X paid Rs. 47 for certain cups of tea and coffee. If tea costs Rs. 5 per cup and coffee costs Rs. 8 per cup, which one of the following statements is correct?

- He drank 8 cups of tea and coffee.
- He drank the same number of cups of tea and coffee.
- He drank more tea than coffee.
- He drank more coffee than tea.

The system of equations 2x + 4y = 6 and 4x + 8y = 8 is

- Consistent with a unique solution
- Consistent with infinitely many solutions
- Inconsistent
- None of the above

Sunil wants to spend Rs.200 on two types of sweets, costing Rs.7 and Rs.10 respectively. What is the maximum number of sweets he can get so that no money is left over?

- 25
- 26
- 27
- 28

Leela got married 6 years ago. Today her age is 1¼ times her age at the time of her marriage. Her son’s age is 1/10 times her age. What is the present age of her son?

- 1 year
- 2 years
- 3 years
- 4 years

The pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0 intersect each other, if

- k = 6
- k ≠ 6
- k = 0
- k ≠ 0

If the roots of the equation (a^{2} - bc)x^{2} + 2(b^{2} - ac)x + (c^{2} - ab) = 0 are equal, where b ≠ 0, then which one of the following is correct?

- a
^{3}+ b^{3}+ c^{3}= 0 - a
^{3}+ b^{3}+ c^{3}= 3abc - a
^{2}+ b^{2}+ c^{2}= 0 - a + b + c = abc

If α and β are the roots of the equation x^{2} - x - 1 = 0, then what is (α^{2} + β^{2})/((α^{2} - β^{2})(α - β))

- 2/5
- 4/5
- 3/5
- 1/5

If x^{2} = 6 + √(6 + √(6 + √(6 + ....∞)), then what is one of the values of x equal to?

- 3
- 4
- 5
- 6

The expression 2x^{3} + x^{2} - 2x - 1 = 0 is divisible by

- 2x - 1
- 2x + 1
- x + 2
- x - 2

In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains -9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was:

- x
^{2}+ 10x + 9 = 0 - x
^{2}- 10x + 16 = 0 - x
^{2}- 10x + 9 = 0 - x
^{2}+ 10x + 16 = 0

The sign of the quadratic polynomial ax^{2} + bx + c is always positive if

- a is positive and b
^{2}- 4ac ≤ 0. - a can be any real number and b
^{2}- 4ac ≤ 0. - a can be any real number and b
^{2}- 4ac ≥ 0. - a is positive and b
^{2}- 4ac ≥ 0.

If a - b = 4 and a^{2} + b^{2} = 40 where a and b are positive integers, where a and b are positive integers, then a^{3} + b^{6} is equal to

- 264
- 280
- 300
- 324

If the roots of the equation Ax^{2} + Bx + C = 0 are -1 and 1, then which one of the following is correct?

- A and B are both positive
- A and C are both negative
- A and C are of opposite sign
- A and C are both zero

The value of x2 - 4x + 11 can never be less than

- 7
- 8
- 11
- 22

Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots (4, 3). Alok made a mistake in writing down the coefficient of x to get roots (3, 2). The correct roots of the equation are

- –4, –3
- 6, 1
- 4, 3
- –6, –1

If α and β are the roots of the equation x^{2} + px + q = 0, then what is α^{2} + β^{2} equal to?

- p
^{2}– 2q - q
^{2}– 2p - p
^{2}+ 2q - q
^{2}– q

Log (40^{2} - 20^{2}) is equal to

- log 3
- log 60 + log 20
- log 40 – log 20
- log 20

If log_{25} 5 = a and log_{25} 15 = b, then the value of log_{25} 27 is

- 3(b+a)
- 3(1-b-a)
- 3(a+b-1)
- 3(1-b+a)

What is the solution of the equation

x log_{10} (10/3) + log_{10} 3 = log_{10} (2 + 3^{x}) + x?

- 10
- 3
- 1
- 0

If x is a real number such that log_{3} 5 = log_{5} (2 + x), then which of the following is true?

- 0 < x < 3
- 23 < x < 30
- x > 30
- 3 < x < 23

If n is a whole number greater than 1, then n^{2}(n^{2} - 1) is always divisible by

- 12
- 24
- 48
- 60

The sum of two numbers is 10 and their product is 20. What is the sum of their reciprocals?

- 1
- 1/2
- 2
- 1/10

What is the last digit in 7^{402} + 3^{402}?

