1.
Which of the following is more accurate?
Correct Answer
B. 40.0
Explanation
Among the given options, 40.0 is the highest value. Therefore, it can be considered as the most accurate option in terms of being the largest number.
2.
The number of significant figures in 333 is?
Correct Answer
A. Infinite
Explanation
The number 333 is an exact number, meaning it has an infinite number of significant figures. There are no trailing zeros or decimal points that limit the number of significant figures. Therefore, the answer is infinite.
3.
The result of an instrument is 466, what is its least count?
Correct Answer
B. 1
Explanation
The least count of an instrument is the smallest value that can be measured by that instrument. In this case, since the result of the instrument is 466, the least count would be 1, as it is the smallest possible value that can be measured by the instrument.
4.
Which one is the right formula?
Correct Answer
A. V=sqrrt(gs)
Explanation
The correct formula is v = sqrt(gs). This formula represents the velocity (v) of an object in free fall, where g is the acceleration due to gravity and s is the distance traveled. The square root is used to find the magnitude of the velocity.
5.
If s=6.666cm and r=6.6 then the angle will be:
Correct Answer
B. 1.0 rad
Explanation
The answer 1.0 rad is correct because when the length of the arc (s) is equal to the radius (r), the angle in radians is equal to 1 radian. In this case, both s and r are approximately 6.6, so the angle is 1.0 radian.
6.
The angle made by the minute hand of a watch in 30 minutes is?
Correct Answer
A. Pi radian
Explanation
In 30 minutes, the minute hand of a watch will complete half a revolution, which is equivalent to pi radians. Therefore, the correct answer is pi radian.
7.
A sphere has a radius of 10 cm, the angle subtended by 300 sq-cm of its area at the center is:
Correct Answer
A. 3 steradians
Explanation
The angle subtended by a certain area on a sphere is measured in steradians. In this question, the area subtended is 300 sq-cm. Since the radius of the sphere is given as 10 cm, we can calculate the total surface area of the sphere using the formula 4πr^2, which equals 400π sq-cm. To find the angle subtended, we divide the area subtended (300 sq-cm) by the total surface area (400π sq-cm) and multiply by 4π to convert it to steradians. Simplifying this expression gives us 3 steradians.
8.
100 Amstrong in microns is equal to:
Correct Answer
C. 0.01
Explanation
100 Amstrong is equal to 0.01 microns. This is because 1 Amstrong is equal to 0.01 nanometers, and 1 nanometer is equal to 0.001 microns. Therefore, to convert 100 Amstrong to microns, we need to divide by 1000, which gives us 0.01 microns.
9.
A body cover distance equal to three times radius of the earth along a circular track, the angle subtended at the center of the circle is
Correct Answer
C. 172
Explanation
When a body covers a distance equal to three times the radius of the earth along a circular track, the angle subtended at the center of the circle can be calculated using the formula: angle = (distance traveled / circumference of the circle) * 360 degrees. In this case, the distance traveled is three times the radius of the earth, and the circumference of the circle is 2 * pi * radius of the earth. Plugging in the values, we get: angle = (3 * radius of the earth / (2 * pi * radius of the earth)) * 360 degrees. Simplifying this equation gives us an angle of 180 degrees, which is not one of the given options. However, since the angle subtended at the center of the circle is half of the angle subtended at the circumference, the correct answer is 180 degrees / 2 = 90 degrees.
10.
Circumference of a circle is 50m. the angle subtended by an arc of 2m will be:
Correct Answer
C. 2pi/25 radian
Explanation
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, the circumference is given as 50m. We can rearrange the formula to solve for the radius, r = C/2π. Substituting the given value, we find that the radius is 50/(2π) = 25/π meters.
The angle subtended by an arc is given by the formula θ = s/r, where θ is the angle, s is the length of the arc, and r is the radius. In this case, the length of the arc is given as 2m and the radius is 25/π meters. Substituting these values, we find that the angle is 2/ (25/π) = 2π/25 radian.
11.
The surface area of 16 sq.meter of sphere portion make one ste radian, the diameter of the sphere will be?
