List of top Computer Science Questions on Matrix Operations

Which of the following statement are false about two circles whose equations are given below? \[ x^2 + y^2 - 10x - 10y - 41 = 0 \] \[ x^2 + y^2 - 22x - 18y + 137 = 0 \]
• [A.] Circles have no common point
• [B.] Circles have one common point
• [C.] Circles have two common points
• [D.] Circles have infinitely many points
Arrange the following steps in sequence to find the variance of individual observations.
• [A.] Compute the mean \(\bar{X}\) of the given observations \(x_1, x_2, \ldots, x_n\).
• [B.] Square the deviations obtained and obtain the sum \(\sum_{i=1}^{n} (x_i - \bar{X})^2\).
• [C.] Divide the sum \(\sum_{i=1}^{n} (x_i - \bar{X})^2\) by \(n\).
• [D.] Take the deviations of the observations from mean i.e., \(x_i - \bar{X}, i=1,2,\ldots,n\).
Choose the correct answer from the options given below:
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Let \(f\) be a function defined by \[ f(x) = \begin{cases} \dfrac{\tan x}{x}, & x \neq 0 1, & x = 0 \end{cases} \] Assertion (A): \(x = 0\) is point of minima of \(f\).
Reason (R): \(f'(0) = 0\). In the light of the above statements, choose the most appropriate answer from the options given below:
In a university, out of 100 students, 15 offered Mathematics only, 12 offered Statistics only, 8 offered Physics only, 40 offered Physics and Mathematics, 10 offered Mathematics and Statistics, 25 offered Physics. What is the number of students who did not offer any of the three subjects?
Arrange the following steps in sequence to find the variance of individual observations.
• [A.] Compute the mean \(\bar{X}\) of the given observations \(x_1, x_2, \ldots, x_n\).
• [B.] Square the deviations obtained and obtain the sum \(\sum_{i=1}^{n} (x_i - \bar{X})^2\).
• [C.] Divide the sum \(\sum_{i=1}^{n} (x_i - \bar{X})^2\) by \(n\).
• [D.] Take the deviations of the observations from mean i.e., \(x_i - \bar{X}, i=1,2,\ldots,n\).
Choose the correct answer from the options given below:
Which of the following statement are false about two circles whose equations are given below? \[ x^2 + y^2 - 10x - 10y - 41 = 0 \] \[ x^2 + y^2 - 22x - 18y + 137 = 0 \]
• [A.] Circles have no common point
• [B.] Circles have one common point
• [C.] Circles have two common points
• [D.] Circles have infinitely many points
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Let \(f\) be a function defined by \[ f(x) = \begin{cases} \dfrac{\tan x}{x}, & x \neq 0 1, & x = 0 \end{cases} \] Assertion (A): \(x = 0\) is point of minima of \(f\).
Reason (R): \(f'(0) = 0\). In the light of the above statements, choose the most appropriate answer from the options given below:
In a university, out of 100 students, 15 offered Mathematics only, 12 offered Statistics only, 8 offered Physics only, 40 offered Physics and Mathematics, 10 offered Mathematics and Statistics, 25 offered Physics. What is the number of students who did not offer any of the three subjects?
Match List-I with List-II.\[\begin{array}{|c|c|} \hline \textbf{List-I} & \textbf{List-II} \\ \hline (A) \; \text{If } A = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}, \; \Delta \text{ is} & (I) \; 0 \\ \hline (B) \; \text{If } A = \begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}, \; \Delta \text{ is} & (II) \; 1 \\ \hline (C) \; \text{If } A = \begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}, \; |A^{-1}| \text{ is} & (III) \; -2 \\ \hline (D) \; \text{If } A = \begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix}, \; a \text{ is} & (IV) \; 2 \\ \hline \end{array}\]