Home
Current Affairs January 2024

What is the correct answer?

4

What is the volume of the region bounded by the surfaces z = x^2 + y^2 and z = 4 - x^2 - y^2?

A. 4p

B. 8p

C. 16p

D. 32p

Correct Answer :

A. 4p


Related Questions

What is the correct answer?

4

If h(x) = e^(2x), what is h'(x)?

A. 2e^(2x)

B. e^(2x)

C. 2e^(x)

D. e^(x)

What is the correct answer?

4

In parametric equations, what do the variables x and y depend on?

A. Time t

B. Angle ?

C. Radius r

D. Both a and b

What is the correct answer?

4

What is the dot product of two vectors a and b?

A. |a| × |b| × cos(?)

B. |a| × |b| × sin(?)

C. |a| + |b|

D. |a| - |b|

What is the correct answer?

4

If f(x) = 3x^2 - 2x + 1, what is the value of f(4)?

A. 25

B. 33

C. 41

D. 49

What is the correct answer?

4

Which of the following limits does not exist?

A. lim (x -> 0) (1/x)

B. lim (x -> 2) (x^2 - 4)/(x - 2)

C. lim (x -> 1) (x^2 - 1)/(x - 1)

D. lim (x -> 3) (1/x^2)

What is the correct answer?

4

What is the equation of the tangent plane to the surface z = 2x^2 + 3y^2 at the point (1, -1, 5)?

A. z = 2x - 3y + 5

B. z = 2x + 3y - 5

C. z = 2x - 3y - 5

D. z = 2x + 3y + 5

What is the correct answer?

4

What is the general solution to the differential equation dy/dx = 3x^2?

A. y = x^3 + C

B. y = 3x + C

C. y = x^3/3 + C

D. y = 3x^3 + C

What is the correct answer?

4

What does the definite integral ?(a to b) f(x) dx represent geometrically?

A. The average value of f(x) on [a, b]

B. The area between the curve y = f(x) and the x-axis on [a, b]

C. The derivative of f(x) at x = a

D. The slope of the tangent line to the curve y = f(x) at x = b

What is the correct answer?

4

If the velocity of an object is given by v(t) = 3t^2, what does ?(1 to 2) v(t) dt represent?

A. The total distance traveled by the object from t = 1 to t = 2

B. The acceleration of the object at t = 1

C. The change in velocity of the object from t = 1 to t = 2

D. The displacement of the object at t = 2

What is the correct answer?

4

What is the unit vector in the direction of vector v = <4, -3>?

A. <1, 1>

B. <2, -1.5>

C. <4/5, -3/5>

D. <0, 0>

What is the correct answer?

4

What is the distance between the points A(2, -1, 3) and B(4, 3, -2)?

A. v42

B. v30

C. v29

D. v35

What is the correct answer?

4

What is the derivative of the vector-valued function r(t) = <2t, t^2, 3t + 1> with respect to t?

A. <2, 2t, 3>

B. <2, 2t, 3t + 1>

C. <2t, 2t^2, 3>

D. <0, 0, 0>

What is the correct answer?

4

What is the equation of the polar curve r = 2cos(?)?

A. A circle centered at the origin

B. A cardioid

C. A parabola

D. A line

What is the correct answer?

4

What is the antiderivative of e^(2x) with respect to x?

A. e^(2x) + C

B. (1/2)e^(2x) + C

C. (1/2)e^(2x^2) + C

D. (1/4)e^(2x) + C

What is the correct answer?

4

What does the second derivative of a function represent?

A. The slope of the tangent line

B. The area under the curve

C. The concavity of the curve

D. The average rate of change

What is the correct answer?

4

If the rate of change of a quantity is given by f'(t) and ?(0 to 4) f'(t) dt = 10, what can you conclude about the quantity at t = 4?

A. The quantity is 10 at t = 4.

B. The quantity is 0 at t = 4.

C. The quantity is increasing at t = 4.

D. Nothing about the quantity at t = 4 can be determined.

What is the correct answer?

4

Which trigonometric substitution is commonly used to integrate rational functions involving v(a^2 - x^2)?

A. u = sin(x)

B. u = cos(x)

C. u = sec(x)

D. u = tan(x)

What is the correct answer?

4

What is the area of the region enclosed by the polar curve r = 2sin(?)?

A. p square units

B. 4 square units

C. 2 square units

D. 0 square units

What is the correct answer?

4

Which test can be used to determine the convergence of a series when its terms are all positive?

A. Alternating Series Test

B. Ratio Test

C. Integral Test

D. Comparison Test

What is the correct answer?

4

What is the integral of 1/(x^2 + 1) with respect to x?

A. arctan(x) + C

B. ln(x^2 + 1) + C

C. 2arctan(x) + C

D. (1/2)ln(x^2 + 1) + C

What is the correct answer?

4

If a car's speed is decreasing over time, what can you conclude about its acceleration?

A. The acceleration is positive.

B. The acceleration is negative.

C. The acceleration is zero.

D. Nothing about the acceleration can be determined.

What is the correct answer?

4

What is the equation of a sphere with center (1, -2, 3) and radius 4?

A. (x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 4

B. (x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 16

C. (x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 4

D. (x + 1)^2 + (y - 2)^2 + (z + 3)^2 = 16

What is the correct answer?

4

What is the line integral ?C F � dr, where C is a curve in the xy-plane and F = ?

A. It depends on the specific curve C.

B. It is always zero.

C. It is equal to the area enclosed by C.

D. It is equal to the circumference of C.

What is the correct answer?

4

What is the limit of (sin x) / x as x approaches 0?

A. 1

B. 0

C. -1

D. Undefined

What is the correct answer?

4

What is the derivative of the constant function f(x) = 7?

A. 0

B. 1

C. 7

D. -7

What is the correct answer?

4

Which test is used to determine the convergence or divergence of an infinite series involving alternating terms?

A. Integral Test

B. Comparison Test

C. Alternating Series Test

D. Divergence Test

What is the correct answer?

4

What is the area under the curve y = sin(x) from x = 0 to x = p?

A. 0

B. 1

C. p

D. 2p

What is the correct answer?

4

If a plane is defined by the equation 2x - 3y + z = 7, what is the normal vector to the plane?

A. <2, -3, 1>

B. <3, 2, -1>

C. <1, 3, -2>

D. <-2, 3, -1>

What is the correct answer?

4

What is the average value of the function f(x) = 2x^2 on the interval [1, 3]?

A. 4/3

B. 8/3

C. 16/3

D. 32/3

What is the correct answer?

4

If f(x) = sin(x), what is f'(x)?

A. cos(x)

B. -cos(x)

C. sin(x)

D. -sin(x)