List of practice Questions

The value of the determinant \(\begin{vmatrix} x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1 \end{vmatrix}\) is :
The ratio of speeds of a motor boat and that of current of water is 35:6. The boat goes against the current in 6 hours 50 minutes. The time taken by boat to come back is :
If \(2\sin2\theta=\sqrt3\), where 0 ≤ 2θ ≤ 90°, then find the value of cos 3θ
An electric company has 300 Transistors, 400 Capacitors and 500 Inductors. The company wishes to make electronic goods using two circuits A and B. Requirement by circuit is as follows :
TransistorCapacitorInductor
A175300200
B125100300
The profit from circuit A and B is ₹2000 and ₹3000 respectively then constrains of the LLP based on this data are :
A cistern is filled in 30 minutes by three pipes A, B and C. The pipe C is thrice as fast as pipe A and pipe B is twice as fast as A. The time taken by pipe A alone to fill the cistern is:
If \(y=x^3\log x, then\ \frac{d^2y}{dx^2}\) is:
The money needed to invest now, so as to get ₹7500 at the beginning of each month forever (starting from the current month) if the money is worth 9% per annuum compounded monthly is.
In how many ways can a committee of 7 members be selected from 6 men and 5 women consisting of 4 men and 3 women ?
In a certain code, COMPUTER is coded as ETUPMOCR. How is INACTIVE written in the same code?
Which of the following is correct for standard deviation, where \(\bar{X}\) = mean 
How many 3-letter words can be formed from the letters of the word 'OBJECTS' if repetition is not allowed?
Which of the following is a correct statement ?
The value of the determinant \(\begin{vmatrix}cos^2θ&cosθsinθ&0 \\-sinθ&cosθ&0 \\ 0&0&1 \end{vmatrix}\) is equal to
For the LPP Max Z=3x+4y, x+y≤40; x+2y≤ 60, x≥0, y≥0 the solution is:
The maximum profit that a company can make if the profit function is given by
\(P(x)=32+24x-18x^2\) is:
A. \(\begin{bmatrix}1& 2& 3   \\[0.3em]2 & 4 & 5   \\[0.3em]3 & 5&6   \\[0.3em] \end{bmatrix}\) is a Symmetric matrix. 
B. \(\begin{bmatrix}0 &0 &0   \\[0.3em]0& 0&0   \\[0.3em] \end{bmatrix}\) is a Null matrix.
C. \(\begin{bmatrix}1& 0& 0   \\[0.3em]0 & 2 & 0\\[0.3em]0 & 0&3\\[0.3em] \end{bmatrix}\) is an Identity matrix.
D. \(\begin{bmatrix}0& 1&2   \\[0.3em]-1 & 0 & 3   \\[0.3em]-2 & 3&0\\[0.3em] \end{bmatrix}\) is a Skew symmetric matrix.
E. \(\begin{bmatrix}\sqrt{3} &0& 0\\[0.3em]0 & \sqrt{3} & 0   \\[0.3em]0 & 0&\sqrt{3}   \\[0.3em] \end{bmatrix}\) is a Scalar matrix
Choose the correct answer from the options given below:
For two events A and B
Match List I with List II
List IList II
A. \(P (\bar{\bigwedge} \cap \bar{B}) = P(\bar{\bigwedge}) . P(\bar{B})\)I. \(P(A/B) \geq P(A)\)
B. \(A \subset B \) and \(P(B) \neq0\)II. \(P(A) = P(B)\)
C. \(P(A \bigcup B) = P(A) + P(B)\)III. A and B are independent events
D. \(P(A|B) = P (B|A)\)IV. A and B are mutually exclusive events

Choose the correct answer from the options given below:
If \(y=sin^{-1}x \) and \((1-x^2)\frac{d^2y}{dx^2} -x \frac{dy}{dx}=K\),then value of K is:
The value of \(sin^{-1}\frac{12}{13} +cos^{-1}\frac45+tan^{-1}\frac{63}{16}\) is :
The coordinates of the foot of the perpendicular drawn from origin to the plane \(2x - 3y + 4z - 6 = 0\) is :
The probability distribution of a discrete random variable \(X\) is given below :
\(X\)\(2\)\(3\)\(4\)\(5\)
\(P(X)\)\(\frac5k\)\(\frac7k\)\(\frac9k\)\(\frac{11}{k}\)

then the value of k is:

The maximum value of\( z=2.5x+y\) subject to the constraints \( x+3y\leq12, 3x+y\leq12, x, y\geq0, \) is: 
If \(A=\begin{bmatrix} -2&6\\-5&-1\end{bmatrix}\) then \(A^{-1}\) is:
A discrete random variable X has the following probability distribution:
X:012345
P(X):b3b5b3b4b6b
The value of b is:
A simple random sample consists of four observations 7, 8, 10, 7. The point estimate of population standard deviation is :