- 0
- 2
- 4
- 8

The difference between the squares of two consecutive odd integers is always divisible by

- 16
- 8
- 7
- 3

If x is a positive even integer and y is a negative odd integer, then x^{y} is

- even integer
- rational number
- odd integer
- none

A student was asked to multiply a number by 25. He instead multiplied the number by 52 and got the answer 324 more than the correct answer. The number to be multiplied was

- 15
- 32
- 12
- 25

What is the maximum value of m if the number

N = 35 × 45 × 55 × 60 × 124 × 75

is divisible by 5^{m}?

- 4
- 5
- 6
- 7

If n is a natural number, then √n is

- always a rational number
- always a natural number
- always an irrational number
- either a natural number or an irrational number

The digit in the units place of the product 81×82×83×84×....×99 is

- 0
- 4
- 6
- 8

If N, N+2 and N+4 are prime numbers, then the number of possible solutions for N are

- 1
- 2
- 3
- 4

The sum of two numbers is 143. If the greater number is divided by the difference of the numbers, the quotient is 7. What is the difference of the two numbers?

- 9
- 11
- 14
- 15

The values of x which satisfy the equation 5^{1+x} + 5^{1–x} = 26 are

- –1, 1
- 0, 1
- 1, 2
- –1, 0

The number of prime numbers which are less than 100 is

- 24
- 25
- 26
- 27

What is the remainder when the number (4444)^{4444} is divided by 9?

- 4
- 6
- 7
- 8

In the following passage, at certain points you are given a choice of three words, one of which fits the meaning of the passage. Choose the best word.

Sometimes the messages are sent with **1. (a) many (b) few (c) no** accompanying words and we speak in **2. (a) body (b) signal (c) foreign** language alone. But what gestures make **3. (a) with body (b) up (c) into** language? Most of us are **4. (a) easy (b) familiar (c) efficient** with the common hand gestures. Some **5. (a) students (b) people (c) officers** cannot talk without using their hands. **6. (a) We (b) Arms (c) They** reach out as they explain almost **7. (a) exacting (b) shaping (c) changing** their words, emphasizing and exaggerating and **8. (a) teaching (b) holding (c) punctuating** their hands. Other people hardly **9. (a) adjust (b) use (c) wave** their hands at all when they **10. (a) lecture (b) unite (c) talk**.

In the following passage, at certain points you are given a choice of three words, one of which fits the meaning of the passage. Choose the best word.

One of the most interesting new books published recently is "Spaceship' by Prof. E.C. Walker, Our earth he says **1. (a) is (b) have been (c) will be** like a spaceship, and all the 400 million people **2. (a) over (b) on (c) upon** earth are passengers on it. And we are heading **3. (a) about (b) to (c) towards** a disaster. The levels of atmospheric pollution **4. (a) increasing (b) arriving (c) coming** in the cities and industrial areas of the world could in time change the weather patterns of the earth, raising the temperature **5. (a) in (b) of (c) for** the whole planet. If this rose a few **6. (a) degrees (b) steps (c) miles** the deserts of the world would expand to double their size. The polar ice caps would start inching. If the polar ice caps melted, the **7. (a) water (b) ice (c) sea** level all over the world would rise **8. (a) in (b) by (c) to** about 60 meters. Prof. Walker's **9. (a) idea (b) thought (c) book** is not at all about gloom and doom. He admits that the **10. (a) ideas (b) changes (c) solutions** he describes could take thousands of years.

In the following passage, at certain points you are given a choice of three words, one of which fits the meaning of the passage. Choose the best word.

I was engaged in many activities and I wanted a proper reconciliation between my activity and thought. Thought without **1. (a) wish (b) action (c) idea** is undeveloped thought. Action without **2. (a) thought (b) wish (c)** idea is folly. Of course we **3. (a) never (b) belatedly (c) sometimes** act on some impulse or **4. (a) peaceful (b) uncontrollable (c) indisputable** urge. If suddenly you through **5. (a) no (b) an (c) a** brick at me and my **6. (a) hand (b) wrist (c) finger** goes up in front to **7. (a) stimulate (b) rescue (c) protect** myself, it is an automatic **8. (a) uncontrollable (b) instinctive (c) impulsive** action and not a result **9. (a) to (b) in (c) of** deliberate thought. Over living is **10. (a) made (b) conditioned (c) developed** by a series of automatic **11. (a) thoughts (b) actions (c) wishes** from morning till night. Anything **12. (a) we (b) I (c) they** do outside that common range of **13. (a) thoughts (b) ideas (c) actions**, however, has to be **14. (a) proceeded (b) preceded (c) followed** by some measure of thinking. **15. (a) Some (b) If (c) The** more action and thought are **16. (a) developed (b) allied (c) hostile** and integrated, the more effective **17. (a) they (b) thoughts (c) we** become and the happier you **18. (a) appear (b) develop (c) grow**. There will then be no **19. (a) reconciliation (b) conflict (c) inflict** between a wish to do something and **20. (a) inability (b) probability (c) plausibility** to act.

