Mathematics Skills Test

Mathematics Skills Test

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While multiplying two numbers say x and y, the value of y was written as 73 instead of 37. Due to this, the result increased by 504. Which of the following should be the actual product?

a. 518

b. 1022

c. 1240

d. 680

e. 492

In how many different ways can the letters of the word 'DETAIN' be arranged so that the vowels occupy only the even positions?

a. 6

b. 12

c. 18

d. 36

A circle is centered at (3,4), and a point (5,2) lies on the circle. What is the area of the circle?

a. (2√2)π

b. 3π

c. 8π

d. (√2)π

Four vertices A,B,C and D of a parallelogram ABCD are (-2,-1),(0,3),(4,0), and (x,y) respectively. What is the value of (x,y)?

a. (2,-1)

b. (3,-2)

c. (4,-3)

d. (-3,4)

e. (2,-4)

This question is based upon the figure shown below

Which of the following lines in the given graph has an undefined slope?

a. A

b. B

c. C

d. D

In how many different ways can you arrange the letters of the word 'AUTHENTICATION' so that the vowels always come together?

a. 12,700,800

b. 4,233,600

c. 101,606,400

d. 8,467,200

The simplified form of equation ((4 + 3i)(4 - 3i)(5 + i))/(1 - 2i) is:

a. 45/√5 + 17/√5i

b. 30/√2 + 56i

c. 15 + 33i

d. 15 + 55i

e. 33 + 55/√3i

The list price of a mobile phone is Rs 30,000. Ms Y gets a discount of 10%. If the sales tax is 8.5%, what will be the final amount paid by Ms Y for the mobile phone?

a. Rs 32,550

b. Rs 25,259

c. Rs 29,550

d. Rs 29,295

Which of the following represents the sum of all the terms of the given infinite geometric sequence?

{1/2,-1/4,1/8,-1/16,......}

a. 1/2

b. -1/3

c. 1/3

d. 8

If we expand sin6(x)-1 then it will result in which of the following?

a. (22 sin[x] - 5 sin[3x] + sin[5x])/16,

b. (-22 - 15 cos[2x] + 6 cos[4x] - cos[6x])/32

c. (22+ 15 cos[2x] + 6 cos[4x] + cos[6x])/32

d. sin(x) (-1+sqrt[5])/ sqrt(10-2 sqrt[5])

What is the number of ways in which the letters of the word 'READING' can be arranged so that all the vowels always come together?

a. 120

b. 360

c. 720

d. 900

Find the values of c if a straight line y = 2x + c,is tangent to the ellipse x²/9 + y2/4 = 1.

a. ± 4√ 5

b. ± 3

c. ± 2

d. ± 2√ 10

If two diameters of a circle have equations 3x - 4y = 5 and 3x - 5y = 7 and area of circle is 154 sq. units, then which of the following is the equation of the circle?

a. x² + y² - 2x + 4y = 45

b. x² + y² + 2x + 4y = 44

c. x² + y² + x + 4y = 44

d. x² + y² - 2x + y = 34

e. x² + y² - 2x + y = 49

Find the sum of the given infinite series:

1 - 0.45 + (0.45)² - (0.45)³ + .....

a. 1.45

b. 1

c. 14.5

d. 100/145

Find the distance of the middle point of the line joining the points (a sec²t-a tan²t, 0) and (0, 2a sin²t+2a cos²t) from the origin.

a. a / 2

b. √ 5a / 4

c. √ 5a / 2

d. √ 3a / 2

Find the distance between the points A(29,25) and B(-32,-15).

a. √(5321)

b. √(5311)

c. √(5312)

d. √(5331)

Which two of the following are the coordinates of a square whose sides are parallel to the coordinate axes and is inscribed in a circle with the equation x² + y² - 4x + 6y + 5 = 0.

a. (4,-1)

b. (-4,-1)

c. (1,-7)

d. (0,-5)

e. (4,0)

