Engineering & Architecture Admissions

JEE Main

Q. What is the value of Planck's constant in Joule seconds?

A. 6.626 x 10^-34
B. 3.14 x 10^-34
C. 1.602 x 10^-19
D. 9.11 x 10^-31

Solution

Planck's constant is approximately 6.626 x 10^-34 Joule seconds.

Correct Answer: A — 6.626 x 10^-34

Q. What is the value of R (ideal gas constant) in L·atm/(K·mol)?

A. 0.0821
B. 8.314
C. 62.36
D. 0.0831

Solution

The ideal gas constant R is 0.0821 L·atm/(K·mol).

Correct Answer: A — 0.0821

Q. What is the value of R in the ideal gas equation PV=nRT?

A. 0.0821 L·atm/(K·mol)
B. 8.314 J/(K·mol)
C. 62.36 L·mmHg/(K·mol)
D. All of the above

Solution

R can have different values depending on the units used, including 0.0821 L·atm/(K·mol), 8.314 J/(K·mol), and 62.36 L·mmHg/(K·mol).

Correct Answer: D — All of the above

Q. What is the value of R in the Ideal Gas Law in terms of L·kPa/(K·mol)?

A. 0.0821
B. 8.314
C. 0.08314
D. 8.31

Solution

The value of R in L·kPa/(K·mol) is 8.314.

Correct Answer: A — 0.0821

Q. What is the value of sec(60°)?

A. 2
B. √3/2
C. 1/2
D. √3

Solution

sec(60°) = 1/cos(60°) = 1/(1/2) = 2.

Correct Answer: A — 2

Q. What is the value of sec(sin^(-1)(1/2))?

A. √3
B. 2
C. √2
D. 1

Solution

sec(sin^(-1)(1/2)) = 1/cos(π/6) = 2.

Correct Answer: B — 2

Q. What is the value of sec(tan^(-1)(1/√3))?

A. 2
B. √3
C. 3/2
D. 1

Solution

Using the triangle with opposite = 1 and adjacent = √3, hypotenuse = 2. Thus, sec(tan^(-1)(1/√3)) = 2.

Correct Answer: A — 2

Q. What is the value of sec(θ) if cos(θ) = 1/3?

A. 3
B. 1/3
C. √3
D. 1

Solution

sec(θ) = 1/cos(θ) = 1/(1/3) = 3.

Correct Answer: A — 3

Q. What is the value of sec(θ) if cos(θ) = 3/5?

A. 5/3
B. 3/5
C. 4/5
D. 1/3

Solution

sec(θ) = 1/cos(θ) = 1/(3/5) = 5/3.

Correct Answer: A — 5/3

Q. What is the value of sec^(-1)(2)?

A. π/3
B. π/4
C. π/6
D. 0

Solution

sec^(-1)(2) = π/3, since sec(π/3) = 2.

Correct Answer: A — π/3

Q. What is the value of sin(2θ) if sin(θ) = 1/√2?

A. 1/√2
B. 1
C. √2/2
D. √2

Solution

Using the double angle formula, sin(2θ) = 2sin(θ)cos(θ) = 2(1/√2)(1/√2) = 1.

Correct Answer: B — 1

Q. What is the value of sin(30°) + cos(60°)?

A. 1
B. 0
C. √3/2
D. 1/2

Solution

sin(30°) = 1/2 and cos(60°) = 1/2. Therefore, sin(30°) + cos(60°) = 1/2 + 1/2 = 1.

Correct Answer: A — 1

Q. What is the value of sin(30°)?

A. 0
B. 1/2
C. √3/2
D. 1

Solution

sin(30°) = 1/2.

Correct Answer: B — 1/2

Q. What is the value of sin(45°) + cos(45°)?

A. √2
B. 1
C. 0
D. √3

Solution

sin(45°) = cos(45°) = √2/2. Therefore, sin(45°) + cos(45°) = √2/2 + √2/2 = √2.

Correct Answer: A — √2

Q. What is the value of sin(90° - x)?

A. cos(x)
B. sin(x)
C. tan(x)
D. sec(x)

Solution

Using the co-function identity, sin(90° - x) = cos(x).

