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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.
| 7801. |
The function \[f:R\to R\] is defined by \[f\left( x \right)={{\cos }^{2}}x+{{\sin }^{4}}x\] for \[x\in R\]. Then the range of \[f(x)\]is |
| A. | \[\left( \frac{3}{4},1 \right]\] |
| B. | \[\left[ \frac{3}{4},1 \right)\] |
| C. | \[\left[ \frac{3}{4},1 \right]\] |
| D. | \[\left( \frac{3}{4},1 \right)\] |
| Answer» D. \[\left( \frac{3}{4},1 \right)\] | |
| 7802. |
If the coordinates of a point be given by the equation \[x=a(1-\cos \theta ),\]\[y=a\sin \theta \], then the locus of the point will be |
| A. | A straight line |
| B. | A circle |
| C. | A parabola |
| D. | An ellipse |
| Answer» C. A parabola | |
| 7803. |
The locus of a point whose difference of distance from points (3, 0) and (-3,0) is 4, is [MP PET 2002] |
| A. | \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{5}=1\] |
| B. | \[\frac{{{x}^{2}}}{5}-\frac{{{y}^{2}}}{4}=1\] |
| C. | \[\frac{{{x}^{2}}}{2}-\frac{{{y}^{2}}}{3}=1\] |
| D. | \[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1\] |
| Answer» B. \[\frac{{{x}^{2}}}{5}-\frac{{{y}^{2}}}{4}=1\] | |
| 7804. |
If \[A(\cos \alpha ,\sin \alpha ),\ B(\sin \alpha ,-\cos \alpha ),\,C(1,\text{ }2)\]are the vertices of a \[\Delta ABC\], then as \[\alpha \]varies, the locus of its centroid is |
| A. | \[{{x}^{2}}+{{y}^{2}}-2x-4y+1=0\] |
| B. | \[3({{x}^{2}}+{{y}^{2}})-2x-4y+1=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\] |
| D. | None of these |
| Answer» C. \[{{x}^{2}}+{{y}^{2}}-2x-4y+3=0\] | |
| 7805. |
A point moves in such a way that its distance from (1,-2) is always the twice from (-3,5), the locus of the point is |
| A. | \[3{{x}^{2}}+{{y}^{2}}+26x+44y-131=0\] |
| B. | \[{{x}^{2}}+3{{y}^{2}}-26x+44y-131=0\] |
| C. | \[3({{x}^{2}}+{{y}^{2}})+26x-44y+131=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 7806. |
If the coordinates of a point be given by the equations \[x=b\sec \varphi ,\ \ y=a\tan \varphi \], then its locus is |
| A. | A straight line |
| B. | A circle |
| C. | An ellipse |
| D. | A hyperbola |
| Answer» E. | |
| 7807. |
If the points (0, 0), \[(2,\,2\sqrt{3})\] and (a, b) be the vertices of an equilateral triangle, then \[(a,\,b)=\] |
| A. | (0, - 4) |
| B. | (0, 4) |
| C. | (4, 0) |
| D. | (- 4, 0) |
| Answer» D. (- 4, 0) | |
| 7808. |
If the point (a, a) are placed in between the lines \[|x+y|=4\], then [AMU 2005] |
| A. | | a| = 2 |
| B. | \[|a|\,=3\] |
| C. | | a| < 2 |
| D. | | a| < 3 |
| Answer» D. | a| < 3 | |
| 7809. |
The coordinates of the point dividing internally the lines joining the points (4, -2) and (8, 6) in the ratio 7 : 5 will be [AMU 1979; MP PET 1984] |
| A. | \[(16,\,18)\] |
| B. | \[(18,\,16)\] |
| C. | \[\left( \frac{19}{3},\,\frac{8}{3} \right)\] |
| D. | \[\left( \frac{8}{3},\frac{19}{3} \right)\] |
| Answer» D. \[\left( \frac{8}{3},\frac{19}{3} \right)\] | |
| 7810. |
If the point (x, - 1), (3, y), (- 2, 3) and (- 3, - 2) be the vertices of a parallelogram, then |
| A. | \[x=2,\,y=4\] |
| B. | \[x=1,\,y=2\] |
