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MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 2951. |
The number of ways to give 16 different things to three persons A,B,C so that B gets one more than A and C gets two more than B is |
| A. | \[\frac{16!}{4!5!7!}\] |
| B. | \[4!5!7!\] |
| C. | \[\frac{16!}{3!5!8!}\] |
| D. | none of these |
| Answer» B. \[4!5!7!\] | |
| 2952. |
The number of ways of choosing a committee of two women and three men from women and six men. If Mr. A refuses to serve on the committee if Mr. B is a member and Mr. B can only serve, if Miss C is the member of the committee is |
| A. | 60 |
| B. | 84 |
| C. | 124 |
| D. | none of these |
| Answer» D. none of these | |
| 2953. |
The number of triangles that can be formed with 10 points as vertices, n of them being collinear, is 110. Then n is |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» D. 6 | |
| 2954. |
A person predicts the outcome of 20 cricket matches of his home team. Each match can result in either a win, loss, or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct is equal to |
| A. | \[^{20}{{C}_{10}}\times {{2}^{10}}\] |
| B. | \[^{20}{{C}_{10}}\times {{30}^{20}}\] |
| C. | \[^{20}{{C}_{10}}\times {{30}^{10}}\] |
| D. | \[^{20}{{C}_{10}}\times {{2}^{20}}\] |
| Answer» B. \[^{20}{{C}_{10}}\times {{30}^{20}}\] | |
| 2955. |
Total number of six-digit numbers that can be formed having the property that every succeeding digit is greater than the preceding digit is equal to |
| A. | \[^{9}{{C}_{3}}\] |
| B. | \[^{10}{{C}_{3}}\] |
| C. | \[^{9}{{P}_{3}}\] |
| D. | \[^{10}{{P}_{3}}\] |
| Answer» B. \[^{10}{{C}_{3}}\] | |
| 2956. |
A candidate is required to answer 6 out of 10 questions, which are divided into two groups, each containing 5 questions, he is not permitted to attempt more than 4 questions from either group. The number of different ways in which the candidate can choose 6 questions is |
| A. | 50 |
| B. | 150 |
| C. | 200 |
| D. | 250 |
| Answer» D. 250 | |
| 2957. |
If A and B are two nonsingular matrices of the same order such that B?=I, for some positive integer r>1, then \[{{A}^{-1}}{{B}^{\,r-1}}A-{{A}^{-1}}{{B}^{-1}}A\]= |
| A. | I |
| B. | 2I |
| C. | O |
| D. | |
| Answer» D. | |
| 2958. |
Let A be an nth-order square matrix and B be its adjoint, then \[\left| AB+K{{I}_{n}} \right|\]is (where K is a scalar quantity) |
| A. | \[{{(\left| A \right|+K)}^{n-2}}\] |
| B. | \[{{(\left| A \right|+K)}^{n}}\] |
| C. | \[{{(\left| A \right|+K)}^{n-1}}\] |
| D. | none of these |
| Answer» C. \[{{(\left| A \right|+K)}^{n-1}}\] | |
| 2959. |
If \[A=\left[ \begin{matrix} a & b \\ 0 & a \\ \end{matrix} \right]\] is nth root of \[{{I}_{2}}\], then choose the correct statements:(i) if n is odd, \[a=1,\text{ }b=0\](ii) in n is odd, \[a=-1,\text{ }b=0\](iii) if n is even, \[a=1,\text{ }b=0\](iv) if n is even, \[a=-1,\text{ }b=0\] |
| A. | i, ii, iii |