According to a report in yesterday's newspaper **1. (a) once (b) a (c) new** police dog was taken to Raj Bhavan **2. (a) at (b) next (c) on** Monday. This was to trace the **3. (a) killers (b) dogs (c) police** of the "very important horse" which **4. (a) has (b) were (c) was** reported missing on Sunday. The dog picked **5. (a) on (b) at (c) up** the scent on some traces of **6. (a) those (b) blood (c) report** and ran a few yards before losing the **7. (a) bet (b) track (c) game**. The police have launched a vigorous **8. (a) search (b) investigation (c) campaign** into the whole affair. They have **9. (a) given up (b) requisitioned (c) report** the services of a forensic expert, **10. (a) a (b) an (c) two** fingerprint expert and a photographer. **11. (a) There (b) We (c) So** are now fourteen horses at Raj Bhavan **12. (a) who (b) where (c) which** are kept in a large shed near the gate.

The multi sourcing of

**P:**financial mess with**Q:**coins led to a**R:**using their own mix of**S:**different mints

metals and alloys.

- SQRP
- QPSR
- RPQS
- PSRQ

In paliopathology

**P:**would be to obtain**Q:**the fundamental objective**R:**background information**S:**as much

on the skeleton as possible.

- PRQS
- QPSR
- SRQP
- RPSQ

The national unity of a free people

**P:**to make it impracticable**Q:**for there to be an arbitrary administration**R:**depends upon a sufficiently even balance of political power**S:**against a revolutionary opposition that is irreconcilably opposed to it

- QRPS
- RSPQ
- QRSP
- RPQS

It is very easy

**P:**a great deal more than one realises**Q:**may mean**R:**that a phrase that one does not quite understand**S:**to persuade oneself

- SPQR
- RSQP
- RQPS
- SRQP

These positive effects vary from genetic changes that

**P:**to other related infections,**Q:**make us more resistant to the diseases responsible**R:**for epidemics and**S:**which have effects on human that are

hard to pin down and quantify.

- QRPS
- SQPR
- PRSQ
- RPQS

All such students

**P:**get success**Q:**who are honest and hard-working**R:**and recognition**S:**in very walk of life

- PSRQ
- SPRQ
- PRQS
- QPRS

He was so kind and generous that

**P:**he not only**Q:**made others do so**R:**but also**S:**helped them himself

- SPQR
- PRSQ
- QPRS
- PSRQ

We must read

**P:**if we want to absorb the fruits of great literature**Q:**but with concentration**R:**them not as we do cricket stories**S:**undefined

- QPSR
- PRQS
- PSQR
- PRSQ

It has been established that

**P:**Einstein was**Q:**although a great scientist**R:**weak in arithmetic**S:**right from his school days

- SRPQ
- QPRS
- RQPS
- QPSR

Education is

**P:**of the proper sense of responsibilities**Q:**the first need**R:**in a citizen**S:**for the development

- SQPR
- QSRP
- QSPR
- PQRS

The first line (S1) is fixed. Arrange the other four lines P, Q, R and S in a logical sequence.

- S1: The beginning of the universe had, of course, been discussed for a long time.
- P: One argument of such a beginning was the feeling that it was necessary to have a first cause to explain the existence of the universe.
- Q: He pointed out that civilization is progressing, and we remember who performed this deed or developed that technique;
- R: According to a number of early cosmologies in the Jewish/Christian/Muslim tradition, the universe started at a finite and not very distant time in the past.
- S: Another argument was put forward by St. Augustine in his book, The City of God.

- QRSP
- RPSQ
- PSQR
- SQPR

The first line (S1) is fixed. Arrange the other four lines P, Q, R and S in a logical sequence.

- S1: I was so eager not to disappoint my parents that I ran errands for anyone.
- P: On the way a boy on a bicycle crashed into me and my left shoulder hurt so much that my eyes watered.
- Q: Only then did I cry
- R: But I still went and bought the maize, took it to my neighbours and then went home.
- S: One day my neighbours asked me to buy some maize for them from the bazaar.

- SPRQ
- PQSR
- QRPS
- RSQP