| C. | \[x=4,\,y=2\] |
| D. | None of these |
| Answer» B. \[x=1,\,y=2\] | |
| 7811. |
The distance between the points (7, 5) and (3, 2) is equal to [Pb. CET 2002] |
| A. | 2 units |
| B. | 3 units |
| C. | 4 units |
| D. | 5 units |
| Answer» E. | |
| 7812. |
The point on y-axis equidistant from the points (3, 2) and (-1, 3) is |
| A. | (0, -3) |
| B. | (0, -3/2) |
| C. | (0, 3/2) |
| D. | (0, 3) |
| Answer» C. (0, 3/2) | |
| 7813. |
The coordinates of a point are (0, 1) and the ordinate of another point is - 3. If the distance between the two points is 5, then the abscissa of another point is |
| A. | 3 |
| B. | -3 |
| C. | \[\pm 3\] |
| D. | 1 |
| Answer» D. 1 | |
| 7814. |
The points (3a, 0), (0, 3b) and (a, 2b) are [MP PET 1982] |
| A. | Vertices of an equilateral triangle |
| B. | Vertices of an isosceles triangle |
| C. | Vertices of a right angled isosceles triangle |
| D. | Collinear |
| Answer» E. | |
| 7815. |
The points \[\left( \frac{a}{\sqrt{3}},a \right),\ \left( \frac{2a}{\sqrt{3}},\,2a \right),\ \left( \frac{a}{\sqrt{3}},\,3a \right)\]are the vertices of |
| A. | An equilateral triangle |
| B. | An isosceles triangle |
| C. | A right angled triangle |
| D. | None of these |
| Answer» C. A right angled triangle | |
| 7816. |
A triangle with vertices (4, 0), (-1, -1), (3, 5) is [AIEEE 2002] |
| A. | Isosceles and right angled |
| B. | Isosceles but not right angled |
| C. | Right angled but not isosceles |
| D. | Neither right angled nor isosceles |
| Answer» B. Isosceles but not right angled | |
| 7817. |
The orthocentre of the triangle with vertices \[\left( 2,\,\frac{\sqrt{3}-1}{2} \right)\], \[\left( \frac{1}{2},\,-\frac{1}{2} \right)\] and \[\left( 2,\,-\frac{1}{2} \right)\] is [IIT 1993] |
| A. | \[\left( \frac{3}{2},\,\frac{\sqrt{3}-3}{6} \right)\] |
| B. | \[\left( 2,\,-\frac{1}{2} \right)\] |
| C. | \[\left( \frac{5}{4},\,\frac{\sqrt{3}-2}{4} \right)\] |
| D. | \[\left( \frac{1}{2},\,-\frac{1}{2} \right)\] |
| Answer» C. \[\left( \frac{5}{4},\,\frac{\sqrt{3}-2}{4} \right)\] | |
| 7818. |
The orthocentre of the triangle formed by (0, 0), (8, 0), (4 6) is [EAMCET 1991] |
| A. | \[\left( 4,\,\frac{8}{3} \right)\] |
| B. | (3, 4) |
| C. | (4, 3) |
| D. | (-3, 4) |
| Answer» B. (3, 4) | |
| 7819. |
Two vertices of a triangle are (5, 4) and (-2, 4). If its centroid is (5, 6) then the third vertex has the coordinates [MP PET 1993] |
| A. | (12, 10) |
| B. | (10, 12) |
| C. | (-10, 12) |
| D. | (12, -10) |
| Answer» B. (10, 12) | |
| 7820. |
If the points \[(x+1,\,2),\ (1,x+2),\ \left( \frac{1}{x+1},\frac{2}{x+1} \right)\]are collinear, then x is [RPET 2002] |
| A. | 4 |
| B. | 0 |
| C. | -4 |
| D. | None of these |
| Answer» D. None of these | |
| 7821. |
Three points \[(p+1,\text{ }1)\], \[(2p+1,\text{ }3\]) and \[(2p+2,\ 2p)\] are collinear, if p = [MP PET 1986] |
| A. | -1 |
| B. | 1 |
| C. | 2 |
| D. | 0 |
| Answer» D. 0 | |
| 7822. |
The area of the triangle with vertices at \[(-4,\text{ }1),\,(1,\text{ }2),\,(4,\text{ }-3)\] is [EAMCET 1980] |
| A. | 14 |
| B. | 16 |