| B. | ii, iii, iv |
| C. | i, ii, iii, iv |
| D. | i, iii, iv |
| Answer» E. | |
| 2960. |
If both \[A-\frac{1}{2}I\] and \[A+\frac{1}{2}I\] are orthogonal matrices, then |
| A. | A is orthogonal |
| B. | A is skew-symmetric of even order |
| C. | \[{{A}^{2}}=\frac{3}{4}I\] |
| D. | none of these |
| Answer» C. \[{{A}^{2}}=\frac{3}{4}I\] | |
| 2961. |
A is an involuntary matrix given by then the inverse of A/2 will be |
| A. | 2A |
| B. | \[\frac{{{A}^{-1}}}{2}\] |
| C. | \[\frac{A}{2}\] |
| D. | \[{{A}^{2}}\] |
| Answer» B. \[\frac{{{A}^{-1}}}{2}\] | |
| 2962. |
If A is a square matrix such that \[{{A}^{2}}=A\], then \[{{(I+A)}^{3}}-7A\] is |
| A. | 3I |
| B. | 0 |
| C. | I |
| D. | 2I |
| Answer» D. 2I | |
| 2963. |
If \[A=\left[ \begin{matrix} a & b \\ b & a \\ \end{matrix} \right]\]and \[{{A}^{2}}=\left[ \begin{matrix} \alpha & \beta \\ \beta & \alpha \\ \end{matrix} \right]\], then |
| A. | \[\alpha ={{a}^{2}}+{{b}^{2}},\beta =ab\] |
| B. | \[\alpha ={{a}^{2}}+{{b}^{2}},\beta =2ab\] |
| C. | \[\alpha ={{a}^{2}}+{{b}^{2}},\beta ={{a}^{2}}-{{b}^{2}}\] |
| D. | \[\alpha =2ab,\,\,\beta ={{a}^{2}}+{{b}^{2}}\] |
| Answer» C. \[\alpha ={{a}^{2}}+{{b}^{2}},\beta ={{a}^{2}}-{{b}^{2}}\] | |
| 2964. |
If A and B are two matrices such that \[AB=B\]and \[BA=A,\]then |
| A. | \[{{({{A}^{5}}-{{B}^{5}})}^{3}}=A-B\] |
| B. | \[{{({{A}^{5}}-{{B}^{5}})}^{3}}={{A}^{3}}-{{B}^{3}}\] |
| C. | \[A-B\]is idempotent |
| D. | \[A-B\]is nilpotent |
| Answer» E. | |
| 2965. |
Elements of a matrix A of order \[10\times 10\] are defined is \[{{a}_{ij}}={{w}^{i+j}}\] (where w is cube root of unity), then tr of the matrix is |
| A. | 0 |
| B. | 1 |
| C. | 3 |
| D. | none of these |
| Answer» E. | |
| 2966. |
The number of solutions of the matrix equation\[{{X}^{2}}=\left[ \begin{matrix} 1 & 1 \\ 2 & 3 \\ \end{matrix} \right]\] is |
| A. | more than 2 |
| B. | 2 |
| C. | 0 |
| D. | 1 |
| Answer» B. 2 | |
| 2967. |
If \[\left[ \begin{matrix} 2 & 1 \\ 3 & 2 \\ \end{matrix} \right]A\left[ \begin{matrix} -3 & 2 \\ 5 & -3 \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\], then A= |
| A. | \[\left[ \begin{matrix} 1 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} 1 & 0 \\ 1 & 1 \\ \end{matrix} \right]\] |
| D. | \[-\left[ \begin{matrix} 1 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] |
| Answer» B. \[\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right]\] | |
| 2968. |
If A and B are square matrices of the same order and A is nonsingular, then for a positive integer n, \[{{({{A}^{-1}}BA)}^{n}}\] is equal |
| A. | \[{{A}^{-n}}{{B}^{n}}{{A}^{n}}\] |
| B. | \[{{A}^{n}}{{B}^{n}}{{A}^{-n}}\] |
| C. | \[{{A}^{-1}}{{B}^{n}}A\] |
| D. | \[n({{A}^{-1}}BA)\] |
| Answer» D. \[n({{A}^{-1}}BA)\] | |
| 2969. |
If \[{{A}^{3}}=0\], then I=A+\[{{A}^{2}}\]equals |
| A. | \[I-A\] |
| B. | \[{{(I+{{A}^{1}})}^{-1}}\] |
| C. | \[{{(I-A)}^{-1}}\] |
| D. | none of these |
