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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.
| 3301. |
The maximum value of \[\sin x\,\,(1+\cos x)\] will be at the [UPSEAT 1999] |
| A. | \[x=\frac{\pi }{2}\] |
| B. | \[x=\frac{\pi }{6}\] |
| C. | \[x=\frac{\pi }{3}\] |
| D. | \[x=\pi \] |
| Answer» D. \[x=\pi \] | |
| 3302. |
The maximum and minimum values of \[{{x}^{3}}-18{{x}^{2}}+96x\] in interval (0, 9) are [RPET 1999] |
| A. | 160, 0 |
| B. | 60, 0 |
| C. | 160, 128 |
| D. | 120, 28 |
| Answer» D. 120, 28 | |
| 3303. |
Divide 20 into two parts such that the product of one part and the cube of the other is maximum. The two parts are [DCE 1999] |
| A. | (10, 10) |
| B. | \[(5,\,\,15)\] |
| C. | (13, 7) |
| D. | None of these |
| Answer» C. (13, 7) | |
| 3304. |
x and y be two variables such that \[x>0\] and\[xy=1\]. Then the minimum value of \[x+y\] is [Kurukshetra CEE 1998; MP PET 2002] |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 0 |
| Answer» B. 3 | |
| 3305. |
What are the minimum and maximum values of the function \[{{x}^{5}}-5{{x}^{4}}+5{{x}^{3}}-10\] [DCE 1999] |
| A. | ? 37, ? 9 |
| B. | 10, 0 |
| C. | It has 2 min. and 1 max. values |
| D. | It has 2 max. and 1 min. values |
| Answer» B. 10, 0 | |
| 3306. |
The minimum value of \[{{e}^{(2{{x}^{2}}-2x+1){{\sin }^{2}}x}}\] is [Roorkee Qualifying 1998] |
| A. | e |
| B. | 1/e |
| C. | 1 |
| D. | 0 |
| Answer» D. 0 | |
| 3307. |
If \[f(x)=\frac{{{x}^{2}}-1}{{{x}^{2}}+1}\], for every real number x, then the minimum value of f [IIT 1998] |
| A. | Does not exist because f is unbounded |
| B. | Is not attained even though f is bounded |
| C. | Is equal to 1 |
| D. | Is equal to ?1 |
| Answer» E. | |
| 3308. |
The maximum value of function \[{{x}^{3}}-12{{x}^{2}}+36x+\]17 in the interval [1, 10] is |
| A. | 17 |
| B. | 177 |
| C. | 77 |
| D. | None of these |
| Answer» C. 77 | |
| 3309. |
20 is divided into two parts so that product of cube of one quantity and square of the other quantity is maximum. The parts are [RPET 1997] |
| A. | 10, 10 |
| B. | 16, 4 |
| C. | 8, 12 |
| D. | 12, 8 |
| Answer» E. | |
| 3310. |
The sum of two non-zero numbers is 4. The minimum value of the sum of their reciprocals is [Kurukshetra CEE 1998] |
| A. | \[\frac{3}{4}\] |
| B. | \[\frac{6}{5}\] |
| C. | 1 |
| D. | None of these |
| Answer» D. None of these | |
| 3311. |
The minimum value of the function \[y=2{{x}^{3}}-21{{x}^{2}}+36x-20\] is [MP PET 1999] |
| A. | ?128 |
| B. | ?126 |
| C. | ?120 |
| D. | None of these |
| Answer» B. ?126 | |
| 3312. |
The minimum value of \[2{{x}^{2}}+x-1\]is [EAMCET 2003] |
| A. | \[-\frac{1}{4}\] |
| B. | \[\frac{3}{2}\] |
| C. | \[\frac{-9}{8}\] |
| D. | \[\frac{9}{4}\] |
| Answer» D. \[\frac{9}{4}\] | |
| 3313. |
If from a wire of length 36 metre a rectangle of greatest area is made, then its two adjacent sides in metre are [MP PET 1998] |
| A. | 6, 12 |
| B. | 9, 9 |
| C. | 10, 8 |
| D. | 13, 5 |
| Answer» C. 10, 8 | |
| 3314. |
Maximum value of \[x{{(1-x)}^{2}}\] when \[0\le x\le 2\], is [MP PET 1997] |
| A. | \[\frac{2}{27}\] |
| B. | \[\frac{4}{27}\] |
| C. | 5 |
| D. | 0 |
| Answer» C. 5 | |
| 3315. |
The minimum value of the expression \[7-20x+11{{x}^{2}}\] is |
| A. | \[\frac{177}{11}\] |
| B. | \[-\frac{177}{11}\] |
| C. | \[-\frac{23}{11}\] |
| D. | \[\frac{23}{11}\] |
| Answer» D. \[\frac{23}{11}\] | |
| 3316. |
If the function \[f(x)={{x}^{4}}-62{{x}^{2}}+ax+9\]is maximum at \[x=1\], then the value of a is |
| A. | 120 |
| B. | ?120 |
| C. | 52 |
| D. | 128 |
| Answer» B. ?120 | |
| 3317. |
The minimum value of the function \[2\cos 2x-\cos 4x\]in \[0\le x\le \pi \]is |
| A. | 0 |
| B. | 1 |
| C. | \[\frac{3}{2}\] |
| D. | ? 3 |
| Answer» E. | |
| 3318. |
The function \[{{x}^{5}}-5{{x}^{4}}+5{{x}^{3}}-10\]has a maximum, when x = [MP PET 1995] |
