hard math mcqs for entrance test

8/22/2019 Hard Math Mcqs for Entrance test

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Maths MCQs By Syed Hashim Shah

Guidelines..

Read the questions carefully and logically understand what it demands..No question

is wrong..Care has been taken to make right options, in case of any error please

report

The difficulty level of these question is quite high, So dont chose any option only

with a little thought.. Practice to solve questions in shortest possible time..In each

question multiple concepts have been checked..Try to find out the shortest possible

but logical way for obtaining solution..

1) If lZl=1 and Z=x+iy, Z represents a

a) Parabola

b) Square

c) Hyperbola

d) Circle

2) If =? Where abs () is magnitude function?

a) 3/625

b) 2/25

c) 8/625 *

d) 6/125

3) If lZl=1 and Z=ax+iby, where a/=b , Z represents a

a) Parabola

b) Ellipse*

c) Triangle

d) Hyperbola

4) If two sets are such that n(AB)=1/2 x n(AB) =6, Then Total number of elements in

these sets is

a) 9


2/10

b) 18 *

c) 16

d) 12

5) If two sets A,B are such that number of elements in both sets is 10 and One set

has 2 more elements than other. Number of subsets containing 20 elements oftheir Cartesian products is ? (given that all elements are distinct..)

a) 10620

b) 10623

c) 10200

d) 10362

6) If Two sets A & B are so that Number of their subsets is equal, and when their

cartesian product Is taken , the number of elements in AxB is equal to number ofsubsets of either of them, The number of elements in A can be?

(This question is meant to be without options)

7) If (AB)= (AB)=A, and P(A) is power set of A, If Power set of A contains 16

elements, then Power set if B contains contains how many element?

a) 24

b) 32

c) 16

d) 64

8) A set A is given without any specifications. which of the following can be

maximum number of subsets

a)10

b)12

c)16

d)20

9) If You differentiate volume of a cube of side lenth L with respect to L. Than that

derivative is:

A) Surface area

B) Partial Surface area


3/10

C) Partial volume

10) If A is sq matrix of order k and u=lAl then l nA l

a) K x u^n

b) u xn*u

c) u x n^k

d) U/n

11) +..to infinite terms=? (GIKI 2012)

a)

b) 1/3

c) *

d) 5/3

12) A tank can be filled in 3 hrs with with a pipe, It can be filled in 5 hrs with

another pipe, it can be drained if full, in 7 hrs by an emergency valve How

many hours it would take if all Pipes and valves are opened simulatenously?

a) 2.56*

b) 3.52

c)4.32

d) 1.98

13) if A and Adj(A) are Equal And lAl=2, Then A is ?

No options for this question

13) Cube roots of unity make a _________ of area _______ on an argand diagram

a) Square , 2.414

b) Triangle, 1.30

c) Pentagon, 1.141

d) Triangle, 1.73

14) If

a) n =10


4/10

b) n=5

c) n=7

d) n=4

15) ~P v P is always

a)false

b) True

)None

17) x^2+mx+1=0 can have atmost how many integer roots?

a) 2

b) 1

c) both a & b

d) none

18) If Two matrices A, B of order 2x2 are such that If Added together they yield a

matrix= A^2 and A^-1 is also equal to A..Then B in terms of A is, if det(A) is

determinant A.

a) B=

b) B=

c) None

d) Both yield same matrix..

19) (1+i3)20/ (1-i3)20 is root of which of the following

a) x^2+2x+1

b)x^2+x+1

c) x^3+x^2+x+1

d)None of these

20) if tan -1 (1/2 )+tan-1(1/3)=tan-1(?)

a)1

b)1/4

c)1/5


5/10

d)2

21) If a,b are roots of equation x^2+mx+c=0 then is

a)2

b)=0

c)1

d)=none

22) =?

a) 0

b)Does not exist

c) none

d) 1

23) If Volume of Sphere and a cube are equal, Then ratio of their surface areas is?

a) 1

b)

c)

d)

