9th Grade Mathematics Combined Counseling Test

1. If mean of data x,x+1,x+3,x+6 is 15/2,then value of x is

3

4

5

6

The mean of a set of numbers is found by adding up all the numbers and dividing by the total count. In this case, we have the numbers x, x+1, x+3, and x+6. So, the sum of these numbers is 4x+10. Dividing this sum by 4 (the count of numbers) gives us (4x+10)/4, which simplifies to x+2. We are given that the mean is 15/2, so we set x+2 equal to 15/2 and solve for x. By subtracting 2 from both sides, we get x=5. Therefore, the value of x is 5.

Explanation

The mean of a set of numbers is found by adding up all the numbers and dividing by the total count. In this case, we have the numbers x, x+1, x+3, and x+6. So, the sum of these numbers is 4x+10. Dividing this sum by 4 (the count of numbers) gives us (4x+10)/4, which simplifies to x+2. We are given that the mean is 15/2, so we set x+2 equal to 15/2 and solve for x. By subtracting 2 from both sides, we get x=5. Therefore, the value of x is 5.

2. Person A has some oranges.By adding 5/3 of these oranges to the original number,the total becomes 80.How many oranges person A has?

30

40

50

60

By adding 5/3 of the original number of oranges to the original number, the total becomes 80. This means that the original number of oranges is 80 - 5/3 of the original number. Simplifying this equation, we get 80 - 5/3x = x, where x represents the original number of oranges. Solving for x, we find that x = 30. Therefore, person A has 30 oranges.

Explanation

By adding 5/3 of the original number of oranges to the original number, the total becomes 80. This means that the original number of oranges is 80 - 5/3 of the original number. Simplifying this equation, we get 80 - 5/3x = x, where x represents the original number of oranges. Solving for x, we find that x = 30. Therefore, person A has 30 oranges.

3. Acceleration due to gravity, as we move up from the Earth's Surface-

Decreases

Increases

No effect

First increases and then decreases

As we move up from the Earth's surface, the acceleration due to gravity decreases. This is because gravity is stronger closer to the Earth's surface and weaker as we move further away. The force of gravity is inversely proportional to the square of the distance between two objects. Therefore, as we move away from the Earth's surface, the distance between us and the center of the Earth increases, resulting in a decrease in the force of gravity and consequently a decrease in acceleration due to gravity.

Explanation

As we move up from the Earth's surface, the acceleration due to gravity decreases. This is because gravity is stronger closer to the Earth's surface and weaker as we move further away. The force of gravity is inversely proportional to the square of the distance between two objects. Therefore, as we move away from the Earth's surface, the distance between us and the center of the Earth increases, resulting in a decrease in the force of gravity and consequently a decrease in acceleration due to gravity.

4. A,B,C are 3 angles of a triangle.If A-B=25 &B-C=10,then angle B is

60

45

55

40

The given information states that the difference between angle A and angle B is 25, and the difference between angle B and angle C is 10. Since the sum of the angles in a triangle is always 180 degrees, we can set up the equation A + B + C = 180. Using this equation, we can substitute the given information to get (B+25) + B + (B-10) = 180. Simplifying this equation gives us 3B + 15 = 180. Solving for B, we find that B is equal to 55. Therefore, the correct answer is 55.

Explanation

The given information states that the difference between angle A and angle B is 25, and the difference between angle B and angle C is 10. Since the sum of the angles in a triangle is always 180 degrees, we can set up the equation A + B + C = 180. Using this equation, we can substitute the given information to get (B+25) + B + (B-10) = 180. Simplifying this equation gives us 3B + 15 = 180. Solving for B, we find that B is equal to 55. Therefore, the correct answer is 55.

5. Which one is having the largest wavelength

Voilet

Green

Red

Infra red rays

In the electromagnetic spectrum, different colors of light have different wavelengths. Violet light has the shortest wavelength, followed by green and red. Infrared rays have the longest wavelength among the options given.

Explanation

In the electromagnetic spectrum, different colors of light have different wavelengths. Violet light has the shortest wavelength, followed by green and red. Infrared rays have the longest wavelength among the options given.

6. Light Year is a measuring unit of

Time

Distance

Speed

Energy

A light year is a unit of distance, not time, speed, or energy. It is the distance that light travels in one year in a vacuum, which is approximately 5.88 trillion miles or 9.46 trillion kilometers. Light years are commonly used in astronomy to measure vast distances between celestial objects, such as stars and galaxies.

Explanation

A light year is a unit of distance, not time, speed, or energy. It is the distance that light travels in one year in a vacuum, which is approximately 5.88 trillion miles or 9.46 trillion kilometers. Light years are commonly used in astronomy to measure vast distances between celestial objects, such as stars and galaxies.

