## JECA - MATHEMATICS

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Question 1 |

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

A | x ^{2} + y^{2} - 2xy dy/dx = 0 |

B | x ^{2} + y^{2} + 2xy dy/dx = 0 |

C | x ^{2} - y^{2} + 2xy dy/dx = 0 |

D | x ^{2} - y^{2} - 2xy dy/dx = 0 |

Question 2 |

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

A | d ^{2}y / dt^{2} - ω^{2}y = 0 |

B | d ^{2}y / dt^{2} - ωy = 0 |

C | d ^{2}y / dt^{2} + ωy = 0 |

D | d ^{2}y / dt^{2} + ω^{2}y = 0 |

Question 3 |

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 4 |

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 5 |

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 6 |

The value of tan 31

^{o}.tan 32^{o}.tan 32^{o}.tan 33^{o}...tan 59^{o}is equal toA | -1 |

B | 0 |

C | 1 |

D | 2 |

Question 8 |

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

^{4}isA | 6 |

B | 5! |

C | 8! |

D | 216 |

Question 9 |

The modulus and principle amplitude of (1 + i√3)

^{2}, respectively areA | 2, - π/2 |

B | 4, 2π/3 |

C | 5/8, tan<>sup>-1(-4/3) |

D | 4, - 3π/4 |

Question 10 |

If log

_{8}m + log_{8}1/6 = 2/3 ,then m is equal toA | 24 |

B | 18 |

C | 12 |

D | 4 |

Question 11 |

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 | 2 ^{5} |

B | 5! |

C | 16 |

D | 8 |

Question 12 |

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 13 |

If b

^{→}is a unit vector in the xy-plane making an angle of π/4 with the x-axis, then b^{→}is equal toA | i ^{ˆ} + j^{ˆ} |

B | i ^{ˆ} - j^{ˆ} |

C | (i ^{ˆ} + j^{ˆ}) / √2 |

D | (i ^{ˆ} - j^{ˆ}) / √2 |

Question 14 |

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 16 |

If a

^{x}= b^{y}= c^{z},and log_{b}a = log_{c}b ,then which one of the following will hold true?A | y ^{2} = xz |

B | x ^{2} = yz |

C | z ^{2} = xy |

D | y = xz |

Question 19 |

A | 1/ x ^{2} |

B | 1/ x ^{3} |

C | 1/ x ^{4} |

D | x ^{4} |

Question 20 |

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 21 |

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 22 |

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 23 |

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 24 |

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 25 |

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 26 |

The number of sides of two regular polygons are in the ratio 5 : 4. The difference between their angles is 9

^{0}. 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 27 |

If 1, ω, ω

^{2}are the cube roots of unity, then value of (x + y)^{2}to (xω + yω^{2})^{2}+ (xω^{2}+ yω)^{2}is equal toA | xy |

B | 3xy |

C | 6xy |

D | 9xy |

Question 28 |

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 toA | 7 or 13 |

B | 7 or 14 |

C | 7 or 15 |

D | 7 or 17 |

Question 29 |

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 30 |

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 31 |

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 32 |

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

A | n ^{C} | A | |

B | C ^{n} | A | |

C | nC | A | |

D | C | A | |

Question 33 |

The binary number 10110100001 in decimal system is

A | 441 |

B | 1441 |

C | 1241 |

D | 241 |

Question 34 |

A | A ^{2} + AB + BA + B^{2} |

B | A ^{2} + 2AB + B^{2} |

C | A ^{2} + AB + BA + B^{2}I |

D | A ^{2}I + AB + BA + B^{2} |

Question 35 |

A | 1/ c ^{2} - b^{2} |

B | 1/ b ^{2} - c^{2} |

C | 1/ c ^{2} - a^{2} |

D | 1/ b ^{2} - a^{2} |

Question 36 |

The binary equivalent to the decimal number 0.3125

A | 0101 |

B | .1010 |

C | .0101 |

D | .1101 |

Question 37 |

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 38 |

A | x - 3 |

B | x - y |

C | y - 3 |

D | (x - 3)(y - 3) |

Question 39 |

A | sin ^{-1} y - sin^{-1} x + c |

B | sin ^{-1} y = 1/2 √1 - x^{2} + 1/2sin^{-1} x + c |

C | sin ^{-1} y = 1/2x √1 - x^{2} + 1/2sin^{-1} x + c |

D | sin ^{-1} y = 1/2x √1 - x^{2} + 1/4cos^{-1} x + c |

Question 40 |

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 41 |

If the equations x

^{2}−px +q = 0 and x^{2}+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 43 |

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 47 |

If (x + 1/x) = 3 , then (x

^{6}+ 1/x^{6}) is equal toA | 927 |

B | 414 |

C | 364 |

D | 322 |

Question 49 |

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

A | 198 |

B | 199 |

C | 200 |

D | 201 |

Question 50 |

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 |

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