1. Consider the differential equation
X^2 d^2/dx^2 + x dy/dx + (x^2 – 4)y = 0. The statement which is not true for it is
a) It is a linear second order ordinary differential equation
b) It can not be reduced to a differential equation with constant coefficients
c) X=0 is a regular singular point
d) It is a non-homogeneous second order ordinary differential equation
2. The sum of two numbers is 16 and the sum of their squares is a minimum. The two numbers are
a) 10,6 b) 9,7 c) 8,8 d) 5,11
3. The value of the definite integral 0?(p/2)^(1/3) x^2 sin(x^3)dx is
a) -1/3 b) 0 c) 1 d) 1/3
4. A circle C2 is concentric with the circle C1 : x^2 + y^2 -4x +6y -12 =0 and has a radius twice that
of C1. The equation of the circle C2 is
a) x^2 + y^2 -4x +6y -13 =0 b) x^2 + y^2 -4x +6y -87 =0 c) x^2 + y^2 -4x +6y -100 =0 d)
x^2 + y^2 -4x +6y -88 =0
5. Consider the quadratic equation x^2 + px + q =0. If p and q are roots of the equation, the values of
p and q are
a) p=0, q=0 only b) p=1, q=-2 only c) p=0, q=0 and p=1, q=-2 d) p=0, q=0 and
6. Consider the list of words: etiquette, accommodate, forty, exaggerate, continous, independent,
receipt. The number of misspelt words are
a) 1 b) 2 c) 3 d) 4
7. Consider the following sentences
1. A few friends he has are all very rich.
2. Do not insult the weak.
3. The later of the two persons was more interesting.
4. All the informations were correct.
Out of these sentences, the grammatically correct sentence is
a) 1 b) 2 c) 3 d) 4
8. The appropriate auxiliary verb to fill in the blank of the sentence “Gandhi knew that he __ soon be
a) would b) will c) shall d) may
9. The number of missing punctuation marks in the sentence “Rajesh along with Amit went to the
a) 0 b) 1 c) 2 d) 3
10. The meaning of the word PLAGIARISM is
a) theft of public money b) theft of ideas c) belief in one god d) belief in many gods
11. The antonym of the word TRANSIENT is
a) certain b) close c) permanent d) fast
12. ACROPHOBIA is the abnormal fear of
a) open spaces b) height c) fire d) water
13. The appropriate pair of prepositions to fill in the blank in the sentence “He was angry __ me,
because my remarks were aimed __ him.”is
a) at,to b) with, at c) with, to d) at, for
14. The appropriate word(s) to fill up the blank in the sentence “ I remember __ voices in the middle
of the night.”is (are)
a) hear b) to hear c) hearing d) heard
15. The passive voice form of the sentence “I have known him for a long time.”is
a) He is known to me for a long time.
b) He is known by me for a long time.
c) He has been known to me for a long time.
d) He has been known by me for a long time.
16. If kennel is to a dog, then __ is to a hen.
a) nest b) coop c) hole d) stable
17. If NATION is to 5236765, then NOTION is to
a) 573675 b) 563765 c) 576375 d) 557365
18. The next two numbers of the series 3,5,11,21 are
a) 34 and 52 b) 34 and 53 c) 35 and 52 d) 35 and 53
19. A, B and C are three places in India with longitudes 80E, 85 E and 90 E respectively. Which one
of the following statements about the local times of the places is true?
a) Local time of C is ahead of that of B.
b) Local time of B is ahead of that of C.
c) Local time of A is ahead of that of C.
d) A, B and C all have the same local time.
20. In this question, notations +, / and * are used as follows
A + B means A is the husband of B.
A / B means A is the sister of B.
A * B means A is the son of B.
With these relations, the relationship denoted by P / Q * R is
a) P is son of R
b) P is daughter of R
c) P is uncle of R
d) P is father of R
21. If DELHI is written as EDHIL, then PARIS is written as
a) APRIS b) SARIP c) SAPIR d) APISR
22. The number of prime numbers between 10 and 50 is
a) 10 b) 11 c) 12 d) 13
23. The odd one in the list : LAN, TCP/IP, HACKER and KILLER is
a) LAN b) TCP/IP c) KILLER d) HACKER
24. SAW is to carpenter as SCALPEL is to
a) surgeon b) mason c) plumber d) tailor