| C. | 15 |
| D. | None of these |
| Answer» B. 16 | |
| 7823. |
If \[A(6,3),\]\[B(-3,5)\], \[C(4,-2)\] and \[D(x,\text{ }3x)\]are four points. If the ratio of area of \[\Delta DBC\]and \[\Delta ABC\]is 1 : 2, then the value of x, will be [IIT 1959] |
| A. | \[\frac{11}{8}\] |
| B. | \[\frac{8}{11}\] |
| C. | \[3\] |
| D. | None of these |
| Answer» B. \[\frac{8}{11}\] | |
| 7824. |
The area of the triangle formed by the lines \[y={{m}_{1}}x+{{c}_{1}},\,\] \[y={{m}_{2}}x+{{c}_{2}}\] and \[x=0\]is |
| A. | \[\frac{1}{2}\frac{{{({{c}_{1}}+{{c}_{2}})}^{2}}}{({{m}_{1}}-{{m}_{2}})}\] |
| B. | \[\frac{1}{2}\frac{{{({{c}_{1}}-{{c}_{2}})}^{2}}}{({{m}_{1}}+{{m}_{2}})}\] |
| C. | \[\frac{1}{2}\frac{{{({{c}_{1}}-{{c}_{2}})}^{2}}}{({{m}_{1}}-{{m}_{2}})}\] |
| D. | \[\frac{{{({{c}_{1}}-{{c}_{2}})}^{2}}}{({{m}_{1}}-{{m}_{2}})}\] |
| Answer» D. \[\frac{{{({{c}_{1}}-{{c}_{2}})}^{2}}}{({{m}_{1}}-{{m}_{2}})}\] | |
| 7825. |
If the vertices of a triangle be \[(am_{1}^{2},2a{{m}_{1}}),\,(am_{2}^{2},2a{{m}_{2}})\] and \[(am_{3}^{2},2a{{m}_{3}}),\] then the area of the triangle is |
| A. | \[a({{m}_{2}}-{{m}_{3}})({{m}_{3}}-{{m}_{1}})({{m}_{1}}-{{m}_{2}})\] |
| B. | \[({{m}_{2}}-{{m}_{3}})({{m}_{3}}-{{m}_{1}})({{m}_{1}}-{{m}_{2}})\] |
| C. | \[{{a}^{2}}({{m}_{2}}-{{m}_{3}})({{m}_{3}}-{{m}_{1}})({{m}_{1}}-{{m}_{2}})\] |
| D. | None of these |
| Answer» D. None of these | |
| 7826. |
Two fixed points are \[A(a,0)\]and\[B(-a,0)\]. If\[\angle A-\angle B=\theta \], then the locus of point C of triangle ABC will be [Roorkee 1982] |
| A. | \[{{x}^{2}}+{{y}^{2}}+2xy\tan \theta ={{a}^{2}}\] |
| B. | \[{{x}^{2}}-{{y}^{2}}+2xy\tan \theta ={{a}^{2}}\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+2xy\cot \theta ={{a}^{2}}\] |
| D. | \[{{x}^{2}}-{{y}^{2}}+2xy\cot \theta ={{a}^{2}}\] |
| Answer» E. | |
| 7827. |
Fifteen persons among whom are A and B, sit down at random at a round table. The probability that there are 4 persons between A and B, is |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{2}{3}\] |
| C. | \[\frac{2}{7}\] |
| D. | \[\frac{1}{7}\] |
| Answer» E. | |
| 7828. |
A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. Find the probability that the fruits are both apples or both oranges [AMU 2002] |
| A. | \[\frac{24}{144}\] |
| B. | \[\frac{56}{144}\] |
| C. | \[\frac{68}{144}\] |
| D. | \[\frac{76}{144}\] |
| Answer» E. | |
| 7829. |
Ten students are seated at random in a row. The probability that two particular students are not seated side by side is |
| A. | \[\frac{4}{5}\] |
| B. | \[\frac{3}{5}\] |
| C. | \[\frac{2}{5}\] |
| D. | \[\frac{1}{5}\] |
| Answer» B. \[\frac{3}{5}\] | |
| 7830. |
Two numbers are selected randomly from the set \[S=\{1,\,2,\,3,\,4,\,5,\,6\}\] without replacement one by one. The probability that minimum of the two numbers is less than 4 is [IIT Screening 2003] |
| A. | \[\frac{1}{15}\] |
| B. | \[\frac{14}{15}\] |
| C. | \[\frac{1}{5}\] |
| D. | \[\frac{4}{5}\] |
| Answer» E. | |
| 7831. |