Which of the following is the equation of a locus of a point, which moves in such a way that its distance from point A (0,ab) is b times its distance from point B (0,a/b) where b > 0 and b ≠ 1?

a. x² + y² = a²

b. x² + y² = a² - 4aby

c. x² + y² = b²

d. 2x² + 2y² = a²

e. x² - y² = b²

Mark bought a laptop priced at $3260 at a discount of 20%. He also paid a sales tax of 8% after the discount. Which of the following is the amount paid by Mark?

a. $3124.50

b. $2650.78

c. $2980.40

d. $2816.64

A banker's gain on a certain amount due 3 years hence is $48. If the rate of interest is 10% per annum, then which of the following is the value of the present worth?

a. 160.36

b. 380.50

c. 533.33

d. 612.43

Complete the following series: 4, 12, __, 108, 324

a. 24

b. 36

c. 64

d. 48

A salesman gained 327 rupees by selling bananas, apples and oranges. He sold 27 bananas and 31 oranges. The selling price of a banana, apple, and orange is 2 rupees, 4.5 rupees, and 3 rupees respectively. The percentage of revenue generated on selling bananas is ______ and on selling apples is ______ of the total revenue.

a. 32.17%, 44.60%

b. 16.51%, 55.05%

c. 12.30%, 62.14%

d. 24.33%, 59.54%

This question is based upon the figure shown below

Which of the following will be the output of the given equation?

a. i

b. 1

c. i +1

d. 2i +1

e. i-1

Find the condition under which the line 3x + 2y + c = 0 may be tangent to the parabola y² = px.

a. p = 3c

b. p = c

c. p = 2c

d. p = 1/2c

Which of the following is the correct slope of a line that makes a 30° angle with the X-axis?

a. 0.41

b. 0.62

c. 0.39

d. 0.58

Which of the following options is the output obtained after simplifying the given expression?

[ i²³ + (1/i)³⁷]²

a. 0

b. -1

c. -2

d. -4

e. 3

f. 6

The slope of the normal to the parabola y²=4ax at point (ap³,4ap) will be:

a. -4p

b. p

c. -2p

d. -p

e. -8p

Find the Cartesian equation of the curves having parametric equations as x=1+4cosθ and y=3+4sinθ.

a. (x-1)²+(y-3)²=4

b. (x)²+(y)²=64

c. (x-1)²+(y-3)²=16

d. (x-4)²+(y-4)²=64

Find the equation of tangent to hyperbola 3x²-2y² = 5 such that it is parallel to line y = 3x+5.

a. y=3x ± √(75/6)

b. y=3x ± √(5)

c. y=3x ± √(89/8)

d. y=3x ± √(61/3)

e. y=3x ± √(23/12)

Which of the following is the correct rectangular form of the given equation?

(2√2/ √3) (cos135° + isin135°)

a. 2√2/3 +i2/3

b. -2/√3 +2i/√3

c. 2√2/3 -2i/3

d. 2/3 -2√2i/3

e. 2/3 -2√2i/3

What will be obtained, if we simplify the given term?

i⁷²⁰² - i⁷²

a. 1

b. -1

c. i

d. -i

e. 2

f. -2

g. 0

If the locus of a point has equation (a-c)x+(b-d)y+e=0 and the point is equidistant from points (a,b) and (c,d) then which of the following is the value of e?

a. -½ (a²+b²+c²+d²)

b. √ (2)(a²-b²-c²-d²)

c. √ (2) (a²+b²-c²-d²)

d. -½ (a²+b²-c²-d²)

The length of a latus rectum of the ellipse having equation 4x² + 25y² = 100 is:

a. 8/5

b. 3/5

c. 2/3

d. 9/4

Consider a bag containing 5 green, 7 black and 4 white marbles. If three marbles are drawn randomly then what is the probability that none of them is white?

a. 10/21

b. 11/28

c. 12/23

d. 13/18

e. 15/17

In how many ways can the letters of the word 'EXPERT' be arranged?

