Mathematics

1.

1 point

Which of the following statement is not correct about the property of closure?

1) Set A = {2, 5, 7, 4} is closed under the addition operation.

3) The set of even numbers are closed under addition, and not closed under division.

2) Set of rational numbers is closed under multiplication, and addition operations.

4) None of the above.

2.

1 point

Which of the following is the completely simplified form of 5/ (8 ̶ i)?

5/63(8 ̶ i)

(8 + i)/13

37i

26i

3.

1 point

What is the complex conjugate of (-625)^1/2 +25?

25( i -1)

5i + 25

25(i +1)

5i + 25

4.

1 point

There are 9 coins in a box, with 2/3 fair coins, and rest unfair with 75% chance of coming up head, when flipped. We randomly choose one coin and flip it 2 times, what is the probability of getting head and head?

3/16

17/48

1/4

17/51

5.

1 point

What is the units digit of (17) ^2 and (17) ^4?

1 and 9

1 and 1

9 and 1

9 and 9

6.

1 point

Which of the following is the correct Anti Derivative of ʃ X (3 ̶ X)?

[(3 - X)^3]/3 - [3(3 - X)^2]/2 + C

3X - X^2

4X - X^2

[(3 - X)^3]/2 - [3(3 - X)^2]/3 + C

7.

1 point

If X = [2/5√36 + 3/2√243], X is equal to which of the following?

17/30

18/19

19/15

21/23

8.

1 point

Which of the following is limit of (X^4 + X)/ (1 ̶ X^2), when X = ̶ 1?

̶ 3/2

3/2

2/3

̶ 2/3

9.

1 point

Which of the following satisfy the inequality {(X- 3) ^3 × (X + 2) ^4}/ {(X + 1)} > 0?

X>3

X> -3

X =0

X> -2

10.

1 point

What is the area between the curve Y = X^2 + 2x and ordinates X = − 1 and X = 0?

2/3

3/2

−2/3

−3/2

11.

1 point

If log (log(x)) =2, then what is x? Base of log assumed to be 2.

4

12

8

16

12.

1 point

If point A (5, 4) rotates by 450 degree anti-clockwise about origin, which of the following is the correct new coordinate of point A?

A(5, 4)

A(-5, -4)

A(-4, 5)

A(-4, -5)

13.

1 point

A Circle with radius R is inscribed in square ABCD, and square MNKP is inscribed in the circle. If we assume a as length of each side of square ABCD and b length of each side of square MNKP, what is the ratio of a/b?

2

1/2

√2

(√2)/2

14.

1 point

Angle A = 18 degrees is inscribed in circle O, and angle B is a central angle of circle O.
If these two angles have the same intercepted arc on circle O, then which of the following is correct?

Angle B = 27 degree

None of the above is correct.

Angle B = 36 degree

Angle B = 9 degree

15.

1 point

What is the possible units digit of (34) ^N, for 0 < N<34, where N=1, 2, 3 ……….?

7 and 8

2 and 6

4 and 6

4 and 3

16.

1 point

If 5 ^N = 7, which of the following is correct?

N = Log 7 in base 5.

N = Log (7/3)

N = Log 3 - Log 7

N = 5 in base 7

17.

1 point

What is the value of f (g (+5)) for functions, f(x) =2(x)^2 -2 and g(x) = -2(x) +5?

48

-50

50

-48

18.

1 point

What is the sum of a geometric series, with common ratio ½, and first term of ½?

1

2

3/2

- 1

19.

1 point

Triangle ABC with vertices A (1, 3), B (4, 2), C (2, 1) encountered a translation, and as an effect B coordinates changed to (3, 3).
Which of the following is the new coordinates of vertex C?

(1, 2)

(4, 2)

(3, 3)

(2, 4)

20.

1 point

A triangle ABC with vertices, A(2, 2), B( -1, 1), and C(0, 3)encounters a dilation with scale factor of 3.
Which of the following is the correct answer for new coordinates of A, B, and C?

A(2, 2), B( -1, 1) and C(0, -2)

A(6, 6), B( -3, 3) and C(0 - 6)

No answer is correct

A(2/3, 2/3), B(-1//3, 1/3) and 0, -2/3)

21.

1 point

What is the determinant of the matrix A, Shown below?
0 5 -1
1 3 2
4 0 -1

-48

57

48

-57

22.

1 point

If M= ∑ (1 – 3k), M is equal to which of the following, for k = 1, 2, 3 ...15?

345

- 345

- 322

322

23.

1 point

What is the limit of e^ (- 5X) + 2, when X → ∞?

2

0

- 2

∞

24.