If four persons are chosen at random from a group of 3 men, 2 women and 4 children. Then the probability that exactly two of them are children, is [Kurukshetra CEE 1996; DCE 1999] |
| A. | \[\frac{10}{21}\] |
| B. | \[\frac{8}{63}\] |
| C. | \[\frac{5}{21}\] |
| D. | \[\frac{9}{21}\] |
| Answer» B. \[\frac{8}{63}\] | |
| 7832. |
A box contains 10 mangoes out of which 4 are rotten. 2 mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is [EAMCET 1992] |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{8}{15}\] |
| C. | \[\frac{5}{18}\] |
| D. | \[\frac{2}{3}\] |
| Answer» D. \[\frac{2}{3}\] | |
| 7833. |
Two persons each make a single throw with a die. The probability they get equal value is\[{{p}_{1}}\]. Four persons each make a single throw and probability of three being equal is\[{{p}_{2}}\], then |
| A. | \[{{p}_{1}}={{p}_{2}}\] |
| B. | \[{{p}_{1}}<{{p}_{2}}\] |
| C. | \[{{p}_{1}}>{{p}_{2}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7834. |
In a lottery 50 tickets are sold in which 14 are of prize. A man bought 2 tickets, then the probability that the man win the prize, is |
| A. | \[\frac{17}{35}\] |
| B. | \[\frac{18}{35}\] |
| C. | \[\frac{72}{175}\] |
| D. | \[\frac{13}{175}\] |
| Answer» B. \[\frac{18}{35}\] | |
| 7835. |
A bag contains 4 white, 5 red and 6 black balls. If two balls are drawn at random, then the probability that one of them is white is |
| A. | \[\frac{44}{105}\] |
| B. | \[\frac{11}{105}\] |
| C. | \[\frac{11}{21}\] |
| D. | None of these |
| Answer» B. \[\frac{11}{105}\] | |
| 7836. |
Two cards are drawn at random from a pack of 52 cards. The probability that both are the cards of spade is |
| A. | \[\frac{1}{26}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{1}{17}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7837. |
For a biased dice, the probability for the different faces to turn up are Face 1 2 3 4 5 6 P 0.01 0.32 0.21 0.15 0.05 0.147 The dice is tossed and it is told that either the face 1 or face 2 has shown up, then the probability that it is face, 1, is |
| A. | \[\frac{16}{21}\] |
| B. | \[\frac{1}{10}\] |
| C. | \[\frac{5}{16}\] |
| D. | \[\frac{5}{21}\] |
| Answer» E. | |
| 7838. |
A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of eleven steps he is one step away from the starting point is |
| A. | \[\frac{{{2}^{5}}{{.3}^{5}}}{{{5}^{10}}}\] |
| B. | \[462\times {{\left( \frac{6}{25} \right)}^{5}}\] |
| C. | \[231\times \frac{{{3}^{5}}}{{{5}^{10}}}\] |
| D. | None of these |
| Answer» C. \[231\times \frac{{{3}^{5}}}{{{5}^{10}}}\] | |
| 7839. |
A coin is tossed thrice. If E be the event of showing at least two heads and F be the event of showing head in the first throw, then find \[P\left( \frac{E}{F} \right)\] |
| A. | \[\frac{4}{3}\] |
| B. | \[\frac{3}{4}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{1}{2}\] |
| Answer» C. \[\frac{1}{4}\] | |
| 7840. |
A and B are two independent witnesses (i.e there in no collision between them) in a case. The probability that A will speak the truth is x and the probability that B will speak the truth is y. A and B agree in a certain statement. The probability that the statement is true is |
