Everything From Algebra To Physics! Only The Smartest Can Crack This Test.

1. If 7th term of an A.P is 24 & 12th term is 49. Find the 15th term:

74

66

64

56

To find the 15th term of an arithmetic progression (A.P.), we need to determine the common difference first. The difference between the 7th and 12th terms is 49 - 24 = 25. Since there are 5 terms between the 7th and 12th terms, the common difference is 25/5 = 5. Now, we can find the 15th term by adding 5 to the 12th term. Thus, the 15th term is 49 + 5 = 54. However, none of the given options match this result. Therefore, the correct answer is not available.

Explanation

To find the 15th term of an arithmetic progression (A.P.), we need to determine the common difference first. The difference between the 7th and 12th terms is 49 - 24 = 25. Since there are 5 terms between the 7th and 12th terms, the common difference is 25/5 = 5. Now, we can find the 15th term by adding 5 to the 12th term. Thus, the 15th term is 49 + 5 = 54. However, none of the given options match this result. Therefore, the correct answer is not available.

2. Time taken by light to reach Earth from the Moon is:

8 min 20s

5 min 20s

1 min 20s

5 min 10s

The correct answer is 1 min 20s. This is because light travels at a speed of approximately 299,792 kilometers per second. The average distance between the Moon and Earth is about 384,400 kilometers. Therefore, to calculate the time taken by light to reach Earth from the Moon, we can divide the distance by the speed of light. This gives us approximately 1 minute and 20 seconds.

Explanation

The correct answer is 1 min 20s. This is because light travels at a speed of approximately 299,792 kilometers per second. The average distance between the Moon and Earth is about 384,400 kilometers. Therefore, to calculate the time taken by light to reach Earth from the Moon, we can divide the distance by the speed of light. This gives us approximately 1 minute and 20 seconds.

3. The smaller a physical quantity to be measured, the more _____ instrument should be used:

Accurate

Precise

Both

Depends on the quantity

A precise instrument should be used when measuring smaller physical quantities. Precision refers to the level of detail or exactness in a measurement. When dealing with smaller quantities, it is important to use an instrument that can provide a high level of precision in order to obtain accurate and reliable measurements. Therefore, the correct answer is "Precise".

Explanation

A precise instrument should be used when measuring smaller physical quantities. Precision refers to the level of detail or exactness in a measurement. When dealing with smaller quantities, it is important to use an instrument that can provide a high level of precision in order to obtain accurate and reliable measurements. Therefore, the correct answer is "Precise".

4. If u= 2i-j+3k. The magnitude of its vector product with itself is:

√14

14

12

0

The magnitude of the vector product of a vector with itself is always zero. This is because the vector product of a vector with itself is a cross product, and the cross product of any vector with itself is always zero. Therefore, the correct answer is 0.

Explanation

The magnitude of the vector product of a vector with itself is always zero. This is because the vector product of a vector with itself is a cross product, and the cross product of any vector with itself is always zero. Therefore, the correct answer is 0.

5. Which color is not used in color printing?

Magenta

Cyan

Black

Green

Green is not used in color printing because color printing typically uses a combination of cyan, magenta, yellow, and black inks to create a wide range of colors. Green can be created by mixing cyan and yellow inks, so there is no need for a separate green ink in the printing process.

Explanation

Green is not used in color printing because color printing typically uses a combination of cyan, magenta, yellow, and black inks to create a wide range of colors. Green can be created by mixing cyan and yellow inks, so there is no need for a separate green ink in the printing process.

6. 3x^₂+2√x+7=0 is a polynomial over:

Z

R

N

W

The given polynomial equation, 3x^2 + 2√x + 7 = 0, is a polynomial over the set of natural numbers (N). This is because the equation contains only whole number coefficients (3, 2, and 7) and the variable x is not restricted to any specific set. Therefore, the equation can be solved using natural numbers as possible solutions.

Explanation

The given polynomial equation, 3x^2 + 2√x + 7 = 0, is a polynomial over the set of natural numbers (N). This is because the equation contains only whole number coefficients (3, 2, and 7) and the variable x is not restricted to any specific set. Therefore, the equation can be solved using natural numbers as possible solutions.

7. Inverse of a Column Matrix is:

Row Matrix

Column Matrix

Symmetric

None of these

The inverse of a column matrix does not exist. Inverse matrices are only defined for square matrices, and a column matrix is not a square matrix. Therefore, the correct answer is "None of these".

Explanation

The inverse of a column matrix does not exist. Inverse matrices are only defined for square matrices, and a column matrix is not a square matrix. Therefore, the correct answer is "None of these".

8. An infinite geometric sequence containing all the numbers from the set of R can't be a/an:

Fluctuating Sequence

Oscillatory Sequence

Constant Sequence

Geometric Sequence

An infinite geometric sequence is defined as a sequence in which each term is obtained by multiplying the previous term by a constant factor. Since the given sequence contains all the numbers from the set of real numbers (R), it cannot be a geometric sequence because a geometric sequence has a common ratio between consecutive terms. In this case, there is no constant factor that can be multiplied to obtain the next term. Therefore, the given sequence cannot be a geometric sequence.

Explanation

An infinite geometric sequence is defined as a sequence in which each term is obtained by multiplying the previous term by a constant factor. Since the given sequence contains all the numbers from the set of real numbers (R), it cannot be a geometric sequence because a geometric sequence has a common ratio between consecutive terms. In this case, there is no constant factor that can be multiplied to obtain the next term. Therefore, the given sequence cannot be a geometric sequence.

9. Rate of change of momentum if a force of 2N acts on a body for 4s is:

4

8

2

0.5

The rate of change of momentum is calculated by dividing the force applied on the body by the time duration for which the force is applied. In this case, a force of 2N is applied on the body for 4 seconds. Therefore, the rate of change of momentum would be 2N divided by 4 seconds, which equals 0.5Ns^-1.

Explanation

The rate of change of momentum is calculated by dividing the force applied on the body by the time duration for which the force is applied. In this case, a force of 2N is applied on the body for 4 seconds. Therefore, the rate of change of momentum would be 2N divided by 4 seconds, which equals 0.5Ns^-1.

10. Area of a room having length 2m & width 5m with absolute uncertainties 1m & 2.5m respectively in m2 might possibly be:

0, 20

9, 11

0, 10

10, 20

The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is given as 2m with an absolute uncertainty of 1m, and the width is given as 5m with an absolute uncertainty of 2.5m. To find the maximum possible area, we add the length and width values with their absolute uncertainties: (2+1) * (5+2.5) = 3 * 7.5 = 22.5m². To find the minimum possible area, we subtract the length and width values with their absolute uncertainties: (2-1) * (5-2.5) = 1 * 2.5 = 2.5m². Therefore, the possible range for the area is 2.5m² to 22.5m², which is equivalent to 0m² to 20m².

Explanation

The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is given as 2m with an absolute uncertainty of 1m, and the width is given as 5m with an absolute uncertainty of 2.5m. To find the maximum possible area, we add the length and width values with their absolute uncertainties: (2+1) * (5+2.5) = 3 * 7.5 = 22.5m². To find the minimum possible area, we subtract the length and width values with their absolute uncertainties: (2-1) * (5-2.5) = 1 * 2.5 = 2.5m². Therefore, the possible range for the area is 2.5m² to 22.5m², which is equivalent to 0m² to 20m².