NEB Question Browser

Consider tan⁻¹(1/2) + cot⁻¹(3) = tan⁻¹x. What is the value of x?

How many three digit numbers can be formed from the digits 2, 3, 4, 5, 6, 7?

What does ‘r’ represent in the above statement?

Write the equation of normal at C(x₁, y₁).

Reduce the given statement when we replace n by (−n)?

Write the equation of tangent at C(x₁, y₁).

Use Cramer’s rule to solve the system of linear equations:
2x + y = 4, 3y − z = 3, 2x + 3z = 11

One of the root of a quadratic equation is 3 + 2√5. What is the sum of roots of the quadratic equation?

Write the necessary conditions of the theorem.

Prove that
∫ dx / (1 − eˣ) = log|eˣ| − log|1 − eˣ| + c

Solve the differential equation:
dy/dx = (1 + y²) / (1 + x²)

Using Simplex method, maximize P(x, y) = 7x + 5y, subject to the constraints
x/3 + y/4 ≤ 1,
x/6 + y/3 ≤ 1; x ≥ 0; y ≥ 0.

What does f′(c) represent?

Find the equation of the plane passing through the points (2, 2, −1) and (2, 3, 1) and parallel to the line
(x − 3)/2 = (y + 1)/3 = (z − 4)/3

Consider a hypothetical economy of two industries A and B represented by the table given below:

The data are in millions of rupees of products. Determine the output vector of the economy if final demand of A is increased by 10% and the final demand of B is decreased by 10%

Find the direction cosines of the plane passing through the points
(2, 0, 0) and (0, 2, 2)

Which one of the following conics is represented by the equation 4x² - 16x + y² = 48?

Consider A and B be two dependent events. If P(A) = 1/2 ; P(B) = 1/13 and P(A ∩ B) = 1/26, what is P(B/A)?

What is the derivative of y = 2sinh(x/2) with respect to x?

If
f(x) = {
  1/2 − x ; x < 1/2
  (1/2 − x)² ; x ≥ 1/2
}

Does f(x) obey mean-value theorem in [0, 1]? Give reason with process.