| A. | 3 |
| B. | 2 |
| C. | 1 |
| D. | 0 |
| Answer» D. 0 | |
| 3319. |
If \[f(x)=2{{x}^{3}}-21{{x}^{2}}+36x-30\], then which one of the following is correct |
| A. | \[f(x)\] has minimum at \[x=1\] |
| B. | \[f(x)\] has maximum at \[x=6\] |
| C. | \[f(x)\]has maximum at \[x=1\] |
| D. | \[f(x)\] has no maxima or minima |
| Answer» D. \[f(x)\] has no maxima or minima | |
| 3320. |
If sum of two numbers is 3, then maximum value of the product of first and the square of second is [MP PET 1996] |
| A. | 4 |
| B. | 3 |
| C. | 2 |
| D. | 1 |
| Answer» B. 3 | |
| 3321. |
A minimum value of \[\int_{0}^{x}{t{{e}^{-{{t}^{2}}}}}\]dt is [EAMCET 2003] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 0 |
| Answer» E. | |
| 3322. |
The value of a so that the sum of the squares of the roots of the equation \[{{x}^{2}}-(a-2)x-a+1=0\] assume the least value, is [RPET 2000; AIEEE 2005] |
| A. | 2 |
| B. | 1 |
| C. | 3 |
| D. | 0 |
| Answer» C. 3 | |
| 3323. |
The largest term in the sequence \[{{a}_{n}}=\frac{{{n}^{2}}}{{{n}^{3}}+200}\] is given by |
| A. | \[\frac{529}{49}\] |
| B. | \[\frac{8}{89}\] |
| C. | \[\frac{49}{543}\] |
| D. | None of these |
| Answer» D. None of these | |
| 3324. |
OR When x is positive, the minimum value of \[{{x}^{x}}\]is [EAMCET 1987] |
| A. | \[{{e}^{-1}}\] |
| B. | \[{{e}^{-1/e}}\] |
| C. | \[{{e}^{1/e}}\] |
| D. | \[{{e}^{e}}\] |
| Answer» C. \[{{e}^{1/e}}\] | |
| 3325. |
\[{{x}^{x}}\] has a stationary point at [Karnataka CET 1993] |
| A. | \[x=e\] |
| B. | \[x=\frac{1}{e}\] |
| C. | \[x=1\] |
| D. | \[x=\sqrt{e}\] |
| Answer» C. \[x=1\] | |
| 3326. |
Local maximum and local minimum values of the function \[(x-1){{(x+2)}^{2}}\]are |
| A. | ? 4, 0 |
| B. | 0, ? 4 |
| C. | 4, 0 |
| D. | None of these |
| Answer» C. 4, 0 | |
| 3327. |
If for a function \[f(x),f'(a)=0,f''(a)=0\], \[{{f}''}'(a)>0\], then at \[x=a\], \[f(x)\] is [MP PET 1994; Pb. CET 2002] |
| A. | Minimum |
| B. | Maximum |
| C. | Not an extreme point |
| D. | Extreme point |
| Answer» D. Extreme point | |
| 3328. |
The least value of the sum of any positive real number and its reciprocal is [MP PET 1994] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 3329. |
The number that exceeds its square by the greatest amount is [Roorkee 1990] |
| A. | ? 1 |
| B. | 0 |
| C. | \[\frac{1}{2}\] |
| D. | 1 |
| Answer» D. 1 | |
| 3330. |
The sum of two numbers is fixed. Then its multiplication is maximum, when |
| A. | Each number is half of the sum |
| B. | Each number is \[\frac{1}{3}\]and \[\frac{2}{3}\] respectively of the sum |
| C. | Each number is \[\frac{1}{4}\] and \[\frac{3}{4}\] respectively of the sum |
| D. | None of these |
| Answer» B. Each number is \[\frac{1}{3}\]and \[\frac{2}{3}\] respectively of the sum | |
| 3331. |
If \[x+y=10\], then the maximum value of xy is |
| A. | 5 |
| B. | 20 |
| C. | 25 |
| D. | None of these |
| Answer» D. None of these | |
| 3332. |
Maximum value of \[{{\left( \frac{1}{x} \right)}^{x}}\] is [DCE 1999; Karnataka CET 1999; UPSEAT 2003] |
| A. | \[{{(e)}^{e}}\] |
| B. | \[{{(e)}^{e}}\] |
| C. | \[{{(e)}^{-e}}\] |
| D. | \[{{\left( \frac{1}{e} \right)}^{e}}\] |
| Answer» C. \[{{(e)}^{-e}}\] | |
| 3333. |
If \[f(x)=2{{x}^{3}}-3{{x}^{2}}-12x+5\]and \[x\in [-2,\,4]\], then the maximum value of function is at the following value of x [MP PET 1987, 2000; Orissa JEE 2005] |
| A. | 2 |
| B. | ?1 |
| C. | ? 2 |
| D. | 4 |
| Answer» E. | |
| 3334. |
The maximum and minimum values of the function \[|\sin 4x+3|\]are |
| A. | 1, 2 |
| B. | 4, 2 |
| C. | 2, 4 |
| D. | ? 1, 1 |
| Answer» C. 2, 4 | |
| 3335. |
36 factorize into two factors in such a way that sum of factors is minimum, then the factors are [MP PET 1987] |
| A. | 2, 18 |
| B. | 9, 4 |
| C. | 3, 12 |
