Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

Find the taylor series for f(x) centered at the given value of a. Assume f(x) = sin(x), a = π.

Answer» Find the taylor series for f(x) centered at the given value of a. Assume f(x) = sin(x), a = π.

Solution:

2.

How many Kilometers in a Mile?

Answer» 1 mile is equal to 1.60934 kilometers.

Kilometerand mile belong to different measurement systems to evaluate length.

3.

What is the solution of the system of equations? y = 3x - 4 and -3y = -9x + 12

Answer» What is the solution of the system of equations? y = 3x - 4 and -3y = -9x + 12

Solution:

4.

Find the area of the parallelogram with vertices a(-3, 0), b(-1, 5), c(7, 4), and d(5, -1)?

Answer» Find the area of the parallelogram with vertices a(-3, 0), b(-1, 5), c(7, 4), and d(5, -1)?

Solution:

5.

The difference of x and a number is 6. What is the other number?

Answer» The other number is y = x + 6.

We will use the concept of algebra to find the other number.

6.

Anumber is divisible by 12. By what other numbers will that number be divisible?

Answer» The number will be divisible by 1, 2, 3, 4, and 6

We will check the factors of 12 to answer this question.

7.

Find the area of the parallelogram with vertices a(-3, 0), b(-1, 3), c(5, 2), and d(3, -1)?

Answer» Find the area of the parallelogram with vertices a(-3, 0), b(-1, 3), c(5, 2), and d(3, -1)?

Solution:

8.

Given that P = (2, 9) and Q = (4, 14), find the component form and magnitude of the vector PQ.

Answer» Given that P = (2, 9) and Q = (4, 14), find the component form and magnitude of the vector PQ.

Solution:

9.

How do you find inverse sin (-1/2)?

Answer» sin-1 (-1/ 2)= -𝜋 / 6

Sine is the primary trigonometry function.

10.

What is the value of r in the equation 4r -8 = 5r + 12?

Answer» What is the value of r in the equation 4r -8 = 5r + 12?

Solution:

11.

If sin-1x + sin-1y + sin-1z = π, then prove that x√1 - x2+ y√1 - y2+ z√1 - z2= 2xyz

Answer» If sin-1x + sin-1y + sin-1z = π, then prove that x√1 - x2+ y√1 - y2+ z√1 - z2= 2xyz

Solution:

12.

In the diagram, what is the measure of WRS?

Answer» In the diagram, what is the measure of WRS?

In the diagram, what is the measure of WRS

13.

How to write 5/6 ×4 as a fraction?

Answer» When we multiply 5/6 by 4, we get 10/3.

Fractions are a very important topicin mathematics. They form an integral part of algebra. All the fundamental operations that can be performed over integers can be performed over fractions as well. Now let's solve a problem related to fractions' multiplication.

14.

What is the value of x in the equation ln (x + 6) -ln (2x -1) = 1? -0.21,0.74,1.35,1.97

Answer» What is the value of x in the equation ln (x + 6) -ln (2x -1) = 1?

Solution:

15.

How Many Grams in a Kilogram?

Answer» There are 1000 grams in a kilogram.

Grams and kilograms are units used to measure mass.

16.

Given the function f(x) = 4|x - 5| + 3, for what values of x is, f(x) = 15?

Answer» Given the function f(x) = 4|x - 5| + 3, for what values of x is, f(x) = 15?

Solution:

17.

How Many mm in a cm?

Answer» There are 10 mm in 1 cm.

Millimeter (mm) and centimeter(cm) are used to measure length.

18.

What time is 13:40?

Answer» What time is 13:40?

Solution:

19.

Derive the equation of the parabola with a focus at (-5, 5) and a directrix of y = -1.

Answer» Derive the equation of the parabola with a focus at (-5, 5) and a directrix of y = -1.

Solution:

20.

Find the integral of (sin x - cos x) / (1 + sin x cos x) with limits 0to π/2.

Answer» Find the integral of (sin x - cos x) / (1 + sin x cos x) with limits 0to π/2.

Solution:

21.

How Many MLin an Ounce?

Answer» There are 29.5735 milliliters in 1 fluid ounce.

Ounces and ml are units used to measure volume or capacity.

22.

How Many tsp in tbsp?

Answer» 1 US tbsp is equal to 3 US tsp.

Tsp stands for teaspoon and tbsp denotes tablespoon.

23.

Find the median. 12, 8 , 5, 6, 1, 10, 13, 11

Answer» Find the median. 12, 8 , 5, 6, 1, 10, 13, 11

Solution:

24.

In each of the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also write them with the appropriate sign (greater than, less than) between them. (a) 530, 503 (b) 370,307 (c) 98765, 56789 (d) 9830415,10023001

Answer» 503 left of 530, 530>503 ; 307 left of 370, 370>307 ;56789 left of 98765, 98765>56789 ; 9830415left of 10023001, 9830415 < 10023001

Anumber lineis a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.