a. 140

b. 144

c. 360

d. 720

Which of the following is the equation of a straight line that passes through point (4,3) and is perpendicular to the line having equation, 2x+y+1=0?

a. 2y-2x-1=0

b. 2y-x-1=0

c. y-x-1=0

d. 2y-x-2=0

The two vertices of an equilateral triangle are (3,2) and (4,-1). Find the third vertex and choose the correct option.

a. ((4 ± 3√ 3) / 2, (2 ± √ 3) / 2)

b. ((7 ± √ 3) / 2, (1 ± √ 3) / 2)

c. ((7 ± 3√ 3) / 2, (1 ± √ 3) / 2)

d. ((1 ± 3√ 3) / 2, (7 ± √ 3) / 2)

If an antenna of 10 m casts a shadow of 10 m on the ground, then what is the sun's elevation?

a. 60°

b. 45°

c. 30°

d. 90°

Consider three points: P(5,9); Q(1,4); and R(x,-1). Find the values of "x" such that the distance between P and Q (PQ) is equal to the distance between Q and R (QR)?

a. 5, -3

b. -5, 5

c. -3, 5

d. -3, 3

e. -3, 4

In a class, there are 15 students (7 boys and 8 girls). 6 students are to be selected to form a committee so that there are at least 4 girls in the committee. In how many ways can it be done?

a. 1498

b. 1862

c. 1470

d. 1890

What is the probability that a number less than or equal to 3 is obtained when a dice is rolled?

a. 1/4

b. 1/2

c. 1/3

d. 1/6

Consider the following equation

((a-2) ÷ (2 +i)) + ((b-2)) ÷ (2-i))= -i

If a and b are real numbers, then which of the following are correct values of a and b?

a. 4, 2

b. 9/2, -1/2

c. -2, 4

d. -5/2, 3/2

e. 1, 2

If the three vertices of a triangle are (4b,3b), (7b,0), and (3b,5b) where b > 0 and area is 24 units, then what will be the centroid?

a. (28/3,29/3)

b. (56/3,32/3)

c. (16,15)

d. (13,8)

e. (20,17)

A man decided to go daily for a morning walk to keep himself fit. He decided to walk for 10 minutes on the first day and increase the time by five minutes each day. On which day, will he be able to walk for 135 minutes?

a. 22th day

b. 24th day

c. 26th day

d. 28th day

Which of the following is the equation of a line that passes through the point (-3,4) and has equal intercepts on coordinate axis?

a. x+y+2=0

b. x+y-1=0

c. -3x-2y-1=0

d. 3x+2y+1=0

Simplify the following expression into a +bi form:

((7 + 2i) ÷ (4- 7i)) * 5i

a. 14/13 + 57i/13

b. – 234/65 + 81i/65

c. – 59i/15 + 18/15

d. – 234i/65 + 61/65

e. –57/13 + 14i/13

A triangle with vertices (3a,a), (a,3a) and (a,a) will have an area of 32 units if:

a. a=±1

b. a=± 4

c. a=± 2

d. a=± 8

A dice is rolled and a coin is tossed. What is the probability of getting an even number and tails together?

a. 1/4

b. 1/2

c. 1/6

d. 1/3

e. 2/3

The points A (4a,0), B (0,4b), and C (2a,2b) are _____________.

a. vertices of an obtuse triangle

b. vertices of an acute triangle

c. vertices of a right-angled triangle

d. collinear

Which of the following is the correct polar form of the equation:

z = 4√3 - 4i

a. z=4√3(cos60° + isin60°)

b. z=4(cos45° – isin45°)

c. z=√8(cos60° + isin60°)

d. z=16(cos30° + isin30°)

e. z=8(cos30° – isin30°)

f. z=8√3(cos45° + isin45°)

This question is based upon the figure shown below

What will be the output after simplifying the given equation?

a. i +1

b. 4i/5 + 2/5

c. 4i/3

d. 2i/3 + 1/3

e. 2i