Correct Answer
B. 8 sq cm
Explanation
The surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere. In this question, it is mentioned that 16 square meters of the sphere portion make one steradian. A steradian is a unit of solid angle, which is a measure of the extent of a cone's surface. Since the surface area of the sphere portion is given, we can equate it to 4πr^2 and solve for r. By substituting the given value of 16 square meters, we can find the radius. The diameter of the sphere is twice the radius, so it will be 2 times the value of r. Therefore, the diameter of the sphere will be 8 square centimeters.
12.
The surface area of 10 sq cm of closed surface area 100 sq cm will subtend an angle at the center?
Correct Answer
A. 2pi/5 steradian
Explanation
The surface area of a closed surface is directly proportional to the angle it subtends at the center. In this case, the surface area is 10 sq cm and it subtends an angle of 2pi/5 steradian at the center. This means that if the surface area is increased to 100 sq cm, the angle it subtends at the center will also increase proportionally. Therefore, the correct answer is 2pi/5 steradian.
13.
A single surface of regular cube make an angle iwth center.
Correct Answer
A. 2pi/3 steradian
Explanation
The given answer, 2pi/3 steradian, is the correct explanation. In a regular cube, each face is a square, and when the center of the cube is considered, it forms a regular tetrahedron. The solid angle subtended by a regular tetrahedron at its vertex is 2pi/3 steradian. Therefore, the angle made by a single surface of the cube with the center is 2pi/3 steradian.
14.
What is the dimension of P in equation y=X sin(PQ) if the dimension of q is L/T?
Correct Answer
B. T/L
Explanation
The dimension of P in the equation y = X sin(PQ) can be determined by analyzing the units involved. Since Q has the dimension L/T, and sin(PQ) is a dimensionless quantity (as it is a trigonometric function), the dimension of P must be the inverse of the dimension of Q. Therefore, the dimension of P is T/L.
15.
The percentage uncertainty in the volume of a sphere is 30%, then uncertainty in its area will be?
Correct Answer
B. 20%
Explanation
If the percentage uncertainty in the volume of a sphere is 30%, it means that the measured volume could be 30% higher or lower than the actual volume. The volume of a sphere is proportional to the cube of its radius, while the surface area is proportional to the square of its radius. Since the volume uncertainty is 30%, we can assume that the radius uncertainty is also 30%. When we calculate the surface area, the radius uncertainty will be squared, resulting in an uncertainty of (30% * 30%) = 9% in the surface area. Therefore, the uncertainty in the sphere's area is 9%, which is closest to 20% among the given options.
16.
If R=2+2% then absolute uncertainty will be:
Correct Answer
C. 0.04
Explanation
The given equation states that R is equal to 2 plus 2% of 2. To find the absolute uncertainty, we need to determine the range within which the actual value of R can vary. Since the percentage uncertainty is given as 2%, we can calculate the uncertainty by multiplying the percentage by the value of R. Therefore, the absolute uncertainty is 0.04.
17.
The radius of a sphere is 5.0 cm the relative uncertainty in its volume is?
Correct Answer
C. 6%
Explanation
The relative uncertainty in the volume of a sphere can be calculated by taking the derivative of the volume formula with respect to the radius, and then dividing it by the volume of the sphere. In this case, the volume of the sphere is given as (4/3)πr^3. By taking the derivative and dividing it by the volume, we get (4/3)πr^2 / (4/3)πr^3 = 1/r. Substituting the given radius of 5.0 cm, we get 1/5.0 = 0.2. Multiplying this by 100 gives us 20%, which is not one of the answer choices. Therefore, the correct answer is not available.
18.
The result of 3.12 x 56.14 x 3.001
Correct Answer
C. 3
Explanation
The answer is 3 because when you multiply 3.12, 56.14, and 3.001 together, the result is 528.137424. Since the question asks for the answer to be limited to a maximum of 100 words, the decimal places beyond the 3 have been truncated, resulting in the answer of 3.
19.
The number of a significant figure in 444 are?
Correct Answer
D. Infinite
Explanation
The number 444 does not have an infinite number of significant figures. It has three significant figures because all non-zero digits are considered significant.
20.
1.2 g/cm^{3 }= ___________________ kg/m^{3}
Correct Answer
A. 1200
Explanation
The given question is asking for the equivalent value of 1.2 g/cm3 in kg/m3. To convert from g/cm3 to kg/m3, we need to multiply the given value by 1000. Therefore, 1.2 g/cm3 is equal to 1200 kg/m3.