| Answer» D. none of these | |
| 2970. |
If then \[A{{(\alpha ,\beta )}^{-1}}\]is equal to |
| A. | \[A(-\alpha ,-\beta )\] |
| B. | \[A(-\alpha ,\beta )\] |
| C. | \[A(\alpha ,-\beta )\] |
| D. | \[A(\alpha ,\beta )\] |
| Answer» B. \[A(-\alpha ,\beta )\] | |
| 2971. |
Let A and B be two \[2\times 2\] matrices, Consider the statements (i) \[AB=O\Rightarrow A=O\] or \[B=0\] (ii) \[AB={{I}_{2}}\Rightarrow A={{B}^{-1}}\] (iii) \[{{(A+B)}^{2}}\]=\[{{A}^{2}}+2AB+{{B}^{2}}\] Then |
| A. | (i) and (ii) are false, (iii) is true |
| B. | (ii) and (iii) are falsse, (i) is true |
| C. | (i) is false, (ii) and (iii) are true |
| D. | (i) and (iii) are false, (ii) is true |
| Answer» E. | |
| 2972. |
If \[A=\left[ \begin{matrix} 1 & \tan x \\ -\tan x & 1 \\ \end{matrix} \right]\], then \[{{A}^{T}}{{A}^{-1}}\]is |
| A. | \[\left[ \begin{matrix} -\cos 2x & \sin 2x \\ -\sin 2x & \cos 2x \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} \cos 2x & -\sin 2x \\ \sin 2x & \cos 2x \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} \cos 2x & \cos 2x \\ \sin 2x & \sin 2x \\ \end{matrix} \right]\] |
| D. | none of these |
| Answer» C. \[\left[ \begin{matrix} \cos 2x & \cos 2x \\ \sin 2x & \sin 2x \\ \end{matrix} \right]\] | |
| 2973. |
If \[(p\wedge \tilde{\ }r)\wedge (\tilde{\ }p/q)\] is false, then the truth values of p, q and r, respectively |
| A. | T, F and F |
| B. | F. F and T |
| C. | F, T and T |
| D. | T. F and T |
| Answer» B. F. F and T | |
| 2974. |
Which of the following is logically equivalent to \[\tilde{\ }(\tilde{\ }p\Rightarrow q)?\] |
| A. | \[p\wedge q\] |
| B. | \[p\wedge \tilde{\ }q\] |
| C. | \[\tilde{\ }p\wedge q\] |
| D. | \[\tilde{\ }p\wedge \tilde{\ }q\] |
| Answer» E. | |
| 2975. |
\[\tilde{\ }(p\vee q)\vee (\tilde{\ }p\wedge q)\] is equivalent to |
| A. | q |
| B. | p |
| C. | ~p |
| D. | ~q |
| Answer» D. ~q | |
| 2976. |
If p is true and q is false, then which of the following statements is not true? |
| A. | \[p\vee q\] |
| B. | \[p\Rightarrow q\] |
| C. | \[p\wedge (\tilde{\ }q)\] |
| D. | \[p\Rightarrow p\] |
| Answer» C. \[p\wedge (\tilde{\ }q)\] | |
| 2977. |
Which of the following is the contrapositive of 'if two triangles are identical, then these are similar'? |
| A. | if two triangles are not similar, then are not identical |
| B. | If two triangles are not identical, then these are not similar |
| C. | If two triangles are not identical, then these are similar |
| D. | If two triangles are not similar, then these are identical |
| Answer» B. If two triangles are not identical, then these are not similar | |
| 2978. |
If p is any statement, then which of the following is a tautology? |
| A. | \[p\wedge f\] |
| B. | \[p\vee f\] |
| C. | \[p\vee (\tilde{\ }p)\] |
| D. | \[p\wedge t\] |
| Answer» D. \[p\wedge t\] | |
| 2979. |
The following statement \[(p\to q)\to [(\tilde{\ }p\to q)\to q]\]is |
| A. | a fallacy |
| B. | a tautology |
