MCQOPTIONS
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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.
| 901. |
Which of the following is not a proposition |
| A. | \[\sqrt{3}\] is a prime |
| B. | \[\sqrt{2}\] is irrational |
| C. | Mathematics is interesting |
| D. | 5 is an even integer |
| Answer» D. 5 is an even integer | |
| 902. |
Consider the statement p: 'New Delhi is 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. | |
| 903. |
Which of the following is the inverse of the proposition: ?if a number is a prime then it is odd.?? |
| A. | If a number is not a prime then it is odd |
| B. | If a number is not a prime then it is not odd |
| C. | If a number is not odd then it is not a prime |
| D. | If a number is not odd then it is a prime? |
| Answer» C. If a number is not odd then it is not a prime | |
| 904. |
If \[S(p,q,r)=(\tilde{\ }p)\vee [\tilde{\ }(q\wedge r)]\] is a compound statement, then \[S(\tilde{\ }p,\tilde{\ }q,\tilde{\ }r)\] is |
| A. | \[\tilde{\ }S(p,q,r)\] |
| B. | \[S(p,q,r)\] |
| C. | \[p\vee (q\wedge r)\] |
| D. | \[p\vee (q\vee r)\] |
| Answer» E. | |
| 905. |
The solution of linear programming problem maximize \[z=3{{x}_{1}}+5{{x}_{2}}\] Subject to \[3{{x}_{1}}+2{{x}_{2}}\le 18,\]\[{{x}_{1}}\le 4,{{x}_{2}}\le 6,{{x}_{1}}\ge 0,{{x}_{2}}\ge 0\] is |
| A. | \[{{x}_{1}}=2,{{x}_{2}}=0,z=6\] |
| B. | \[{{x}_{1}}=2,{{x}_{2}}=6,z=36\] |
| C. | \[{{x}_{1}}=4,{{x}_{2}}=3,z=27\] |
| D. | \[{{x}_{1}}=4,{{x}_{2}}=6,z=42\] |
| Answer» C. \[{{x}_{1}}=4,{{x}_{2}}=3,z=27\] | |
| 906. |
The true statement for the graph of in equations\[3x+2y\le 6\] and \[6x+4y\ge 20,\] is |
| A. | Both graph are disjoint |
| B. | Both contain (0, 3) |
| C. | Both contain point (1, 1) |
| D. | None of these |
| Answer» B. Both contain (0, 3) | |
| 907. |
The inequalities \[5x+4y\ge 20,x\le 6,y\le 4\]from |
| A. | A square |
| B. | A rhombus |
| C. | A triangle |
| D. | A quadrilateral |
| Answer» E. | |
| 908. |
A brick manufacture has two depots A and B, with stocks of 30000 and 20000 bricks respectively. He receive orders form three builders P, Q and R for 15000, 20,000 and 15000 bricks respectively. The cost (in) of transporting 1000 bricks to the builders form the deposits as given in the table. To From Transportation cost per 1000 bricks (in Rs.) P Q R A 40 20 20 B 20 60 40 The manufacturer wished to find how to fulfill the order so that transportation cost is minimum. Formulation of the L.P.P., is given as |
| A. | Minimize \[Z=40x-20y\] Subject to, \[x+y\ge 15,x+y\le 30,x\ge 15,y\le 20,\]\[x\ge 0,y\ge 0\] |
| B. | Minimize \[Z=40x-20y\] Subject to, \[x+y\ge 15,x+y\le 30,x\le 15,y\ge 20,\]\[x\ge 0,y\ge 0\] |
| C. | Minimize \[Z=40x-20y\] Subject to, \[x+y\ge 15,x+y\le 30,x\le 15,y\le 20,\]\[x\ge 0,y\ge 0\] |
| D. | Minimize \[Z=40x-20y\] Subject to, \[x\ge 0,y\ge 0\] |
| Answer» D. Minimize \[Z=40x-20y\] Subject to, \[x\ge 0,y\ge 0\] | |
| 909. |
The constraints \[-{{x}_{1}}+{{x}_{2}}\le 1,-{{x}_{1}}+3{{x}_{2}}\le 9;\]\[{{x}_{1}},{{x}_{2}}\ge 0\] defines on |
| A. | Bounded feasible space |
| B. | Unbounded feasible space |
| C. | Both bounded and unbounded feasible space |
| D. | None of these |
| Answer» C. Both bounded and unbounded feasible space | |
| 910. |
The Maximum value of \[z=5x+3y\], subjected to the conditions\[3x+5y\le 15,5x+2y\le 10,x,y\ge 0\]is |
| A. | \[\frac{235}{19}\] |
| B. | \[\frac{325}{19}\] |
| C. | \[\frac{523}{19}\] |
| D. | \[\frac{532}{19}\] |
| Answer» B. \[\frac{325}{19}\] | |
| 911. |
The maximum value of \[z=3x+2y,\]subjected to the conditions \[x+2y\ge 2,x+2y\le 8,x,y\ge 0\] is |
| A. | 32 |
| B. | 24 |
| C. | 40 |
| D. | None of these |
| Answer» C. 40 | |
| 912. |
The number of corner points of the L.P.P. Max \[Z=20x+3y\] subject to the constraints \[x+y\le 5,2x+3y\le 12,x\ge 0,y\ge 0\] are |
| A. | 4 |
| B. | 3 |
| C. | 2 |
| D. | 1 |
| Answer» B. 3 | |
| 913. |
A vertex of bounded region of inequalities \[x\ge 0\]\[x+2y\ge 0\] and \[2x+y\le 4\]is |
| A. | (1, 1) |
| B. | (0, 1) |
| C. | (3, 0) |
| D. | (0, 4) |
| Answer» E. | |
| 914. |
An oil company required 12000, 20000 and 15000 barrels of high-grade, medium grade and low grade oil, respectively. Refinery A produces 100, 300 and 200 barrels per day of high-grade, medium-grade and low-grade oil, respectively, while refinery B produces 200, 400 and 100 barrels per day of high-grade. Medium-grade and low grade oil, respectively. If refinery A costs 400 per day and refinery B costs 300 per day to operate, then the days should each he run to minimize costs while satisfying requirements are |
| A. | 30, 60 |
| B. | 60, 30 |
| C. | 40, 60 |
| D. | 60, 40 |
| Answer» C. 40, 60 | |
| 915. |
The maximum value of \[z=2x+5y\] subject to the constraints \[2x+5y\le 10,x+2y\ge 1,x-y\le 4,x\ge y\ge 0,\] Occurs at |
| A. | Exactly one pint |
| B. | Exactly two points |
| C. | Infinitely many points |
| D. | None of these |
| Answer» D. None of these | |
| 916. |
For the constraint of a linear optimizing function\[z={{x}_{1}}+{{x}_{2}},\] Given by \[{{x}_{1}}+{{x}_{2}}\le 1,3{{x}_{1}}+{{x}_{2}}\ge 3\]and\[{{x}_{1}},{{x}_{2}}\ge 0\]. |
| A. | There are two feasible regions |
| B. | There are infinite feasible regions |
| C. | There is no feasible region |
| D. | None of these |
| Answer» D. None of these | |
| 917. |
The maximum value \[z=5x+2y,\]subject to the constraints \[x+y\le 7,x+2y\le 10,x,y\ge 0\]is |
| A. | 10 |
| B. | 26 |
| C. | 35 |
| D. | 70 |
| Answer» D. 70 | |
| 918. |
Which of the following is not a vertex of the positive region bounded by the inequalities \[2x+3y\le 6,5x+3y\le 15\] and \[x,y\ge 0\] |
| A. | (0, 2) |
| B. | (0, 0) |
| C. | (3, 0) |
| D. | All of these |
| Answer» E. | |
| 919. |
Maximize \[Z=3x+5y,\] subject to \[x+4y\le 24,\]\[3x+y\le 21,\]\[x+y,\le 9,\]\[x\ge 0,y\ge 0,\] is |
| A. | \[20\,at\,(1,0)\] |
| B. | \[30\,\,at\,\,(0,6)\] |
| C. | \[37\,at\,(4,5)\] |
| D. | \[33\,\,at\,\,(6,3)\] |
| Answer» D. \[33\,\,at\,\,(6,3)\] | |
| 920. |
Consider the objective function \[Z=40x+50y.\] The minimum number of constraints that are required to maximize Z are |
| A. | 4 |
| B. | 2 |
| C. | 3 |
| D. | 1 |
| Answer» D. 1 | |
| 921. |
A company manufactures two types of products A and B. The storage capacity of its go down is 100 units. Total investment amount is 30,000. The cost price of A and B are 400 and 900 respectively. Suppose all the product have sold and per unit profit is 100 and 120 through A and B respectively. If X units of A and Y units of B be produced, then two linear constraints and is profit line are respectively |
| A. | \[x+y=100;4x+9y=300,100x+120y=c\] |
| B. | \[x+y\le 100;4x+9y\le 300,x+2y=c\] |
| C. | \[x+y\le 100;4x+9y\le 300,100x+120y=c\] |
| D. | \[x+y\le 100;9x+4y\le 300,x+2y=c\] |
| Answer» D. \[x+y\le 100;9x+4y\le 300,x+2y=c\] | |
| 922. |
The constraints\[-{{x}_{1}}+{{x}_{2}}\le 1,-{{x}_{1}}+3{{x}_{2}}\le 9,{{x}_{1}},{{x}_{2}}\ge 0\] Define on |
| A. | Bounded feasible space |
| B. | Unbounded feasible space |
| C. | Both bounded and unbounded feasible space |
| D. | None of these |
| Answer» C. Both bounded and unbounded feasible space | |
| 923. |
The maximum value of \[z=4x+3y\] subject to the constraints \[3x+2y\ge 160,5x+2y\ge 200,x+2y\ge 80,\]\[x,y\ge 0\] is. |
| A. | 320 |
| B. | 300 |
| C. | 230 |
| D. | None |
| Answer» E. | |
| 924. |
A shop-keeper deals in the sale of TV s and VCPs. He has 5.2 lacs to invest. He has only space for 50 pieces. ATV costs 20,000/- and a VCP costs 8,000/- From a TV and VCP he earns a profit of 1500/- and 800/- respectively. Assuming that he sells all the items that he purchases, the number of TVs and VCPs he should buy in order to Maximize his profit, is equal to |
| A. | 60, 000 |
| B. | 55, 000 |
| C. | 51, 000 |
| D. | 47, 000 |
| Answer» E. | |
| 925. |
Ravi obtained 70 and 75 marks in first two unit tests. Then the minimum marks he should get in the third test to have an average of at least 60 marks, are |
| A. | 45 |
| B. | 35 |
| C. | 25 |
| D. | None of these |
| Answer» C. 25 | |
| 926. |
The Solution set of constraints \[x+2y\ge 11,\]\[3x+4y\le 30,\]\[2x+5y\le 30\] and \[x\ge 0,\]\[y\ge 0,\] includes the point |
| A. | (2, 3) |
| B. | (3, 2) |
| C. | (3, 4) |
| D. | (4, 3) |
| Answer» D. (4, 3) | |
| 927. |
If \[5\{x\}=x+[x]\] and \[[x]-\{x\}=\frac{1}{2}\] when \[\{x\}\] and \[[x]\] are fractional and integral part of x then x is |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{3}{2}\] |
| C. | \[\frac{5}{2}\] |
| D. | \[\frac{7}{2}\] |
| Answer» C. \[\frac{5}{2}\] | |
| 928. |
The inequality representing the following graph is |
| A. | \[\left| x \right|<3\] |
| B. | \[\left| x \right|\le 3\] |
| C. | \[\left| x \right|>3\] |
| D. | \[\left| x \right|\ge 3\] |
| Answer» B. \[\left| x \right|\le 3\] | |
| 929. |
The number of real roots of the equation \[\left| 2-\left| 1-\left| x \right| \right| \right|=1\] is |
| A. | 1 |
| B. | 3 |
| C. | 5 |
| D. | 6 |
| Answer» D. 6 | |
| 930. |
Number of real roots of the equation \[\sqrt{x}+\sqrt{x-\sqrt{1-x}}=1\] is |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» C. 2 | |
| 931. |
If \[{{(\sqrt{2})}^{x}}+{{(\sqrt{3})}^{x}}={{(\sqrt{13})}^{x/2}},\] then the number of values of x is |
| A. | 2 |
| B. | 4 |
| C. | 1 |
| D. | None of these |
| Answer» D. None of these | |
| 932. |
Solution of \[\left| 2x-3 \right| |
| A. | \[\left( -\infty ,\frac{1}{3} \right)\] |
| B. | \[\left( \frac{1}{3},5 \right)\] |
| C. | \[(5,\infty )\] |
| D. | \[\left( -\infty ,\frac{1}{3} \right)\cup (5,\infty )\] |
| Answer» C. \[(5,\infty )\] | |
| 933. |
The least integer a, for which \[1+{{\log }_{5}}({{x}^{2}}+1)\le lo{{g}_{5}}(a{{x}^{2}}+4x+a)\] is true for all \[x\in R\] is |
| A. | 6 |
| B. | 7 |
| C. | 10 |
| D. | 1 |
| Answer» C. 10 | |
| 934. |
If a, b and c are three positive real numbers such that \[a+b\ge c,\] then |
| A. | \[\frac{a}{1+a}+\frac{b}{1+b}\ge \frac{c}{1+c}\] |
| B. | \[\frac{a}{1+a}+\frac{b}{1+b}<\frac{c}{1+c}\] |
| C. | \[\frac{a}{1+a}+\frac{b}{1+b}>\frac{c}{1+c}\] |
| D. | None of these |
| Answer» B. \[\frac{a}{1+a}+\frac{b}{1+b}<\frac{c}{1+c}\] | |
| 935. |
The set of real value of x satisfying \[\left| |x-1|-1 \right|\le 1\]is |
| A. | \[[-1,3]\] |
| B. | \[[0,2]\] |
| C. | \[[-1,1]\] |
| D. | None of these |
| Answer» B. \[[0,2]\] | |
| 936. |
The solution set of the inequality \[37-(3x+5)\ge 9x-8(x-3)\] is |
| A. | \[(-\infty ,2)\] |
| B. | \[(-\infty ,-2)\] |
| C. | \[(-\infty ,2]\] |
| D. | \[(-\infty ,-2]\] |
| Answer» D. \[(-\infty ,-2]\] | |
| 937. |
If the equation \[{{2}^{x}}+{{4}^{y}}={{2}^{y}}+{{4}^{x}}\] is solved for y in terms of x where\[x |
| A. | \[x{{\log }_{2}}(1-{{2}^{x}})\] |
| B. | \[x+{{\log }_{2}}(1-{{2}^{x}})\] |
| C. | \[{{\log }_{2}}(1-{{2}^{x}})\] |
| D. | \[x{{\log }_{2}}({{2}^{x}}+1)\] |
| Answer» C. \[{{\log }_{2}}(1-{{2}^{x}})\] | |
| 938. |
Solution set of the inequality \[\frac{1}{{{2}^{x}}-1}>\frac{1}{1-{{2}^{x-1}}}\] is |
| A. | \[(1,\infty )\] |
| B. | \[(0,lo{{g}_{2}}(4/3))\] |
| C. | \[(-1,\infty )\] |
| D. | \[(0,lo{{g}_{2}}(4/3))\cup (1,\infty )\] |
| Answer» E. | |
| 939. |
Consider the following statements. I. Solution set of the inequality \[-15 |
| A. | Only I and II are true. |
| B. | Only II and III are true. |
| C. | Only I and III are true. |
| D. | All are true. |
| Answer» B. Only II and III are true. | |
| 940. |
Number of integral values of x satisfying the inequality \[{{\left( \frac{3}{4} \right)}^{6x+10-{{x}^{2}}}} |
| A. | 5 |
| B. | 6 |
| C. | 7 |
| D. | 8 |
| Answer» D. 8 | |
| 941. |
If \[\frac{\left| x+3 \right|+x}{x+2}>1,\] then \[x\in \] |
| A. | \[(-5,-2)\] |
| B. | \[(-1,\infty )\] |
| C. | \[(-5,-2)\cup (-1,\infty )\] |
| D. | None of these |
| Answer» D. None of these | |
| 942. |
A vertex of a feasible region by the linear constraints \[3x+4y\le 18,\,\,\,2x+3y\ge 3\] and \[x,y\ge 0\], is |
| A. | \[(0,2)\] |
| B. | \[(4.8,0)\] |
| C. | \[(0,3)\] |
| D. | None of these |
| Answer» E. | |
| 943. |
For \[x\in R,\,\,\,\,\left\langle x \right\rangle \] is defined as follows: \[\left\langle x \right\rangle =\left\{ \begin{matrix} x+1, \\ \left| x-4 \right|, \\ \end{matrix}\,\,\,\begin{matrix} 0\le x |
| A. | \[\{-1,1\}\] |
| B. | \[[2,\infty )\] |
| C. | \[[0,2)\] |
| D. | \[\{0,2\}\] |
| Answer» E. | |
| 944. |
Solve for \[x,\,\,\,\frac{\left| x+3 \right|+x}{x+2}>1\] |
| A. | \[x\in (-5,-2)\cup (-1,\infty )\] |
| B. | \[x\in (5,2)\cup (-1,\infty )\] |
| C. | \[x\in (5,2)\] |
| D. | \[x\in (-1,\infty )\] |
| Answer» B. \[x\in (5,2)\cup (-1,\infty )\] | |
| 945. |
Set of values of x satisfying the inequality \[\frac{{{x}^{2}}+6x-7}{\left| x+4 \right|} |
| A. | \[(-\infty ,-7)\] |
| B. | \[(-7,4)\] |
| C. | \[(-4,1)\] |
| D. | \[(1,\infty )\] |
| Answer» D. \[(1,\infty )\] | |
| 946. |
If, a, b, c, distinct positive real numbers then the expression \[\left( b+c-a \right)\text{ }\left( c+a-b \right)\text{ }\left( a+b-c \right)-abc\] is |
| A. | Positive |
| B. | Negative |
| C. | Non-positive |
| D. | Non-negative |
| Answer» C. Non-positive | |
| 947. |
Solution of \[\left| x-1 \right|\ge \left| x-3 \right|\] is |
| A. | \[x\le 2\] |
| B. | \[x\ge 2\] |
| C. | \[[1,3]\] |
| D. | None of these |
| Answer» C. \[[1,3]\] | |
| 948. |
A manufacturer has 600 liters of a 12% solution of acid. How many liters of a 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%? |
| A. | More than 120 liters but less than 300 liters |
| B. | More than 140 liters but less than 600 liters |
| C. | More than 100 liters but less than 280 liters |
| D. | More than 160 liters but less than 500 liters |
| Answer» B. More than 140 liters but less than 600 liters | |
| 949. |
The area and perimeter of a rectangle are A and P respectively. Then P and A satisfy the inequality. |
| A. | \[P+A>PA\] |
| B. | \[{{P}^{2}}\le A\] |
| C. | \[A-P<2\] |
| D. | \[{{P}^{2}}\ge 16A\] |
| Answer» E. | |
| 950. |
If \[\left| \frac{12x}{4{{x}^{2}}+9} \right|\ge 1\] for all real values of \[x,\] the inequality being satisfied only if \[\left| x \right|\] is equal to |
| A. | \[\frac{3}{2}\] |
| B. | \[\frac{2}{3}\] |
| C. | \[\frac{1}{3}\] |
| D. | \[\frac{1}{2}\] |
| Answer» B. \[\frac{2}{3}\] | |