| A. | \[\frac{x-y}{x+y}\] |
| B. | \[\frac{xy}{1+x+y+xy}\] |
| C. | \[\frac{x-y}{1-x-y+2xy}\] |
| D. | \[\frac{xy}{1-x-y+2xy}\] |
| Answer» E. | |
| 7841. |
A problem in mathematics is given to three students, A, B, C and their respective probability of solving the problem is\[\frac{1}{2}\], \[\frac{1}{3}\]and\[\frac{1}{4}\]. Probability that the problem is solved is |
| A. | \[\frac{3}{4}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{1}{3}\] |
| Answer» B. \[\frac{1}{2}\] | |
| 7842. |
A box contains N cons, m of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is \[\frac{1}{2},\] while it is \[\frac{2}{3}\] when a biased coin is tossed. A coin is drawn from the box at random and it tossed twice. Then the probability that the coin drawn is fair, is |
| A. | \[\frac{9m}{8N+m}\] |
| B. | \[\frac{9m}{8N-m}\] |
| C. | \[\frac{9m}{8m-N}\] |
| D. | \[\frac{9m}{8m+N}\] |
| Answer» B. \[\frac{9m}{8N-m}\] | |
| 7843. |
In a book of 500 pages, it is found that there are 250 typing errors. Assume that Poisson law holds for the number of errors per page. Then, the probability that a random sample of 2 pages will contain no error, is |
| A. | \[{{e}^{-0.3}}\] |
| B. | \[{{e}^{-0.5}}\] |
| C. | \[{{e}^{-1}}\] |
| D. | \[{{e}^{-2}}\] |
| Answer» D. \[{{e}^{-2}}\] | |
| 7844. |
A fair coin is tossed 99 times. If X is the number of times head occurs, \[P(X=r)\] is maximum when r is |
| A. | 49 or 50 |
| B. | 50 or 51 |
| C. | 51 |
| D. | None of these |
| Answer» B. 50 or 51 | |
| 7845. |
Let \[0 |
| A. | \[P(B/A)=P(B)-P(A)\] |
| B. | \[P(A'\cup B')=P(A')+P(B')\] |
| C. | \[P(A\cap B)=P(A')P(B')\] |
| D. | None of these |
| Answer» E. | |
| 7846. |
The probability of guessing correctly at least 8 out of 10 answers on a true-false examination is |
| A. | \[\frac{5}{128}\] |
| B. | \[\frac{19}{128}\] |
| C. | \[\frac{11}{128}\] |
| D. | \[\frac{7}{128}\] |
| Answer» E. | |
| 7847. |
In from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is |
| A. | \[\frac{13}{32}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{1}{32}\] |
| D. | \[\frac{3}{16}\] |
| Answer» B. \[\frac{1}{4}\] | |
| 7848. |
In praxis business school Kolkata, 50% students like chocolate, 30% students like cake and 10% like booth. If a student is selected at random then what is the probability that he likes chocolates if it is known that he likes cake? |
| A. | 44256 |
| B. | 44318 |
| C. | 44319 |
| D. | None of these |
| Answer» B. 44318 | |
| 7849. |
For two events A and B it is given that \[P(A)=P\left( \frac{A}{B} \right)=\frac{1}{4}\] and \[P\left( \frac{B}{A} \right)=\frac{1}{2}.\] Then, |
| A. | A and B are mutually exclusive events |
| B. | A and B are dependent events |
| C. | \[P\overline{\left( \frac{A}{b} \right)}=\frac{3}{4}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7850. |
A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads is |
| A. | \[\frac{15}{{{2}^{8}}}\] |
| B. | \[\frac{2}{15}\] |
| C. | \[\frac{15}{{{2}^{13}}}\] |
| D. | None of these |
| Answer» D. None of these | |