24) If a line is drawn from a vertice of a triangle to its opposite side which cuts it

into two portions in ratrio n+1 : n-1, The ratio of areas of two triangles formed?

a) n+1:n-1

b)n-1:n+1

c)n:n+1

25) The shape which is a locus of points, the difference of distance of whom from

two points is constant is

A) Parabola

b)Circle

C)Hyperbola

D)Ellipse


6/10

26)A pipe can fill a tank in one hour, 2nd can empty in 2 hrs, 3rd can fill it in 3 hrs, 4th

can drain in 4 hrs, 5th can drain it 5 hrs if such a pattern continues till infinity i.e

there are infinite such pipes..After how much time the tank will be filled?

A)1.44 HRS

B)2.41 HRS

C)1.32 HRS

D)1 HRS

29) lA-1l=?

a) 1/lAl

b) lAl

c) None

30)

a) a2 b2c2

b)4 a2 b2c2

c) 4abc+

d)

31) The set of real roots of equation log(5x+4)(2x+3)3 log(2x+3)(10x^2

+23x+12)= 1 is

A) {-1}

B) {-3/5 }

C) Null set

D) {-1/3}

32) The Value of k if k>0 for which the equations x^2+kx+64=0 and x^2-

8x+k=0 have real roots is

A) 8

B) -16

C) -64


7/10

D) 16

33) If for a matrix A , A5 =I then A-1 is

a. A2

b. A3

c. A4

d. None of above

34) if a+b+c=0, Then both the roots of equation ax2+bx+c=0 are

a. Rational

b. Irrational

c. Non-Real

d. Zero

35) The equation

a. Only one real solution

b. Exactly three real solutions

c. Exactly one real solution

d. Non-real roots

36) If Then f(x)=?

a) k/ln(x)

b) k ln(x)

c) k/x

d) None

37) If a^x= b^y=c^z and a,b,c are in GP then x,y,z are in

a) HP

b) AP


8/10

c) GP

d) None

38) if then a/b is

a)

b)

c) LogBA

d) None

39) If =?

a) aln(a)

b) ln(a)

c) 1

d) e

39) Let the sequence 1, 2,2,4,4,4,4,8,8,8,8,8,8,8,8,. Where n consecutive terms

have value n, then 1025th term is

a) 2^9

b) 2^10

c) 2^11

d) 2^12

40) What is the number when divided by 2 gives remainder 1, divided by 3 gives

remainder 2, Divided by 4 gives remainder 3, divided by 5 gives remainder 4

a) 69

b)59

c)29

d) none of these

41) Which of the following is integer for all n

a) (3^2n +2^n)/5

b) ( 3^2n -2^2n)/5

c) ( 3^n -2^n)/5


9/10

d) None

42) Sum of the coefficients of the trinomial expansion (a+b+c)^8 is ?

a) 2^8

b) 3^8

c) 8^2

d) 8^3

43) Inscribed circle of a triangle has radius of 2 cm..The Perimeter of triangle was

10 cm whats the value of r1r2r3?

a) 50 cm 3

b) 50

c) 25cm^2

d) 19cm^3

44) There are two parallel lines on a plane..Five points are marked on each of these

lines. How many triangles are possible to form

a. 10 x 5C2

b. 5C3

c. 2x 5C2

d. 10C3

45) A man Walks on completely spherical planet 50 km south, 100 km east and 50

km north..The distance between his final and original position is

a) 100km

b) 50 km

c) 0

d) 70 km

46) The number of triplets satisfying (x,y,z) sin-1x+cos-1y+sin-1z = 2pi

A) 0

B) 2


10/10

C) 1

D) INFINITE

47) Three vectors a,b,c are such they have equal magnitudeGiven that a+b+c=

2a.. if lal=1

Whats the value of a.b+b.c+c.a

(make options)

48) An ellipse is elevated at an angle of 30 degrees with a plane. When illuminated

from top forms a circle of Area 5..Whats the area of ellipse?

a) 5

b)5.5

c) 5.8

d) 4.7

hard math mcqs for entrance test

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