# eLitmus/Engineering eLitmus Aptitude Sample Test,Sample questions

1.31 and 41

2.13 and 67

3.17 and 7

4.None

## Question: ``` Centre of a circle is (2, 3). If the line x + y = 1 touches, its equation is ```

1.x2 + y2 - 4x - 6y + 4 = 0

2. x2 + y2 - 4x - 6y + 5 = 0

3.x2 + y2 - 4x - 6y - 5 = 0

4.None of these

1.9

2.10

3.11

4.12

1.5 x 2^99 - 6

2. 5 x 2^99 + 6

3.6 x 2^99 + 5

4.6 x 2^99 - 5

1.0

2.1

3.2

4.3

1.{-1, 1}

2. {-1, 0}

3. {0, 1}

4.{-1, 0, 1}

## Question: ``` PT Usha and Shelly John decide to run a marathon between Ramnagar and Jamnagar. Both start from Ramnagar at 1 pm. On the way are two towns Ramgarh and Rampur, separated by a distance of 15 km. PT Usha reaches Ramgarh in 90 minutes running at a constant speed of 40 kmph. She takes additional 30 minutes to reach Rampur. Between Rampur and Jamnagar she maintains an average speed of V kmph (where V is a whole number),Shelly John being a professional marathon runner, maintains a constant speed of 18 kmph. They both reach Jamnagar together after 'n' hours, 'n' being a whole number. What could be total time taken by PT Usha? ```

1.5 hours

2.15 hours

3.41 hours

4.All of the above

## Question: ```-------------- is equal to ```

1.cos isin - ?

2.. cos9 isin9 ? - ?

3.sin icos ?- ?

4.sin 9 icos9 ? - ?

1.2

2.9

3.11

4.27

1.45 kmph

2.50 kmph

3.35 kmph

4.None of these

1.1100 yards

2.1200 yards

3.1300 yards

4.1400 yards

1.A and B

2. A and C

3.B and C

4.A and D

1. y = x + 4v5

2.y = x + v53

3. y= x + z

4.None of These

1.70%

2.75%

3.80%

4. 60%

1.112

2.140

3.164

4.None of these

1.1

2.1/256

3.81/256

4.175/256

1.100 v3

2.200 v3 / 3

3.100 v3 / 3

4.200 v3

## Question: ```A real number x satisfying 1- (1/n) Ã¢â€°Â¤ 3 + (1/n), for every positive integer n, is best described by Ã¢â€°Â¤ ```

1.1 < x < 4

2.1 < x Ã¢â€°Â¤ 3

3. 0 < x Ã¢â€°Â¤4

4.1 Ã¢â€°Â¤ x Ã¢â€°Â¤ 3

## Question: `A rectangular sheet of paper, when halved by folding it at the midpoint of its longer side, results in a rectangle, whose longer and shorter sides are in the same proportion as the longer and shorter sides of the original rectangle. If the shorter side of the original rectangle is 2, what is the area of the smaller rectangle?`

1.4âˆš2

2.2âˆš2

3.âˆš2

4.None of the above

1.25:64

2.16:25

3.64:25

4. 4:5

## Question: ```Angle between the pair of straight lines x2 â€œ xy â€œ 6y2 â€œ 2x + 11y â€œ 3 = 0 is ```

1.450 , 1350

2. tan-1 2, p = tan-1 2

3. tan-1 3, p = tan-1 3

4.None of these

1.p = q

2.p < q

3.p > q

4.p = q/2

1.(3 , 3 / 2)

2.(3 / 2 , 3)

3.(-3 , 3 / 2)

4.(-3 , -3 / 2)

1.75

2.84

3.80

4.None of These

1.6

2.5

3.4

4.3

## Question: ```Given that -1 Ã¢â€°Â¤ v Ã¢â€°Â¤ 1, -2 Ã¢â€°Â¤ u Ã¢â€°Â¤ -0.5, and -2 Ã¢â€°Â¤ z Ã¢â€°Â¤ -0.5 and w = vz/u, then which of the following is necessarily true? ```

1.-0.5 Ã¢â€°Â¤ w Ã¢â€°Â¤ -2

2.-4 Ã¢â€°Â¤ w Ã¢â€°Â¤ 4

3.-4 Ã¢â€°Â¤ w Ã¢â€°Â¤ 2

4. -2 Ã¢â€°Â¤ w Ã¢â€°Â¤ -0.5

1.41/2 days

2. 21/2 days

3.63/4 days

4. 65/4 days

## Question: ```If 1/a + 1/b + 1/c = 1 / (a + b + c); where a + b + c 1 0; abc 1 0, then what is the value of ( a + b ) ( b + c ) ( c + a )? ```

1.Equal to 0

2.Greater than 0

3.Less than 0

4.Cannot be determined

1.3/2

2. sqrt(15)

3.sqrt(6)/2

4.15

1. A = 2B

2.1 / 3 B

3.A = B

4.3A = 2B

1.x1x2x3x4 = 0

2. y1y2y3y4 = 1

3. y1y2y3y4 = 0

4.x1x2x3x4 = -1

## Question: ```If a circle passes through the point (a, b) and cuts the circle x2 + y2 = 4 orthogonally, then locus of its centre is ```

