Objective Questions

Which of the following circuit element stores energy in electromagnetic field?

A parallel plate air capacitor with no dielectric between the plates is connect…

A galvanometer has spring constant 'k', a magnetic field 'B' and deflection ang…

Electric field is steepest in the direction in which the potential

When a positive charge is moved in an electrostatic field from a point at high …

A galvanometer of 50 ? gives full scale deflection with 2 mA current. To conver…

Determine the electric flux emerging from a circular surface radius 0.025m if t…

Stationary points of \( y = x^3 + 12x^2 + 45x + 50 \) are?

An alternating voltage whose peak value is 80 volts is connected across a 60 oh…

A current 3A flows through a metre length conductor. Calculate the force experi…

A given RLC circuit has R=100Ω, L=1H and C=10μF all connected in series with a …

A magnetic induction of 20μT is applied to a long straight current-carrying wir…

A metal ball of 10kg with 5 C charge is moving perpendicular to a magnetic fiel…

Which of the following circuit elements stores energy in an electromagnetic fie…

Simplify \( \int 3x^2 e^{x^3} dx \)

A galvanometer has a spring constant 'k', a magnetic field 'B' and deflection a…

If \( y = \int f(x)dx+C \), then \( f(x)dx \) is called the ____.

Which of the following copper conductors has the least resistance?

A given RLC circuit has R=100Ω, L=1H and C=10μF all connected in serie…

In a semiconductor crystal, if current flows due to breakage of crystal bonds, …

Which of the following circuit element stores energy in a magnetic field?

A galvanometer has spring constant 'k', a magnetic field 'B' and deflection ang…

Which of the following copper conductor would have the least resistance?

A capacitor has a capacitance of 4.0 μF. The resistor has a resistance of 2.…

One electronVolt is defined as:

An infinite number of charges, each equal to q, are placed along the x-axis at …

Determine the force between two protons placed at a distance of 1μm.

Evaluate ∫ dx / (x² + 4x + 7)

If y = ∫ f(x)dx + C, then f(x) is…

Range where \( y = 2x^3 - 3x^2 - 12x + 2 \) is increasing?

The resonant frequency of a circuit is 1000 KHz. If each of capacitance and …

Range where \( y = 1 - 3x^2 - x^3 \) is decreasing?

Differentiate \( y = \ln(5x^2 + 3)^4 \).

Find dy/dx if y = log_e(cos x).

If y = e^2x log(x+6), find dy/dx.

Evaluate ∫ (e^2x + e^-2x)/(e^2x - e^-2x

Simplify ∫ ln x dx.

Find dy/dx if y = log_e(cos x)

Evaluate the integral ∫ dx / (x² + 4x + 7).

Evaluate lim(x→5) (2x²-9x-5)/(x²-x-20)

Evaluate lim(x→1/2) (8x³-1)/(2x-1)

Evaluate lim(x→0) (√(x+9)-3)/(2x)

Evaluate lim(x→π/2) cot(x)/cos(x)

Evaluate lim(x→0) sin(x)(1-cos(x))/x

Differentiate e^(5x²+1) + 4^(cos3x) with respect to x

Find d/dt[cosec⁻¹(3t)]

Evaluate ∫x·e^(x²) dx

Evaluate ∫x·e^(6x) dx

Evaluate ∫₋₁² x·e^(6x) dx

Given f(0)=1, f'(0)=5, f(2)=3, f'(2)=7, and f, f' exist, find the value of ∫₀² …

Evaluate ∫₀^π sin³(t) dt

Calculate ∫₋₁⁰ z·e^(-z) dz

Evaluate ∫₁⁴ (⅛x^(3/2) - 4/x) dx, x>0

A child has 200ft of fence wire and wants to enclose a rectangular area for pet…

A certain substitution gives ∫sin²x·cosⁿx dx = ∫uⁿ - u⁷ du. What is n?

Differentiate (x+3)/(2x-5)

Differentiate e^(2x)/(2x-3)²

Find dy/dx of y = sin(x)/x

The first derivative of ln(x²/(x²+1)) is

Find dy/dx of the implicit function x²y + x(y+1)² = 2 at (x,y) = (1,1)

Find dy/dx at (1,1) of the implicit function x²+x+y³=0

Evaluate dx/dy at (1,-1) of the implicit function x²+x+y³=0

Evaluate dy/dx of the implicit function e^(x+y) - (x²+1)y = 5

Evaluate the second derivative of y = tan(3x) with respect to x

Obtain the nth derivative of y = 3e^(-4x) with respect to x

Find the second derivative of y = e^(tanx) with respect to x

Evaluate the second derivative of y = 3∛x² - 5/∛x with respect to x

Given the implicit function (x+y)²=5, find dy/dx

Find the maximum value of y if y = x³-3x²+3

Evaluate lim(x→2) (x⁶-64)/(x³-8)

Evaluate lim(x→3) (x⁴-81)/(x³-27)

Find the first derivative of 2∛x + 2/√x² with respect to x

Evaluate lim(x→∞) (2x²-5x+1)/(3+7x²)

Given f(t)=(4t+1)/(t-2), find f(1/t)

Given two functions f(t)=(3t+2)/(t-1) and g(t)=5t-2, find f⁻¹(g(2))

Use reduction formula to evaluate ∫sin³(5x) dx

Evaluate ∫₀^π x·cos(x) dx

Given k is a positive constant and ∫₂ᵇ (3eˣ+6e⁻²ˣ) dx = 0, find the value of b

Determine the indefinite integral ∫cos⁴x dx

Evaluate ∫_(π/4)^0 secx(secx+tanx) dx

Given a is a positive constant and ∫ₐ^(3a) (3x-1)/x dx = 6+ln(1/2), find the va…

∫x·cos(x²) dx

The nth term of the Maclaurin series expansion of sin(x) is

Find two positive numbers whose sum is 80 and whose product is maximum

Find two positive numbers whose sum is 150 and whose product is maximum

Which option is incorrect? A. cosh²x-sinh²x=1 B. cosh²x+sinh²x=cosh2x C. tanh…

Differentiate e^(ln3x)/x with respect to x

Differentiate log₁₀(y)=5x+1 with respect to x (i.e. find dy/dx)

Evaluate d/dx[a·e^(f(x))]

Obtain the first derivative of y=a^(sin2x) with respect to x, where a is a cons…

d/dx[cot(5x+1)] equals

d/dx[e^(cosec3x)/3] equals

∫sin(2x)·cos(x) dx

∫(sin⁻¹x)/√(1-x²) dx

Given f(x,y)=3tanx·log_ey - y²e^(3x), compute f_x(x,y)

Given f(x,y)=3tanx·log_ey - y²e^(3x), compute f_y(x,y)

Given f(x,y)=3tanx·log_ey - y²e^(3x), compute f_xx(x,y)

Given f(x,y)=3tanx·log_ey - y²e^(3x), compute f_yy(x,y)

Given f(x,y)=3tanx·log_ey - y²e^(3x), compute f_xy(x,y)

If y=2^(3x²+5), then dy/dx is