1 point

What is the coordinates of vertex of graph y=∣x -3∣ +3?

x= +3 and y=+3

x= -3 and y= +3

x= -3 and y= -3

None of the above

25.

1 point

Equation of a line is given by y=2x -1, if we rotate this line by 180 degrees anticlockwise, which of the following is equation of the line after rotation?

y=-2x -2

y=2x -1

y=-2x +1

y=2x +1

26.

1 point

What is the radius of the circle with equation X^2 + Y^2 +8y ̶ 6X + 9+0?

4

-3

3

-2

27.

1 point

If grades in math at a school are normally distributed and 68% of the grades are between 35 and 67, which of the following is the correct answer for SD (Standard Deviation)?

50.5

12

16

34.5

28.

1 point

If y=e^(-2x), which of the following is the second derivative of y?

4 e^(-2x)

-2 e^(-2x)

-4 e^(-2x)

2 e^(-2x)

29.

1 point

If we flip a biased coin with the two sides labeled c and d, and an unbiased coin with two sides labeled e and f. If probability of d is ¼, what is the probability of (c, e) and (d, f)?

3/8 and 1/8

1/8 and 3/8

1/4 and 1/4

1/8 and 1/8

30.

1 point

If F(x) =∫(sinx)^2 dx, what is the value of F(x) in [0, ᴨ/2]?

ᴨ/4

ᴨ/2

ᴨ/2 + 1/4

ᴨ/4 + 1/2

31.

1 point

If f(x)=x^x which choice is correct answer for df(x)/dx?

[Ln(x) - 1]

Ln(x)

y[Ln(x) +1]

x*x^(x-1)

32.

1 point

If B and I are inverse and identity matrices of matrix A, then which of the following is correct?

[A]I =[B]

[A]/I =[B]

I/ [A] =[B]

None of the above

33.

1 point

Which statement is correct for functions, f(x) =x^2 +1 and g(x) =x^3 -2?

f(x) is not one to one, but it does have an inverse.

g(x) is one to one, and it does have an inverse.

g(x) is not one to one, and it does not have inverse.

f(x) is one to one, and it does have inverse.

34.

1 point

Equation of a hyperbola is (X/4) ^2 – (Y/8) ^2 = 1, which of the following are slope of asymptotes?

+2 and -2

+4 and -8

+1/2 and -1/2

-8 and -4

35.

1 point

What is the minimum value of 3P7 + 58M – 2N9?

678

588

687

669

36.

1 point

Point A (3, 1) is reflected over the line Y=X, which of the following is the coordinate image of A?

(-3, 1)

(1, 3)

(-1, 3)

(-3, -3)

37.

1 point

Which of the following is a correct class interval?

0 – 5, 6 – 10, 10 – 15, 16 – 21

0 – 5, 6 – 10, 10 – 15, 16 – 19

0 – 5, 6 – 10, 11 – 15, 16 – 19

0 – 5, 5 – 10, 10 – 15, 15 – 19

38.

1 point

In triangle ABC, side AB=21 cm, and side BC=11 cm, which of the following is the correct range of side AC?

10< Range <32

8< Range <32

10>Range >35

8>Range <25

39.

1 point

Cube ABCDEFGH has a surface area of 1734 square meter, and an edge length of (x-2), what is the volume of a cube with an edge length x?

6859 Cubic meter

3375 Cubic meter

4913 Cubic meter

361 Square meter

40.

1 point

5 pair of socks (10 socks) are in a box, and only one pair is blue. If randomly we choose two socks, which of the following is the probability to pick both socks blue?

1/45

1/25

1/50

1/49

41.

1 point

What is the common ratio in the geometric sequence, - 27, 81, - 243, 729?

1/3

3

- 1/3

- 3

42.

1 point

What is the area of the segment cut between the curve Y = X (4 ̶ 2X) and the line Y = 2X?

2/5

4/5

8/3

4/3

43.

1 point

What is the domain of function f(x) =√ (2x -3)?

(3/2, ∞]

(2/3, ∞)

[3/2, ∞)

[2/3, ∞]

44.

1 point

In the sequence of 3, 5, 7, and 9… the value of term 15 and sum of the first 15 terms respectively are:

33 and 255

33 and 270

31 and 270

31 and 255

45.

1 point

What is the limit of (X^5)/ (√(X^10 + 1)) when X → − ∞?

1/2

−1/2

− 1

1

46.

1 point

The product and sum of two integers are, -6 and +1, if these two integers are denoted by N and Z, then N and Z respectively are which of the following?

3 and -3

-2 and 3

2 and 2

1 and -6