1.2ax + 2by + (a2 + b2 + 4) = 0

2.2ax + 2by - (a2 + b2 + 4) = 0

3.2ax - 2by + (a2 + b2 + 4) = 0

4.2ax - 2by - (a2 + b2 + 4) = 0

## Question: ```If a, ÃƒÅ¸ are the roots of ax2 - 2bx + c = 0 then a3 ÃƒÅ¸3 + a2ÃƒÅ¸3 + a3ÃƒÅ¸2 is ```

1.c2(c + 2b) / a3

2.bc3 / a3

3.c2 / a3

4.None of these

1.15 / 15

2. 21 / 20

3.15 / 21

4.20 / 21

1.120 v2 / 23cm

2. 60 v2 / 23cm

3.30 v2 / 23cm

4.None of these

1.v2 cos?

2.- v2 sin?

3.- v2 cos?

4.None of these

1.2

2.4

3.6

4.8

1.c2 = 2a2

2. c = 2a

3. 2c2 = a2

4.None of These

## Question: ```If the product of n positive numbers in 1, then their sum is ```

1.pa ositive integer

2.divisible by n

3.equal to n + (1 / n)

4.never less than n

1.1 + x / n

2.1 + n / x

3.1 + 1 / x

4.n(1 + 1 / x)

1.-2/5

2.-2

3.10/17

4.None of these

## Question: ```In how many ways can 10 engineers and 4 doctors be seated at a round table if all the 4 doctors do not sit together? ```

1.13! - (10! Ãƒâ€” 4!)

2.13! Ãƒâ€” 4!

3.14!

4.10! Ãƒâ€” 4!

## Question: ```Incentre of the triangle whose vertices are (6, 0) (0, 6) and (7, 7) is ```

1.(9 / 2 , 9 / 2)

2.(7 / 2 , 7 / 2)

3.(11 / 2 , 11 / 2)

4.None of these

1.7236

2.7362

3.7326

4.None of These

1.7236

2.7362

3.7326

4.None of These

1.90

2.82

3.84

4.64

1.4

2. 6

3.8

4.10

1.x < 3

2. x > 3

3.x = 3

4.x = 3

1.900

2.300

3. tan-1(Â½)

4.450

## Question: ```The area bounded by curve y = 4x â€œ x2 and x â€œ axis is ```

1.30 / 7 sq. units

2. 31 / 7sq. units

3.32 / 3 sq. units

4.34 / 3 sq. units

## Question: ```The area bounded by curve y = 4x â€œ x2 and x â€œ axis is ```

1.30 / 7 sq. units

2.31 / 7sq. units

3.32 / 3 sq. units

4.34 / 3 sq. units

1.91 / 15

2.91 / 30

3.19 / 30

4.None of these

1.1

2.2

3.2 v2

4.4

1.2 v2a2

2.2a2

3.4a2

4.None of these

## Question: ```The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x2 + y2 = 9 is ```

1.(3 / 2 , 1 / 2)

2. (1 / 2 , 3 / 2)

3. (1 / 2 , 1 / 2)

4. (1 / 2 , -2Â½)

## Question: ```The coordinates of foot of the perpendicular drawn from the point (2, 4) on the line x + y = 1 are ```

1.(1 / 2 , 3 / 2)

2.(-1 / 2 , 3 / 2)

3.(3 / 2 , -1 / 2)

4. (-1 / 2 , -3 / 2)

1.7 / 2

2. 7 / 3

3.7 / 5

4.7 / 10

1.4/3

2.7/16

3.3 / 17

4.3 / 4

1. m = 1

2.m = 2

3.m = 3

4.m = 4

1.R

2.R "â€œ {1}

3.(-1)

4. R "â€œ {-1}

1.a = 1/b

2. a = c

3.b = ac

4.a = b

## Question: ```The set of all integers x such that |x â€œ 3| < 2 is equal to ```

1.{1, 2, 3, 4, 5}

2.{1, 2, 3, 4}

3.{2, 3, 4}

4.{-4, -3, -2}

1.300

2.450

3.600

4.750

1.1/39

2.1/28

3.1/17

4.1/6

1. isosceles

2.right angled

3.equilateral

4.None of these

1.e

2.e^2

3.e-p/2

4.2v2

## Question: ```Three lines 3x + 4y + 6 = 0, 2x 3y 2 2 0 + + = and 4x 7y 8 0 + + = are ```

1.Parallel

2.Sides of a triangles

3.Concurrent

4.None of these

1.5/27

2.4/27

3.5/36

4.None of these

1. Rs. 93,300

2.Rs. 93,200

3. Rs. 93,100

4.None of these

1.1/18

2.64/4032

3.63/64

4.1/9

1.-1 / 2

2.1 / 2

3.v3 / 2

4.None of these

1.85

2.86

3.84

4.89

## More MCQS

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