JECA – MATHEMATICS

JECA - MATHEMATICS

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Congratulations - you have completed JECA - MATHEMATICS. You scored %%SCORE%% out of %%TOTAL%%. Your performance has been rated as %%RATING%%

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Question 1

The number of words that can be formed from the letters of the word INDRAPRASTHA when the vowels are never separated is

A	727560
B	725760
C	752760
D	757260

Question 2

If the equations x² −px +q = 0 and x² +qx -p = 0 have a common root, then which one of the following will hold true?

A	p = q
B	p + q = 2
C	p + q = 1
D	p – q = 1

Question 3

y – A cos ωt + B sin ωt is a solution of the differential equation

A	d²y / dt² - ω²y = 0
B	d²y / dt² - ωy = 0
C	d²y / dt² + ωy = 0
D	d²y / dt² + ω²y = 0

Question 4

The number of 2-digit even numbers that can be formed from the digits 1, 2, 3, 4 and 5, repetition being not allowed, is

A	2⁵
B	5!
C	16
D	8

Question 5

If 1, ω, ω² are the cube roots of unity, then value of (x + y)² to (xω + yω²)² + (xω² + yω)² is equal to

A	xy
B	3xy
C	6xy
D	9xy

Question 6

If

then (A +B)² is not equal to

A	A² + AB + BA + B²
B	A² + 2AB + B²
C	A² + AB + BA + B²I
D	A²I + AB + BA + B²

Question 7

The number of ways in which 6 people can be seated at a round table is

A	6
B	60
C	120
D	720

Question 8

The general solution of dy/dx + y = sin x is

A	y = ce^-2x + 1/4 sin x - 1/2 cos x
B	y = ce^-x + 1/2 sin x - 1/2 cos x
C	y = ce^-3x + sin x
D	y = ce^-x

Question 9

The binary number 10110100001 in decimal system is

A	441
B	1441
C	1241
D	241

Question 10

If b^→ is a unit vector in the xy-plane making an angle of π/4 with the x-axis, then b^→ is equal to

A	i^ˆ + j^ˆ
B	i^ˆ - j^ˆ
C	(i^ˆ + j^ˆ) / √2
D	(i^ˆ - j^ˆ) / √2

Question 11

The solution of

is

A	sin^-1 y - sin^-1 x + c
B	sin^-1 y = 1/2 √1 - x² + 1/2sin^-1 x + c
C	sin^-1 y = 1/2x √1 - x² + 1/2sin^-1 x + c
D	sin^-1 y = 1/2x √1 - x² + 1/4cos^-1 x + c

Question 12

The binary equivalent to the decimal number 0.3125

A	0101
B	.1010
C	.0101
D	.1101

Question 13

If(x - 2)(x +6 ) ≥ 0, then the solution set is

A	(x:x ≥ 2)
B	(x:x ≤ 6 )
C	(x:x ≤ -6 )
D	(x:x ≥ 2 or x ≤ -6 )

Question 14

If in the binomial expansion of (1 + x)ⁿ when n is a natural number, the coefficients of the 5th, 6th and 7th terms are in A.P., then n is equal to

A	7 or 13
B	7 or 14
C	7 or 15
D	7 or 17

Question 15

The the mth and the nth terms of an H.P. are n and m respectively, then the mnth term is

A	0
B	1
C	2
D	1/2

Question 16

If

Fullscreen capture 12-06-2013 113634 AM.bmp

then

A	x = -3 , y = 4
B	x = 3 , y = 4
C	x = 3 , y = -4
D	x = -3 , y = -4

Question 17

If

Fullscreen capture 12-06-2013 115109 AM.bmp

, then

A	both AB and BA exist
B	neither AB nor BA exists
C	AB exists but BA does not exists
D	AB does not exist but BA exist

Question 18

The binary number 1101101 + 1011011 is written in decimal system as

A	198
B	199
C	200
D	201

Question 19

If A be an n × n matrix and C any scalar, then | CA |

A	n^C \| A \|
B	Cⁿ \| A \|
C	nC \| A \|
D	C \| A \|

Question 20

If a^x = b^y = c^z ,and log_ba = log_cb ,then which one of the following will hold true?

A	y² = xz
B	x² = yz
C	z² = xy
D	y = xz

Question 21

If A ≠ O and both the conditions (i) A.B = A.C (ii) A×B = AxC hold simultaneously, then

A	B=C=0
B	B=C
C	B ≠ C
D	B ≠ 0 , C ≠ 0

Question 22

There are 600 students in a school, If 400 of them can speak Telugu, 300 can speak Hindi, then the number of students who can speak both Telugu and Hindi are

A	100
B	200
C	300
D	400

Question 23

Distance between two points whose position vectors are 3i^ˆ + j^ˆ - 2k^ˆ and i^ˆ - 3j^ˆ + 5k^ˆ

A	69 units
B	√69 units
C	13 units
D	29 units

Question 24

If log₈m + log₈1/6 = 2/3 ,then m is equal to

A	24
B	18
C	12
D	4

Question 25

The value of

is equal to

A	3
B	3/2
C	0
D	2

Question 26

The differential of the system of circles touching the y-axis at the origin, is given by

A	x² + y² - 2xy dy/dx = 0
B	x² + y² + 2xy dy/dx = 0
C	x² - y² + 2xy dy/dx = 0
D	x² - y² - 2xy dy/dx = 0

Question 27

The value of 3 - 1 + 1/3 - 1/9 =..... is equal to

A	20/9
B	9/20
C	9/4
D	4/9

Question 28

is equal to ?