| D. | None of these |
| Answer» E. | |
| 3336. |
The area of a rectangle will be maximum for the given perimeter, when rectangle is a [AI CBSE 1991; RPET 1999] |
| A. | Parallelogram |
| B. | Trapezium |
| C. | Square |
| D. | None of these |
| Answer» D. None of these | |
| 3337. |
Of the given perimeter, the triangle having maximum area is |
| A. | Isosceles triangle |
| B. | Right angled triangle |
| C. | Equilateral |
| D. | None of these |
| Answer» D. None of these | |
| 3338. |
The necessary condition to be maximum or minimum for the function is |
| A. | \[f'(x)=0\]and it is sufficient |
| B. | \[f''(x)=0\]and it is sufficient |
| C. | \[f'(x)=0\]but it is not sufficient |
| D. | \[f'(x)=0\]and \[f''(x)=-ve\] |
| Answer» D. \[f'(x)=0\]and \[f''(x)=-ve\] | |
| 3339. |
The adjacent sides of a rectangle with given perimeter as 100 cm and enclosing maximum area are [MP PET 1993] |
| A. | 10 cm and 40 cm |
| B. | 20 cm and 30 cm |
| C. | 25 cm and 25 cm |
| D. | 15 cm and 35 cm |
| Answer» D. 15 cm and 35 cm | |
| 3340. |
If two sides of a triangle be given, then the area of the triangle will be maximum if the angle between the given sides be |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | \[\frac{\pi }{6}\] |
| D. | \[\frac{\pi }{2}\] |
| Answer» E. | |
| 3341. |
The function \[x\sqrt{1-{{x}^{2}}},(x>0)\]has |
| A. | A local maxima |
| B. | A local minima |
| C. | Neither a local maxima nor a local minima |
| D. | None of these |
| Answer» B. A local minima | |
| 3342. |
If \[x+y=16\] and \[{{x}^{2}}+{{y}^{2}}\] is minimum, then the values of x and y are |
| A. | 3, 13 |
| B. | 4, 12 |
| C. | 6, 10 |
| D. | 8, 8 |
| Answer» E. | |
| 3343. |
Negation of ?Paris in France and London is in England? is |
| A. | Paris is in England and London is in France |
| B. | Paris is not in France or London is not in England |
| C. | Paris is in England or London is in France |
| D. | None of these |
| Answer» C. Paris is in England or London is in France | |
| 3344. |
Negation of the conditional : ?If it rains, I shall go to school? is |
| A. | It rains and I shall go to school |
| B. | It rains and I shall not go to school |
| C. | It does not rains and I shall go to school |
| D. | None of these |
| Answer» C. It does not rains and I shall go to school | |
| 3345. |
Which of the following is an open statement |
| A. | x is a natural number |
| B. | Give me a glass of water |
| C. | Wish you best of luck |
| D. | Good morning to all |
| Answer» B. Give me a glass of water | |
| 3346. |
\[(p\ \wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q)\] is [Karnataka CET 2003] |
| A. | A tautology |
| B. | A contradiction |
| C. | Both a tautology and a contradiction |
| D. | Neither a tautology nor a contradiction |
| Answer» C. Both a tautology and a contradiction | |
| 3347. |
\[\tilde{\ }p\wedge q\] is logically equivalent to [Karnataka CET 2004] |
| A. | \[p\to q\] |
| B. | \[q\to p\] |
| C. | \[\tilde{\ }(p\to q)\] |
| D. | \[\tilde{\ }(q\to p)\] |
| Answer» E. | |
| 3348. |
Which of the following is not a proposition [Karnataka CET 2002] |
| 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 | |
| 3349. |
The false statement in the following is [Karnataka CET 2002] |
| A. | \[p\wedge (\tilde{\ }p)\] is a contradiction |
| B. | \[(p\Rightarrow q)\Leftrightarrow (\tilde{\ }q\Rightarrow \ \tilde{\ }p)\] is a contradiction |
| C. | \[\tilde{\ }(\tilde{\ }p)\Leftrightarrow p\] is a tautology |
| D. | \[p\vee (\tilde{\ }p)\]Û is a tautology |
| Answer» C. \[\tilde{\ }(\tilde{\ }p)\Leftrightarrow p\] is a tautology | |
| 3350. |
If \[p\Rightarrow (\tilde{\ }p\vee q)\] is false, the truth values of p and q are respectively [Karnataka CET 2002] |
| A. | F, T |
| B. | F, F |
| C. | T, T |
| D. | T, F |
| Answer» E. | |