7. For what value of x,the ratio 3+x:2+4x is equal to the ratio 2:3

-2

-1

0

1

To find the value of x, we can set up a proportion using the given ratios. The proportion is (3+x)/(2+4x) = 2/3. Cross-multiplying gives us (3+x)*3 = (2+4x)*2. Expanding both sides gives us 9+3x = 4+8x. Rearranging the equation gives us 5x = -5, and dividing both sides by 5 gives us x = -1. Therefore, the value of x that satisfies the given condition is -1.

Explanation

To find the value of x, we can set up a proportion using the given ratios. The proportion is (3+x)/(2+4x) = 2/3. Cross-multiplying gives us (3+x)*3 = (2+4x)*2. Expanding both sides gives us 9+3x = 4+8x. Rearranging the equation gives us 5x = -5, and dividing both sides by 5 gives us x = -1. Therefore, the value of x that satisfies the given condition is -1.

8. Isobars have same

Mass no.

Atomic no.

Neutrons

None of above

Isobars are atoms of different elements that have the same mass number. The mass number is the sum of the protons and neutrons in the nucleus of an atom. Isobars may have different atomic numbers, which represent the number of protons in the nucleus, and different numbers of neutrons, but they will always have the same mass number. Therefore, the correct answer is "mass no."

Explanation

Isobars are atoms of different elements that have the same mass number. The mass number is the sum of the protons and neutrons in the nucleus of an atom. Isobars may have different atomic numbers, which represent the number of protons in the nucleus, and different numbers of neutrons, but they will always have the same mass number. Therefore, the correct answer is "mass no."

9. 4.4gm of CO₂has following no. of atoms

Avagadro's No.

Avagadro's No * 10

Avagadro's No / 10

Avagadro's No / 4.4

The correct answer is Avagadro's No / 10. Avogadro's number represents the number of atoms or molecules in one mole of a substance. Since the question asks for the number of atoms in 4.4 grams of CO2, we need to divide Avogadro's number by 10 to find the number of atoms in one-tenth of a mole.

Explanation

The correct answer is Avagadro's No / 10. Avogadro's number represents the number of atoms or molecules in one mole of a substance. Since the question asks for the number of atoms in 4.4 grams of CO2, we need to divide Avogadro's number by 10 to find the number of atoms in one-tenth of a mole.

10. Rain is hitting vertically to a man at a speed of 3m/s when he is at rest. When he moves at a speed of 4m/s then relative velocity is-

3m/s

4m/s

5m/s

0m/s

The speed of the rain (vertical) = 3 m/s

The speed of the man (horizontal) = 4 m/s

The relative velocity of the rain with respect to the man can be found using the Pythagorean theorem:

Relative velocity = √((3 m/s)² + (4 m/s)²)

Relative velocity = √(9 + 16)

Relative velocity = √25

Relative velocity = 5 m/s

Therefore, the relative velocity of the rain with respect to the man when he is moving at 4 m/s is 5 m/s.

Explanation

The speed of the rain (vertical) = 3 m/s

The speed of the man (horizontal) = 4 m/s

The relative velocity of the rain with respect to the man can be found using the Pythagorean theorem:

Relative velocity = √((3 m/s)² + (4 m/s)²)

Relative velocity = √(9 + 16)

Relative velocity = √25

Relative velocity = 5 m/s

Therefore, the relative velocity of the rain with respect to the man when he is moving at 4 m/s is 5 m/s.

11. DNA has following base pairs

A with T and C with G

A with G and C with T

A with U and C with G

A with T and C with U

The correct answer is A with T and C with G. This is because in DNA, adenine (A) always pairs with thymine (T) and cytosine (C) always pairs with guanine (G). This pairing is essential for DNA replication and transcription processes.

Explanation

The correct answer is A with T and C with G. This is because in DNA, adenine (A) always pairs with thymine (T) and cytosine (C) always pairs with guanine (G). This pairing is essential for DNA replication and transcription processes.

12. Fill in the blank of the series- 1, 3/5, 2/5, 5/17, __ .

4/10

7/37

3/13

6/17

The given series follows a pattern where each term is obtained by dividing the numerator of the previous term by the denominator of the previous term and then adding the numerator and denominator of the previous term in reverse order. Starting with 1, we divide 1 by 5 and obtain 1/5. Then, we add 3 and 5 to get 8, resulting in 3/8. Continuing this pattern, the next term should be obtained by dividing 3 by 13, resulting in 3/13. Therefore, the correct answer is 3/13.

Explanation

The given series follows a pattern where each term is obtained by dividing the numerator of the previous term by the denominator of the previous term and then adding the numerator and denominator of the previous term in reverse order. Starting with 1, we divide 1 by 5 and obtain 1/5. Then, we add 3 and 5 to get 8, resulting in 3/8. Continuing this pattern, the next term should be obtained by dividing 3 by 13, resulting in 3/13. Therefore, the correct answer is 3/13.