A	e + 1
B	e - 1
C	e + 2
D	e

Question 29

is equal to ?

A	1 + e^x + c
B	1/2 log(1 + e^x) + c
C	log(1 + e^x) + c
D	2log(1 + e^x) + c

Question 30

The value of tan 31^o .tan 32^o .tan 32^o .tan 33^o ...tan 59^o is equal to

A	-1
B	0
C	1
D	2

Question 31

The rate at which bacteria multiply is proportional to the instantaneous number present. If the original number doubles in 2 hours, then they will triple in

A	4 log 2/log 3 hours
B	5 log 2/log 3 hours
C	2 log 2/log 3 hours
D	log 2/log 3 hours

Question 32

The solution of equations 3x + y + 2z = 3; 2x - 3y - z = -3 and x + 2y + z = 4 is

A	x= 3 , y= 2 , z= -2
B	x= 2 , y= 1 , z= 3
C	x= 1 , y= 2 , z= -1
D	x= 1 , y= 2 , z= 1

Question 33

The coefficient of the middle term in the expansion of (2 + 3x)⁴ is

A	6
B	5!
C	8!
D	216

Question 34

The value of the determinant

Fullscreen capture 12-06-2013 113830 AM.bmp

is

A	gfkl
B	abhg
C	abdl
D	ablc

Question 35

If (x + 1/x) = 3 , then (x⁶ + 1/x⁶) is equal to

A	927
B	414
C	364
D	322

Question 36

If a, b, c are in G.P., then

is

A	1/ c² - b²
B	1/ b² - c²
C	1/ c² - a²
D	1/ b² - a²

Question 37

is equal to ?

A	π/2
B	0
C	π/4
D	π/8

Question 38

The modulus and principle amplitude of (1 + i√3)² , respectively are

A	2, - π/2
B	4, 2π/3
C	5/8, tan<>sup>-1(-4/3)
D	4, - 3π/4

Question 39

The complex number z, satisfying the equation

lies on

A	a circle with the centre (0, 0) and radius 1
B	the x-axis
C	the y-axis
D	the line y = x + 1

Question 40

α, β, ξ, η are non-empty sets then

A	(α x β) ∪ (ξ x η) = (α x β) ∩ (ξ x η)
B	(α x β) ∩ (ξ x η) = (α x ξ) ∩ (β x η)
C	(α x β) x (ξ x η) = (α x ξ) ∪ (β x η)
D	(α x β) x (ξ x η) = (α x η) ∪ (β x ξ )

Question 41

The value of

is equal to

A	2
B	3
C	√6
D	6

Question 42

In a Euclidean plane, which one of the following is not an equivalence relation?

A	Parallelism of lines (a line being deemed parallel to itself)
B	Congruence of triangles
C	Similarity of triangles
D	Orthogonality of lines

Question 43

If

, then the value of α and β are given by

A	α = 1/√2 , β = 1/√2
B	α = -1/√2 , β = 1/√2
C	α = β = ±1/√2
D	α = -β = ±1/√2

Question 44

The area bounded by the coordinate axes and the curve √x + √y = 1 is equal to ?

A	1
B	1/2
C	1/3
D	1/6

Question 45

The degree of the differential equation

is ?

A	2
B	3
C	4
D	5

Question 46

The rank of the matrix

Fullscreen capture 12-06-2013 110051 AM.bmp

is equal to

A	1
B	2
C	3
D	4

Question 47

The number of sides of two regular polygons are in the ratio 5 : 4. The difference between their angles is 9⁰. Which one of the following is correct?

A	One of them is a pentagon and the other is a rectangle.
B	One of them must be a hexagon.
C	One of them is an octagon.
D	One of the has 20 sides and the other has 16 sides.

Question 48

The differential equation

is not linear. The integrating factor to solve this equation

A	1/ x ²
B	1/ x ³
C	1/ x ⁴
D	x ⁴

Question 49

The expansion of the determinant

Fullscreen capture 12-06-2013 113714 AM.bmp

contains which one of the following as a factor?

A	x - 3
B	x - y
C	y - 3
D	(x - 3)(y - 3)

Question 50

The matrix

Fullscreen capture 12-06-2013 113527 AM.bmp

is

A	symmetric
B	skew symmetric
C	non-singular
D	orthogonal

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A	n^C \| A \|
B	Cⁿ \| A \|
C	nC \| A \|
D	C \| A \|

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JECA – MATHEMATICS

JECA - MATHEMATICS

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