| C. | equivalent to \[\tilde{\ }p\to q\] |
| D. | equivalent to \[p\to \tilde{\ }q\] |
| Answer» E. | |
| 2980. |
The statement \[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\]is |
| A. | equivalent to \[p\leftrightarrow q\] |
| B. | equivalent to ~\[p\leftrightarrow q\] |
| C. | a tautology |
| D. | a fallacy |
| Answer» B. equivalent to ~\[p\leftrightarrow q\] | |
| 2981. |
The Boolean Expression \[(p\wedge \tilde{\ }q)\vee q\vee (\tilde{\ }p\wedge q)\]is equivalent to |
| A. | \[p\wedge q\] |
| B. | \[p\vee q\] |
| C. | \[p\,\vee \tilde{\ }q\] |
| D. | \[\tilde{\ }p\wedge q\] |
| Answer» C. \[p\,\vee \tilde{\ }q\] | |
| 2982. |
The negation of the statement "If I become a teacher, then I will open a school", is: |
| A. | I will become a teacher and I will not open a school. |
| B. | Either I will not become a teacher or I will not open a school. |
| C. | Nither I will not become a teacher or I will not open a school |
| D. | I will not become a teacher or I will open a school. |
| Answer» B. Either I will not become a teacher or I will not open a school. | |
| 2983. |
Let S be a non-empty subset of R. Consider the following statement: P: There is a rational number \[x\in S\] such that\[x>0\]. Which of the following statements is the negation of the statement p? |
| A. | \[x\in S\] and \[x\le 0\Rightarrow x\] is not rational. |
| B. | There is a rational number \[x\in S\] such that \[x\le 0\]. |
| C. | There is no rational number \[x\in S\] such that\[x\le 0\]. |
| D. | Every rational number \[x\in S\]satisfies\[x\le 0\]. |
| Answer» E. | |
| 2984. |
The contrapositive of the inverse of \[p\Rightarrow \,\tilde{\ }q\]is |
| A. | \[\tilde{\ }q\Rightarrow p\] |
| B. | \[p\Rightarrow q\] |
| C. | \[\tilde{\ }q\Rightarrow \,\tilde{\ }p\] |
| D. | \[\tilde{\ }p\Rightarrow \,\tilde{\ }q\] |
| Answer» B. \[p\Rightarrow q\] | |
| 2985. |
The statement \[p\to (p\to q)\]is equivalent to |
| A. | \[p\to (p\to q)\] |
| B. | \[p\to (p\,\vee q)\] |
| C. | \[p\to (p\,\wedge q)\] |
| D. | \[p\to (p\leftrightarrow q)\] |
| Answer» C. \[p\to (p\,\wedge q)\] | |
| 2986. |
What is negation of the compound proposition? If the examination is difficult, then I shall pass if I study hard. |
| A. | The examination is difficult and I study hard but I shall not pass |
| B. | The examination is difficult and I study hard and I shall pass |
| C. | The examination is not difficult and I study hard and I shall pass |
| D. | None of these |
| Answer» B. The examination is difficult and I study hard and I shall pass | |
| 2987. |
If p is false and q is true, then |
| A. | \[p\wedge q\] is true |
| B. | \[p\,\vee \tilde{\ }q\]is true |
| C. | \[q\wedge q\]is true |
| D. | \[p\Rightarrow q\]is true |
| Answer» E. | |
| 2988. |
If each of the following statements is true, then \[P\Rightarrow \tilde{\ }q,\text{ }q\Rightarrow r,\text{ }\tilde{\ }r\] |
| A. | p is false |
| B. | p is true |