25.

How Many Liters Are in a Gallon?

Answer» There are 3.78541 liters in 1 US gallon.

Liters and US gallons belong to different systems of measurement for volume or capacity.

26.

What are the zeros of the function f(x) = x2 + 8x + 4, expressed in simplest radical form?

Answer» What are the zeros of the function f(x) = x2+ 8x + 4, expressed in simplest radical form?

Solution:

27.

If Sally walked 1/2 kilometer in 1/4 hour, how fast, in kilometers per hour, was she walking?

Answer» If Sally walked 1/2 kilometer in 1/4hour, how fast, in kilometers per hour, was she walking?

Solution:

28.

Suppose g is an odd function and let h = f.g. Is h always an odd function?

Answer» Suppose g is an odd function and let h = f.g. Is h always an odd function?

Solution:

29.

Find the equation of the circle whose center = ( 5, 6) and radius = 3?

Answer» Find the equation of the circle whose center = ( 5, 6) and radius = 3?

Solution:

30.

How many Inches are 8 Feet?

Answer» There are 96 inches in 8 feet.

Inches and feet are units required to quantify length.

31.

Find the equation of a line that is perpendicular to a given lineand passes through the point.

Answer» For a given straight line ax + by + c = 0, and given point (u, v), the equation of a line perpendicular to the given line and passing through the point is bx - ay + bu - av = 0.

Straightlines are a very important topic one must understand in order to do well in coordinate geometry. They are used to graphically represent linear equations and fin their applications in various fields related toengineering and science. For understanding them, we first need to understand how an equation is represented by a straight line, and how to deal with perpendicular lines.

32.

How Many MLin a Gallon?

Answer» 1 US gallon is equal to 3785.41 milliliters.

When we measure volume we use units such as ml and US gallons.

33.

How many Inches are 7 Feet?

Answer» There are 84 inches in 7 feet.

Inches and feet both are units that give the measure oflength.

34.

How many Inches in a Square Foot?

Answer» 1 square foot equals 144 square inches.

Square inch and square foot are units used to measure area.

35.

What is 7.5 as a fraction in simplest form?

Answer» The value of 7.5as a fraction in simplest form is 15/2 or 7½.

To writea fraction in its simplest form means that the numerator and denominatorcan no longer be divided by the same whole number exactly or evenly.

36.

How Many MLare in a Teaspoon?

Answer» 1 teaspoon equals 4.929 ml.

ML and teaspoon measure the quantity of volume or capacity.

37.

How many Inches in a Mile?

Answer» There are 63360 inches in a mile.

Miles and inches are both measurements of length.

38.

How many Inches in a Centimeter?

Answer» There are 0.393701 inches in 1 centimeter.

Inches and centimeters are units used to quantify length in different measurement systems.

39.

Simplify the expression: cot x sin x - sin quantity pi divided by two minus x. + cos x

Answer» Simplify the expression: cot x sin x - sin quantity pi divided by two minus x. + cos x

Solution:

40.

What is the arc length if theta is 7π/ 4, and the radius is 5?

Answer» What is the arc length if theta is 7π/ 4, and the radius is 5?

Solution:

41.

What is 6/7as a decimal?

Answer» 6/7as a decimal is equal to 0.857.

Thefractionsanddecimalsare just two ways to represent the same numbers.

42.

How Many Feet in an Acre?

Answer» There are 43560 square feet in an acre.

Feet and acres are units to measure area.

43.

How many Inches is 30 cm?

Answer» 30 cm equals 11.811 inches.

To quantify length we can use different units including centimeters and inches.

44.

Which equation can be used to solve for c? c = (5)cos(35°) c = 5/cos(35°) c = (5)sin(35°) c = 5/sin(35°)

Answer» Which equation can be used to solve for c?

Solution:

45.

How do you express sin 3θin terms of trigonometric functions of theta?

Answer» We can express sin 3θ as3 sin θ - 4 sin3θ

Trigonometric functions(also calledcircular functions or angle functions) are real functions that relate an angle of a right-angled triangle to the ratio of the other two side lengths.

46.

How much is 6 to the power of 5?

Answer» 6 to the power of 5 is 7776.

The powerof a numberisalso called the exponent. The exponent rulestell us that how many times anumbermultiply by itself.

47.

What is 4 to the power of 0?

Answer» 4to the power of 0 is 1.

We will solve the above question by using thezero property ofexponents.

48.

Evaluate the summation of 25 times 0.3 to the n plus 1 power, from n equals 2 to 10.

Answer» Evaluate the summation of 25 times 0.3 to the n plus 1 power, from n equals 2 to 10.

Solution:

49.

Let f(x) = 27x5-33x4-21x3 and g(x) = 3x2. Find f(x)/g(x)?

Answer» Let f(x) = 27x5-33x4-21x3 and g(x) = 3x2. Find f(x)/g(x)?

Solution:

50.

If a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)?

Answer» If a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)?

Solution: