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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.
| 7951. |
If p and q are two statements, then \[(p\Rightarrow q)\Leftrightarrow (\tilde{\ }q\Rightarrow \tilde{\ }p)\]is a |
| A. | contradiction |
| B. | tautology |
| C. | neither [a] nor [b] |
| D. | none of the above |
| Answer» C. neither [a] nor [b] | |
| 7952. |
Consider \[\frac{x}{2}+\frac{y}{4}\ge 1\] and \[\frac{x}{3}+\frac{y}{2}\le 1,x,y\ge 0.\] Then number of possible solutions are: |
| A. | Zero |
| B. | Unique |
| C. | Infinite |
| D. | None of these |
| Answer» D. None of these | |
| 7953. |
The maximum value of \[z=3x+4y\] subject to the condition \[x+y\le 40,x+2y\le 60,x,y\ge 0\] is |
| A. | 130 |
| B. | 120 |
| C. | 40 |
| D. | 140 |
| Answer» E. | |
| 7954. |
The feasible region for an LPP is shown shaded in the figure. Let \[Z=3x-4y\] be the objective function. Minimum of Z occurs at |
| A. | (0, 0) |
| B. | (0, 8) |
| C. | (5, 0) |
| D. | (4, 10) |
| Answer» C. (5, 0) | |
| 7955. |
A printing company prints two types of magazines A and B. The company earns 10 and 15 on each magazine A and B respectively. These are processed on three machines I, II & III and total time in hours available per week on each machine is as follows: Magazine \[\to \] A(x) B(y) Time available \[\downarrow \]Machine I 2 3 36 II 5 2 50 III 2 6 60 The number of constraints is |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» D. 6 | |
| 7956. |
The maximum value of \[P=x+3y\] such that \[2x+y\le 20,x+2y\le 20,x\ge 0,y\ge 0\] is |
| A. | 10 |
| B. | 60 |
| C. | 30 |
| D. | None of these |
| Answer» D. None of these | |
| 7957. |
Shamli wants to invest 50,000 in saving certificates and PPF. She wants to invest at least 15,000 in saving certificate and at least 20, 000 in PPF. The rate of interest on saving certificates is \[8%P.a.\]and that on PPF is 9% P. a formulation of the above problem as LPP to determine maximum Yearly income, is |
| A. | Maximize \[Z=0.08x+0.09y\] subject to, \[x+y\le 50,000,x\ge 15000,\] |
| B. | Maximize \[Z=0.08x+0.09y\] subject o, \[x+y\le 50,000,x\ge 15000,y\le 20,000\] |
| C. | Maximize \[Z=0.08x+0.09y\]subject to, \[x+y\le 50,000,x\le 15000,y\ge 20,000\] |
| D. | Maximize \[Z=0.08x+0.09y\] subject to, \[x+y\le 50,000,x\le 15000,y\le 20,000\] |
| Answer» B. Maximize \[Z=0.08x+0.09y\] subject o, \[x+y\le 50,000,x\ge 15000,y\le 20,000\] | |
| 7958. |
\[Z=7x+y,\] subject to\[5x+y\ge 5,x+y\ge 3,x\ge 0,y\ge 0.\] The minimum value of Z occurs at |
| A. | (3, 0) |
| B. | \[\left( \frac{1}{2},\frac{5}{2} \right)\] |
| C. | (7, 0) |
| D. | (0, 5) |
| Answer» E. | |
| 7959. |
In equations \[3x-y\ge 3\] and \[4x-y\ge 4\] |
| A. | Have solution for positive x and y |
| B. | Have no solution for positive x and y |
| C. | Have solution for all x |
| D. | Have solution for all y |
| Answer» B. Have no solution for positive x and y | |
| 7960. |
Maximize \[Z=4x+6y,\] subject to \[3x+2y\le 12,\]\[x+y\ge 4,x,y\ge 0,\]is |
| A. | \[16\,\,at\,(4,0)\] |
| B. | \[24\,\,at\,\,(0,4)\] |
| C. | \[24\,\,at\,(6,0)\] |
| D. | \[36\,\,at\,(0,6)\] |
| Answer» E. | |
| 7961. |
Every gram of wheat provides 0.1 g of proteins and 0.25g of carbohydrates. The corresponding values of rice are 0.05 g and 0.5 g respectively. Wheat costs Rs. 4 per kg and rice Rs. 6. The minimum daily requirements of proteins and carbohydrates for an average child are 50 g and 200 g respectively. Then in what quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirement of proteins and carbohydrates at minimum cost |
| A. | 400, 200 |
| B. | 300, 400 |
| C. | 200, 400 |
| D. | 400, 300 |
| Answer» B. 300, 400 | |
| 7962. |
The solution set of the following system of in equations: \[x+2y\le 3,\] \[3x+4y\ge 12,\]\[x\ge 0,\]\[y\ge 1,\] is |
| A. | Bounded region |
| B. | Unbounded region |
| C. | Only one point |
| D. | Empty set |
| Answer» E. | |
| 7963. |
Corner points of the feasible region for an LPP are\[(0,2)\]\[(3,0)\]\[(6,0)\],\[(6,8)\] and \[(0,5)\].Let \[F=4x+6y\] be the objective function. The minimum value of F occurs at |
| A. | \[(0,2)\] Only |
| B. | \[(3,0)\] Only |
| C. | The mind-point of the line segment joining the points \[(0,2)\] and \[(3,\,\,2)\]only |
| D. | Any point on the line segment joining the points \[(0,2)\] and \[(3,0)\] |
| Answer» E. | |
| 7964. |
Consider: \[z=3x+2y\] Minimize subject to:\[x+y\ge 8\]\[3x+5y\le 15\]\[x,y\ge 0\] It has: |
| A. | Infinite feasible solutions |
| B. | Unique feasible solution |
| C. | No feasible solution |
| D. | None of these |
| Answer» D. None of these | |
| 7965. |
The maximum value of \[z=6x+8y\] subject to constraints \[2x+y\le 30,x+2y\le 24\] and \[x\ge 0,y\ge 0\] is |
| A. | 90 |
| B. | 120 |
| C. | 96 |
| D. | 240 |
| Answer» C. 96 | |
| 7966. |
Which of these terms is not used in a linear programming problem? |
| A. | Slack variables |
| B. | Objective function |
| C. | Concave region |
| D. | Feasible solution |
| Answer» D. Feasible solution | |
| 7967. |
Feasible region for an LPP is shown shaded in the following figure. Minimum of \[Z=4x+3y\]occurs at the point. |
| A. | (0, 8) |
| B. | (2, 5) |
| C. | (4, 3) |
| D. | (9, 0) |
| Answer» C. (4, 3) | |
| 7968. |
A wholesale merchant wants to start the business of cereal with 24000. Wheat is 4000 per quintal and rice is 600 per quintal. He has capacity to store 200 quintal cereal. He earns the profit 25 per quintal on wheat and 40 per quintal on rice. If he store x quintal rice and y quintal wheat then for maximum profit, the objective function is |
| A. | \[25x+40y\] |
| B. | \[40x+25y\] |
| C. | \[400x+600y\] |
| D. | \[\frac{400}{40}x+\frac{600}{25}y\] |
| Answer» C. \[400x+600y\] | |
| 7969. |
The maximum value of \[z=4x+2y\]subject to constraints \[2x+3y\le 18,x+y\ge 10\] and \[x,y\ge 0\], is |
| A. | 36 |
| B. | 40 |
| C. | 20 |
| D. | None of these |
| Answer» E. | |
| 7970. |
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. \[\left[ -1,\,6 \right)\] | |
| 7971. |
The system \[2(2x+3)-10 |
| A. | infinite |
| B. | two solutions |
| C. | three sollutionns |
| D. | no solutions |
| Answer» B. two solutions | |
| 7972. |
Which of the following is not the solution of \[\left| x \right|-3|>1\]? |
| A. | \[-2<x<2\] |
| B. | \[x<-4\] |
| C. | \[x>4\] |
| D. | None of these |
| Answer» D. None of these | |
| 7973. |
To maximize the objective function \[z=2x+3y\] under the constraints \[x+y\le 30,\ x-y\ge 0,\ y\le 12,\] \[x\le 20,\] \[y\ge 3\] and \[x,\ y\ge 0\] |
| A. | \[x=12,\ y=18\] |
| B. | \[x=18,\ y=12\] |
| C. | \[x=12,\ y=12\] |
| D. | \[x=20,\ y=10\] |
| Answer» C. \[x=12,\ y=12\] | |
| 7974. |
The minimum value of\[z=2{{x}_{1}}+3{{x}_{2}}\] subject to the constraints\[2{{x}_{1}}+7{{x}_{2}}\ge 22\],\[{{x}_{1}}+{{x}_{2}}\ge 6\],\[5{{x}_{1}}+{{x}_{2}}\ge 10\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\] is [MP PET 2003] |
| A. | 14 |
| B. | 20 |
| C. | 10 |
| D. | 16 |
| Answer» B. 20 | |
| 7975. |
If the function\[f(x)=\frac{x(x-2)}{{{x}^{2}}-4},x\ne \pm 2\]is continuous at\[x=2\], then what is \[f(2)\] equal to? |
| A. | 0 |
| B. | \[\frac{1}{2}\] |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 7976. |
What is the derivative of\[{{\tan }^{-1}}\left( \frac{\sqrt{1+{{x}^{2}}}-1}{x} \right)\] with respect to \[{{\tan }^{-1}}x\]? |
| A. | 0 |
| B. | \[\frac{1}{2}\] |
| C. | 1 |
| D. | x |
| Answer» C. 1 | |
| 7977. |
If \[s=\sqrt{{{t}^{2}}+1}\], then \[\frac{{{d}^{2}}s}{d{{t}^{2}}}\] is equal to |
| A. | \[\frac{1}{s}\] |
| B. | \[\frac{1}{{{s}^{2}}}\] |
| C. | \[\frac{1}{{{s}^{3}}}\] |
| D. | \[\frac{1}{{{s}^{4}}}\] |
| Answer» D. \[\frac{1}{{{s}^{4}}}\] | |
| 7978. |
Which one of the following is correct in respect of the function \[f(x)=\left| x \right|+{{x}^{2}}\] |
| A. | \[f(x)\] is not continuous at x = 0 |
| B. | \[f(x)\] is differentiable at x = 0 |
| C. | \[f(x)\] is continuous but not differentiable at x = 0 |
| D. | None of the above |
| Answer» D. None of the above | |
| 7979. |
If \[{{(x-a)}^{2}}+{{(y-b)}^{2}}={{c}^{2}}\], for some c > 0, then\[\frac{{{\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]}^{\frac{3}{2}}}}{\frac{{{d}^{2}}y}{d{{x}^{2}}}}\] is |
| A. | Is a constant dependent on a |
| B. | Is a constant dependent on b |
| C. | Is a constant independent of a and b |
| D. | 0 |
| Answer» D. 0 | |
| 7980. |
The function \[f(x)=\frac{1-\sin x+\cos x}{1+\sin x+\cos x}\] is not defined at \[x=\pi \]. The value of \[f(\pi )\], so that \[f(x)\] is continuous at \[x=\pi \], is |
| A. | \[-\frac{1}{2}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[-1\] |
| D. | 1 |
| Answer» D. 1 | |
| 7981. |
Which of the following function is continuous at for all value of x?(i) \[f\left( x \right)\] =sgn\[({{x}^{3}}-x)\](ii) \[f\left( x \right)\] =sgn\[(2\cos x-1)\](iii) \[f\left( x \right)\] =sgn\[({{x}^{2}}-2x+3)\] |
| A. | Only (i) |
| B. | Only (iii) |
| C. | Both (ii) and (iii) |
| D. | None of these |
| Answer» C. Both (ii) and (iii) | |
| 7982. |
The set of points of discontinuity of the function\[f(x)=\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{(2\,\sin \,x)}^{2}}^{n}}{{{3}^{n}}-{{(2\cos \,x)}^{2n}}}\] is given by |
| A. | R |
| B. | \[\left\{ n\pi \pm \frac{\pi }{3},n\in I \right\}\] |
| C. | \[\left\{ n\pi \pm \frac{\pi }{6},n\in I \right\}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7983. |
Let \[0 |
| A. | \[\frac{1}{2}\] |
| B. | \[-\frac{1}{2}\] |
| C. | \[2\] |
| D. | \[-2\] |
| Answer» C. \[2\] | |
| 7984. |
Which one of the following functions is differentiable for all real values of x? |
| A. | \[\frac{x}{\left| x \right|}\] |
| B. | \[x\left| x \right|\] |
| C. | \[\frac{1}{\left| x \right|}\] |
| D. | \[\frac{1}{x}\] |
| Answer» C. \[\frac{1}{\left| x \right|}\] | |
| 7985. |
The function \[f(x)=\frac{1-\sin x+\cos x}{1+\sin x+\cos x}\] is not defined at \[x=\pi \]. The value of \[f(\pi )\] so that \[f(x)\] is continuous at \[x=\pi \] is |
| A. | \[-\frac{1}{2}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[-1\] |
| D. | \[1\] |
| Answer» D. \[1\] | |
| 7986. |
If \[y={{(1+1/x)}^{x}}\] then \[\frac{2\sqrt{{{y}_{2}}(2)+1/8}}{(log\,3/2-1/3)}\] is equal to- |
| A. | 3 |
| B. | 4 |
| C. | 1 |
| D. | 2 |
| Answer» B. 4 | |
| 7987. |
The derivative of \[{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\] with respect to \[{{\cos }^{-1}}\left[ \frac{1-{{x}^{2}}}{1+{{x}^{2}}} \right]\] is equal to: |
| A. | 1 |
| B. | -1 |
| C. | 2 |
| D. | None of these |
| Answer» B. -1 | |
| 7988. |
Let \[f(x)=[{{x}^{3}}-3],[x]=\]G.I.F. Then the no. of points in the interval (1, 2) where function is discontinuous is |
| A. | 5 |
| B. | 4 |
| C. | 6 |
| D. | 3 |
| Answer» D. 3 | |
| 7989. |
Let \[f:R\to R\] be a function defined by f(x) max\[\{x,\text{ }{{x}^{3}}\}\]. The set of all points where f(x) is NOT differentiable is |
| A. | {-1, 1} |
| B. | {-1, 0} |
| C. | {0, 1} |
| D. | {-1, 0, 1} |
| Answer» E. | |
| 7990. |
Let \[f(x)=\left\{ \begin{matrix} 3x-4, & 0\le x\le 2 \\ 2x+\ell , & 2 |
| A. | 0 |
| B. | 2 |
| C. | -2 |
| D. | -1 |
| Answer» D. -1 | |
| 7991. |
What is \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\sqrt{1+x}-1}{x}\] equal to? |
| A. | 0 |
| B. | \[\frac{1}{2}\] |
| C. | 1 |
| D. | \[-\frac{1}{2}\] |
| Answer» C. 1 | |
| 7992. |
Which of the following functions is not differentiable at\[x=1\]? |
| A. | \[f(x)=({{x}^{2}}-1)\left| (x-1)(x-2) \right|\] |
| B. | \[f(x)=\sin (\left| x-1 \right|)-\left| x-1 \right|\] |
| C. | \[f(x)=\tan (\left| x-1 \right|)+\left| x-1 \right|\] |
| D. | None of these |
| Answer» D. None of these | |
| 7993. |
If the function \[f(x)=\left\{ \begin{align} & \frac{k\,\,\cos \,\,x}{\pi -2x},when\,x\ne \frac{\pi }{2} \\ & 3,when\,x=\frac{\pi }{2} \\ \end{align} \right.\,\,be\]continuous at \[x=\frac{\pi }{2},\] then k = |
| A. | 3 |
| B. | 6 |
| C. | 12 |
| D. | None of these |
| Answer» C. 12 | |
| 7994. |
If \[f(x)={{(x+1)}^{\cot \,x}}\] is continuous at\[x=0\], then what is f (0) equal to? |
| A. | 1 |
| B. | e |
| C. | \[\frac{1}{e}\] |
| D. | \[{{e}^{2}}\] |
| Answer» C. \[\frac{1}{e}\] | |
| 7995. |
If \[f(x)=x+\frac{x}{1+x}+\frac{x}{{{(1+x)}^{2}}}+....to\,\,\infty \], then at \[x=0,f(x)\] |
| A. | Has no limit |
| B. | Is discontinuous |
| C. | Is continuous but not differentiable |
| D. | Is differentiable |
| Answer» C. Is continuous but not differentiable | |
| 7996. |
A function f is defined as follows \[f(x)={{x}^{p}}\cos \left( \frac{1}{x} \right),x\ne 0f(0)=0\] What conditions should be imposed on p so that f may be continuous at x = 0? |
| A. | p = 0 |
| B. | p > 0 |
| C. | p < 0 |
| D. | No value of p |
| Answer» C. p < 0 | |
| 7997. |
A function \[f:R\to R\] is defined as \[f(x)={{x}^{2}}\] for \[x\ge 0\] and \[f(x)=-x\] for \[x |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» B. 2 only | |
| 7998. |
If the derivative of the function\[f(x)=\left\{ \begin{matrix} a{{x}^{2}}+b & x |
| A. | a=2, b=3 |
| B. | a=3, b=2 |
| C. | a=-2, b=-3 |
| D. | a=-3, b=-2 |
| Answer» B. a=3, b=2 | |
| 7999. |
What is the derivative of \[{{x}^{3}}\] with respect to\[{{x}^{2}}\]? |
| A. | \[3{{x}^{2}}\] |
| B. | \[\frac{3x}{2}\] |
| C. | x |
| D. | \[\frac{3}{2}\] |
| Answer» C. x | |
| 8000. |
The derivative of ln \[(x+sin\text{ }x)\] with respect to \[(x+cos\text{ }x)\] is |
| A. | \[\frac{1+\cos x}{(x+\sin x)(1-\sin x)}\] |
| B. | \[\frac{1-\cos x}{(x+\sin x)(1+\sin x)}\] |
| C. | \[\frac{1-\cos x}{(x-\sin x)(1+\cos x)}\] |
| D. | \[\frac{1+\cos \,\,x}{(x-sin\,\,x)(1-cos\,\,x)}\] |
| Answer» B. \[\frac{1-\cos x}{(x+\sin x)(1+\sin x)}\] | |