Question
The direction cosines of the y-axis are:

Answer

  1. (0, 1, 0)

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Which of the following is correct?
  1. Determinant is a square matrix
  2. Determinant is a number associated to a matrix
  3. Determinant is a number associated to a square matrix
  4. None of these
The value of b for which the function $\text{f(x)}=\begin{cases}5\text{x}-4,&0<\text{x}\leq1\\4\text{x}^2+3\text{bx},&1<\text{x}<2\end{cases}$ is continuous at every point of its domain, is:
  1. -1
  2. 0
  3. $\frac{13}{3}$
  4. 1
A box contain 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens draws one by one with replacement at most one is defective?
  1. $\big(\frac{9}{10}\big)^5$
  2. $\frac{1}{2}\big(\frac{9}{10}\big)^4$
  3. $\frac{1}{2}\big(\frac{9}{10}\big)^5$
  4. $\big(\frac{9}{10}\big)^5+\frac{1}{2}\big(\frac{9}{10}\big)^4$
The projections of a line segment on x, y and z axes are 12, 4 and 3 respectively. The length and direction cosines of the line segment are:
The corner points of the feasible region determined by the following system of linear inequalities:
2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5).
Let Z = px + qy, where p.q > 0.
Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is:
The solution of $\frac{\text{dy}}{\text{dx}}+\frac{\text{y}}{\text{x}}=\frac{1}{\sqrt{1+\text{x}^2}}$ is:
  1. $\text{y}=\frac{1+\text{x}^2}{\text{x}}+\frac{\text{c}}{\text{x}}$
  2. $\text{y}=\frac{\sqrt{1+\text{x}^2}}{\text{x}}+\frac{\text{c}}{\text{x}}$
  3. $\text{y}=\frac{\text{x}}{\sqrt{1+\text{x}^2}}+\text{cx}$
  4. $\text{None of these}$
A bag contains 5 red and 3 blue balls are drawn at random without replacement, then the probability of getting exactly one red ball is.
  1. $\frac{15}{29}$
  2. $\frac{15}{56}$
  3. $\frac{45}{196}$
  4. $\frac{135}{392}$
Choose the correct answer
Distance between the two planes: 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is:
  1. $2\ \text{units}$
  2. $4\ \text{units}$
  3. $8\ \text{units}$
  4. $\frac{2}{\sqrt{29}}\ \text{units}.$
A binary operation * on Z defined by a * b = 3a + b for all a, b ∈ Z, is:
  1. Commutative.
  2. Associative.
  3. Not commutative.
  4. Commutative and associative.
The area of the ellipse $\frac{\text{x}2}{9}+\frac{\text{y}^2}{4}=1$ in first quadrant is $6\pi$ sq. units.
The ellipse is rotated about its centre in anti-clockwise direction till its major axis coincides with y-axis. Now the area of the ellipse in first Quadrant is $\pi$ sq. units.
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  2. 4
  3. 6
  4. 8