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math & puzzles Online Quiz - 73

Description: math & puzzles Online Quiz - 73
Number of Questions: 20
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Tags: math & puzzles
Attempted 0/20 Correct 0 Score 0

Find the next element in the following seriesS,M,T,_

  1. T

  2. S

  3. W

  4. F


Correct Option: C

Find the next element in the following series S,M,T,__

  1. T

  2. S

  3. W

  4. F


Correct Option: C

Find the missing elements in the following series(in order) J,,M,A,,J

  1. M,J

  2. J,F

  3. M,F

  4. F,M


Correct Option: D

Find the missing elements in the following series J,,M,A,,J

  1. M,F

  2. J,M

  3. J,F

  4. F,M


Correct Option: D

Robert sold 2/3 of his pencils for $0.15 each. If he has 8 pencils left, how much money did he collect for the pencils he sold?

  1. $2.4

  2. $3.20

  3. $1.60

  4. $0.80


Correct Option: A

What is the perimeter of a regular hexagon with sides that are 22 centimeters long?

  1. 28 meters

  2. 14 meters

  3. 8 meters

  4. 7 meters


Correct Option: B

What is the perimeter of a regular hexagon with sides that are 22 centimeters long?

  1. 176 centimeter

  2. 132 centimeter

  3. 198 centimeter

  4. 66 centimeter


Correct Option: B

1 ton = 2000 pounds. If a truck weighs 2.5 tons, how many pounds does it weigh?

  1. 800 pounds

  2. 25000 pounds

  3. 5000 pounds

  4. 5500 pounds


Correct Option: C

If the perimeter of a square is 56 meters, how long is one side?

  1. 28 meters

  2. 14 meters

  3. 8 meters

  4. 7 meters


Correct Option: B

Mary is 54 years old, and her mother is 80. How many years ago was her mother three times the age of her daughter Mary?

  1. 41 years

  2. 32 years

  3. 26 years

  4. 21 years

  5. 45 years


Correct Option: A

1) A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis is

  1. 4/3

  2. 8/3

  3. 7/3

  4. 5/3


Correct Option: B

A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

  1. (0,2)

  2. (0,1)

  3. (1,0)

  4. (2,0)


Correct Option: C

The point diametrically opposite to the point P (1, 0) on the circle x2 + y2 + 2x + 4y - 3 = 0 is

  1. (-3,-4)

  2. (-3,4)

  3. (3,4)

  4. (-4,-1)


Correct Option: A

The conjugate of a complex number is 1/i-1. Then the complex number is

  1. -1/i-1

  2. 1/i+1

  3. 1/i-1

  4. -1/i+1


Correct Option: D

Let R be the real line. Consider the following subsets of the plane R × R. S = {(x, y) : y = x + 1 and 0 < t =" {(x,">

  1. neither S nor T is an equivalence relation on R

  2. both S and T are equivalence relations on R

  3. S is an equivalence relation on R but T is not

  4. T is an equivalence relation on R but S is not


Correct Option: D

The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y-intercept - 4. Then a possible value of k is

  1. 1

  2. -4

  3. 3

  4. 2


Correct Option: B

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

  1. a = 0, b = 7

  2. a = 5, b = 2

  3. a = 3, b = 4

  4. a = 2, b = 4


Correct Option: C

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

  1. -2

  2. -4

  3. -12

  4. 8


Correct Option: C

How many real solutions does the equation x7 + 14x5 + 16x3 + 30x – 560 = 0 have?

  1. 1

  2. 4

  3. 7

  4. 5


Correct Option: A

AI Explanation

To determine the number of real solutions for the equation x^7 + 14x^5 + 16x^3 + 30x - 560 = 0, we can use the concept of the Intermediate Value Theorem.

The Intermediate Value Theorem states that if a continuous function takes on two different values at two points, then it must also take on every value in between those two points.

In this case, the equation is a polynomial function of degree 7. Since polynomial functions are continuous, we can apply the Intermediate Value Theorem to determine the number of real solutions.

By plugging in some values for x, we can find that the function takes on both positive and negative values. For example:

  • When x = -10, the function value is negative.
  • When x = 0, the function value is negative.
  • When x = 10, the function value is positive.

Since the function changes sign between x = -10 and x = 0 and also between x = 0 and x = 10, by the Intermediate Value Theorem, there must be at least one real solution in each of these intervals.

Therefore, the equation x^7 + 14x^5 + 16x^3 + 30x - 560 = 0 has at least 2 real solutions.

Since the degree of the polynomial is 7, it can have at most 7 real solutions (counting multiplicities).

However, the correct answer is A) 1, which means that there is only one real solution. This suggests that there are multiple complex solutions (which are not real).

Therefore, the equation x^7 + 14x^5 + 16x^3 + 30x - 560 = 0 has 1 real solution.

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz-plane at the point (0, 17/2, -13/2) Then

  1. a = 2, b = 8

  2. a = 4, b = 6

  3. a = 6, b = 4

  4. a = 8, b = 2


Correct Option: C
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