)3/7 (C)1/7 (D)5/7**

**Sol**:

**A leap year has 366 days => 365/7 weeks = 52 weeks + 2 days**

**=> For a leap year to have 53 Saturdays, either one of the first two days of first week of the year (Jan 1**^{st}or 2^{nd}) must be a Saturday. So the probability is 2 out of 7

**Ans:****A**

5. In the summer of 2012, in New

__Delhi, the mean temperature of Monday to Wednesday was 41__^{0}C and of Tuesday to Thursday was 43^{0}C. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in^{o}C on Thursday was
(A)40 (B)43 (C)46 (D)49

__Sol:__
Let the temperatures on Monday,Tuesday,Wednesday and Thursday is
M,T,W and Th respectively.

The mean temperature of Monday to Wednesday was 41

^{0}C => (M+T+W)/3 = 41
=> M+T+W = 123 ---(1)

The mean temperature of Tuesday to Thursday was 43

^{0}C=> (T+W+Th)/3 = 43
=> T+W+Th = 129 ---(2)

(2)-(1) => Th-M = 6 ---(3)

temperature on Thursday was 15% higher than that of Monday =>
Th = 1.15*M ---(4)

From 93) and (4), 0.15M = 6 => M = 6/0.15 => Th =
1.15*6/0.15 = 46

Ans: **C**
6. They were requested not to quarrel with others.

Which one of the following is the closest in meaning to the word
quarrel?

(A)
make out (B)
call out (C) dig out (D) fall out
Ans:

(A)
Because I have a nice caller tune

(B) Because I have a better telephone facility

(C) Because a friend in need is a friend in deed

(D) Because you need not pay towards the telephone bills when you give me a ring

**D****7. Statement You can always give me a ring whenever you need****Which one of the following is the inference from the above statement?**

(B) Because I have a better telephone facility

(C) Because a friend in need is a friend in deed

(D) Because you need not pay towards the telephone bills when you give me a ring

__Explanation:__
All the other options except (C) can be easily eliminated as they
are illogical

Ans**: C****8.**

**Statement**There were different streams of freedom movements in colonial India carried out by the moderates, liberals, radicals, socialists and so on.**Which one of the following is the best inference from the above statement?**

**(A)The emergence of colonial India led to our independence**

**(B)Nationalism in India is emerged in the context of colonialism**

**(C)Nationalism in India is homogeneous**

**
**

(D)Nationalism in India is heterogeneous

**As the movement is in different forms, we can say that nationalism is heterogeneous**

__Explanation__:

Ans:

**D****9. Choose the grammatically CORRECT sentence:**

**(A) Two and two add four (B) Two and two become four**

**(C) Two and two are four (D) Two and two make four**

__This is a question on English usage and 'make' makes sense here__**Explanation:**
Ans:

10. Complete the sentence:

**D**10. Complete the sentence:

Dare ______ mistakes.

(A)
commit (B)
to commit

**(C) committed (D) committing**
Ans:

**A**
OMG..!!! I put wrong answer for 10+84+734+… sum....!!! :( :(

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