Correct Answer: A — cos(x)

Q. What is the value of sin(90°)?

A. 0
B. 1
C. √2
D. √3

Solution

sin(90°) = 1.

Correct Answer: B — 1

Q. What is the value of sin^(-1)(1/2) + cos^(-1)(1/2)?

A. π/3
B. π/2
C. π/6
D. π/4

Solution

sin^(-1)(1/2) = π/6 and cos^(-1)(1/2) = π/3. Therefore, sin^(-1)(1/2) + cos^(-1)(1/2) = π/6 + π/3 = π/2.

Correct Answer: B — π/2

Q. What is the value of sin^(-1)(1/2) + sin^(-1)(√3/2)?

A. π/3
B. π/2
C. 2π/3
D. π

Solution

sin^(-1)(1/2) = π/6 and sin^(-1)(√3/2) = π/3. Therefore, π/6 + π/3 = π/2.

Correct Answer: B — π/2

Q. What is the value of sin^(-1)(1/2)?

A. π/6
B. π/4
C. π/3
D. π/2

Solution

sin^(-1)(1/2) = π/6, since sin(π/6) = 1/2.

Correct Answer: A — π/6

Q. What is the value of sin^(-1)(sin(π/4))?

A. π/4
B. 3π/4
C. π/2
D. 0

Solution

sin^(-1)(sin(π/4)) = π/4, as π/4 is in the range of sin^(-1).

Correct Answer: A — π/4

Q. What is the value of sin^2(x) + cos^2(x)?

A. 1
B. 0
C. sin(x)
D. cos(x)

Solution

By the Pythagorean identity, sin^2(x) + cos^2(x) = 1 for all x.

Correct Answer: A — 1

Q. What is the value of sin^2(θ) + cos^2(θ)?

A. 1
B. 0
C. sin(θ)
D. cos(θ)

Solution

By the Pythagorean identity, sin^2(θ) + cos^2(θ) = 1.

Correct Answer: A — 1

Q. What is the value of tan(30°)?

A. √3/3
B. 1/√3
C. √3
D. 3

Solution

tan(30°) = sin(30°)/cos(30°) = (1/2)/(√3/2) = 1/√3.

Correct Answer: A — √3/3

Q. What is the value of tan(45°)?

A. 0
B. 1
C. √3
D. ∞

Solution

tan(45°) = 1.

Correct Answer: B — 1

Q. What is the value of tan^(-1)(1) + tan^(-1)(1)?

A. π/2
B. π
C. 0
D. 1

Solution

tan^(-1)(1) = π/4, thus tan^(-1)(1) + tan^(-1)(1) = π/4 + π/4 = π/2.

Correct Answer: A — π/2

Q. What is the value of tan^(-1)(1) + tan^(-1)(2)?

A. π/4
B. π/3
C. π/2
D. π/6

Solution

Using the formula tan^(-1)(a) + tan^(-1)(b) = tan^(-1)((a+b)/(1-ab)), we have tan^(-1)(1) + tan^(-1)(2) = tan^(-1)((1+2)/(1-1*2)) = tan^(-1)(3/-1) = π - tan^(-1)(3) = π/4.

Correct Answer: A — π/4

Q. What is the value of tan^(-1)(1)?

A. π/4
B. π/3
C. π/2
D. 0

Solution

tan^(-1)(1) = π/4, since tan(π/4) = 1.

Correct Answer: A — π/4

Q. What is the value of tan^(-1)(√3)?

A. π/3
B. π/4
C. π/6
D. π/2

Solution

tan^(-1)(√3) corresponds to the angle π/3.

Correct Answer: A — π/3

Q. What is the value of the derivative of f(x) = ln(x^2 + 1) at x = 1?

A. 0
B. 1/2
C. 1
D. 1/3

Solution

f'(x) = (2x)/(x^2 + 1). At x = 1, f'(1) = 2/(1 + 1) = 1.

Correct Answer: B — 1/2

Q. What is the value of the determinant of the matrix \( \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \)?

A. 0
B. 1
C. 2
D. 3

Solution

The determinant of the matrix is 0 because the rows are linearly dependent.

Correct Answer: A — 0

Showing 4591 to 4620 of 5779 (193 Pages)