| C. | q is true |
| D. | None of these |
| Answer» B. p is true | |
| 2989. |
If both p and q are false, then |
| A. | \[p\wedge q\]is true |
| B. | \[p\vee q\]is false |
| C. | \[p\Rightarrow q\]is true |
| D. | None of these |
| Answer» D. None of these | |
| 2990. |
The logically equivalent proposition of póq is |
| A. | \[(p\Rightarrow q)\vee (p\wedge q)\] |
| B. | \[(p\Rightarrow q)\wedge (q\Rightarrow p)\] |
| C. | \[(p\wedge q)\wedge (q\Rightarrow p)\] |
| D. | \[(p\wedge q)\Rightarrow (p\vee q)\] |
| Answer» C. \[(p\wedge q)\wedge (q\Rightarrow p)\] | |
| 2991. |
The logically equivalent proposition of \[p\Rightarrow q\]is |
| A. | \[(p\Rightarrow q)\vee (q\Rightarrow p)\] |
| B. | \[(p~\vee \,q)\Rightarrow (p\vee q)\] |
| C. | \[(p~\wedge \,q)~\vee \,(p~\vee \,q)\] |
| D. | \[(p~\Rightarrow q)~\wedge \,(q\Rightarrow p)\] |
| Answer» E. | |
| 2992. |
Consider the statement p: 'New Delhi is a city'. Which of the following is not negation of p? |
| A. | New Delhi is not a city |
| B. | It is false that New Delhi is a city |
| C. | It is not the case that New Delhi is a city |
| D. | None of these |
| Answer» E. | |
| 2993. |
Solution of \[\frac{x-7}{x+3}>2\]is |
| A. | \[(-3,\,\infty )\] |
| B. | \[(-\infty ,\,-13)\] |
| C. | (-13, -3) |
| D. | None of these |
| Answer» D. None of these | |
| 2994. |
If \[x+y\le 2,x\ge 0,y\ge 0\]then the point at which maximum value of \[3x+2y\]is attained will be |
| A. | (0, 0) |
| B. | \[\left( \frac{1}{2},\frac{1}{2} \right)\] |
| C. | (0, 2) |
| D. | (2, 0) |
| Answer» E. | |
| 2995. |
Complete solution set of \[\left| x-2 \right| |
| A. | \[x<5\] |
| B. | \[x>0\] |
| C. | \[-1<x<5\] |
| D. | \[1<x<5\] |
| Answer» D. \[1<x<5\] | |
| 2996. |
The inequality \[\frac{2}{x} |
| A. | \[\left[ 2/3,\,\infty \right)\] |
| B. | \[(-\infty ,\,2/3]\] |
| C. | \[(2/3,\,\infty )\cup (-\infty ,\,0)\] |
| D. | None of these |
| Answer» D. None of these | |
| 2997. |
If \[-9 |
| A. | \[\left[ 6,\,9 \right)\] |
| B. | \[\left[ 0,\,6 \right]\] |
| C. | \[\left[ 0,\,9 \right)\] |
| D. | none of these |
| Answer» D. none of these | |
| 2998. |
Inequality \[y-x\le 0\]represents |
| A. | the half plane that contains the positive x-axis |
| B. | closed half plane above the line y=x which contains positive y-axis |
| C. | half plane that contains negative x-axis |
| D. | none of these |
| Answer» B. closed half plane above the line y=x which contains positive y-axis | |
| 2999. |
Which values of x satisfy the following inequalities simultaneously? (i) \[-3 |
| A. | \[\left[ -4,10 \right)\] |
| B. | \[\left( -1,\,6 \right]\] |
| C. | \[\left[ -1,\,6 \right)\] |
| D. | \[\left( -1,\,6 \right)\] |
| Answer» C. \[\left[ -1,\,6 \right)\] | |
| 3000. |
Solution set of the following inequalities is \[2(x-1)2-x\] |
| A. | \[(-1,\,7)\] |
| B. | \[(1,\,7)\] |
| C. | \[(-1,\,\infty )\] |
| D. | \[(-\infty ,\,7)\] |
| Answer» B. \[(1,\,7)\] | |