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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.
| 751. |
Slope of a line which cuts intercepts of equal lengths on the axes is [MP PET 1986]o00000 |
| A. | - 1 |
| B. | 0 |
| C. | 2 |
| D. | \[\sqrt{3}\] |
| Answer» B. 0 | |
| 752. |
\[\overset{\to }{\mathop{a}}\,\text{ },\overset{\to }{\mathop{b}}\,\,\,and\,\,\vec{c}\] are three vectors with magnitude \[|\overset{\to }{\mathop{a}}\,|=4,|\overset{\to }{\mathop{b}}\,|=4,|\overset{\to }{\mathop{c}}\,|=2\] and such that \[\overset{\to }{\mathop{a}}\,\] is perpendicular to is perpendicular to \[(\overset{\to }{\mathop{b}}\,+\overset{\to }{\mathop{c}}\,),\overset{\to }{\mathop{b}}\,\] is perpendicular to \[(\overset{\to }{\mathop{c}}\,+\overset{\to }{\mathop{a}}\,)\] and \[\overset{\to }{\mathop{c}}\,\] is perpendicular to \[(\overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\,)\]. It follows that \[|\overset{\to }{\mathop{a}}\,+\overset{\to }{\mathop{b}}\,+\overset{\to }{\mathop{c}}\,|\] is equal to: |
| A. | 9 |
| B. | 6 |
| C. | 5 |
| D. | 4 |
| Answer» C. 5 | |
| 753. |
A vector \[\overset{\to }{\mathop{a}}\,=(x,y,z)\] of length \[2\sqrt{3}\] which makes equal angles with the vectors \[\overset{\to }{\mathop{b}}\,=(y,\,\,-2z,\,\,3x)\] and \[\overset{\to }{\mathop{c}}\,=(2z,\,\,3x,\,\,-y)\] is perpendicular to \[\overset{\to }{\mathop{d}}\,=(1,-1,2)\] and makes an obtuse angle with y-axis is |
| A. | (- 2, 2, 2) |
| B. | \[(1,\,\,1,\,\,\sqrt{10})\] |
| C. | (2, - 2, - 2) |
| D. | None of these |
| Answer» D. None of these | |
| 754. |
If \[\vec{a}=2\hat{i}+2\hat{j}+3\hat{k},\vec{b}=-\hat{i}+2\hat{j}+\hat{k}\] and \[\overrightarrow{c}=3\hat{i}+\hat{j}\]are three vectors such that \[\vec{a}+t\vec{b}\] is perpendicular to \[\vec{c}\], then what is t equal to? |
| A. | 8 |
| B. | 6 |
| C. | 4 |
| D. | 2 |
| Answer» B. 6 | |
| 755. |
The number of solutions of \[{{\log }_{4}}(x-1)={{\log }_{2}}(x-3)\] [IIT Screening 2001] |
| A. | 3 |
| B. | 1 |
| C. | 2 |
| D. | 0 |
| Answer» C. 2 | |
| 756. |
If the equation of the tangent to the circle \[{{x}^{2}}+{{y}^{2}}-2x+6y-6=0\] parallel to \[3x-4y+7=0\] is \[3x-4y+k=0\], then the values of k are [Kerala (Engg.) 2005] |
| A. | 5, -35 |
| B. | -5, 35 |
| C. | 7, -32 |
| D. | -7, 32 |
| E. | 3, -13 |
| Answer» B. -5, 35 | |
| 757. |
Solution of the differential equation \[\frac{dy}{dx}\tan y=\sin (x+y)+\sin (x-y)\] is [Kerala (Engg.) 2005] |
| A. | \[\sec y+2\cos x=c\] |
| B. | \[\sec y-2\cos x=c\] |
| C. | \[\cos y-2\sin x=c\] |
| D. | \[\tan y-2\sec y=c\] |
| E. | \[\sec y+2\sin x=c\] |
| Answer» B. \[\sec y-2\cos x=c\] | |
| 758. |
The least difference between the roots, in the first quadrant \[\left( 0\le x\le \frac{\pi }{2} \right),\] of the equation \[4\cos x(2-3{{\sin }^{2}}x)+(\cos 2x+1)=0\]is |
| A. | \[\frac{\pi }{6}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | \[\frac{\pi }{3}\] |
| D. | \[\frac{\pi }{2}\] |
| Answer» B. \[\frac{\pi }{4}\] | |
| 759. |
If A, B and C are any three sets, then \[A\text{ }\times \text{ }\left( B\text{ }\cup \text{ }C \right)\] is equal to [Pb. CET 2001] |
| A. | \[\left( A\text{ }\times \text{ }B \right)\text{ }\cup \text{ }\left( A\text{ }\times \text{ }C \right)\] |
| B. | \[\left( A\text{ }\cup \text{ }B \right)\text{ }\times \text{ }\left( A\text{ }\cup \text{ }C \right)\] |
| C. | \[\left( A\text{ }\times \text{ }B \right)\text{ }\cap \text{ }\left( A\text{ }\times \text{ }C \right)\] |
| D. | None of these |
| Answer» B. \[\left( A\text{ }\cup \text{ }B \right)\text{ }\times \text{ }\left( A\text{ }\cup \text{ }C \right)\] | |
| 760. |
The number of six digit numbers that can be formed from the digits \[1,2,3,4,5,6\] and 7 so that digits do not repeat and the terminal digits are even, is |
| A. | 144 |
| B. | 72 |
| C. | 288 |
| D. | 720 |
| Answer» E. | |
| 761. |
The number of solutions of the equation \[{{\sin }^{5}}x-{{\cos }^{5}}x=\frac{1}{\cos x}-\frac{1}{\operatorname{sinx}}(\sin x\ne \cos x)\]is |
| A. | 0 |
| B. | 1 |
| C. | infinite |
| D. | None of these |
| Answer» B. 1 | |
| 762. |
A point equidistant from the points (2, 0) and (0, 2) is |
| A. | (1, 4) |
| B. | (2, 1) |
| C. | (1, 2) |
| D. | (2, 2) |
| Answer» E. | |
| 763. |
The part of circle \[{{x}^{2}}+{{y}^{2}}=9\] in between \[y=0\] and \[y=2\] is revolved about y-axis. The volume of generating solid will be [UPSEAT 1999] |
| A. | \[\frac{46}{3}\pi \] |
| B. | \[12\pi \] |
| C. | \[16\pi \] |
| D. | \[28\pi \] |
| Answer» B. \[12\pi \] | |
| 764. |
Let \[f(x)=2{{x}^{2}},g(x)=3x+2\] and \[fog(x)=18{{x}^{2}}+24x+c,\]Then c= |
| A. | 2 |
| B. | 8 |
| C. | 6 |
| D. | 4 |
| Answer» C. 6 | |
| 765. |
If \[f(x)=x-{{x}^{2}}+{{x}^{3}}-{{x}^{4}}+...to\] \[\infty \] for \[\left| x \right| |
| A. | \[\frac{x}{1+x}\] |
| B. | \[\frac{x}{1-x}\] |
| C. | \[\frac{1-x}{x}\] |
| D. | \[\frac{1}{x}\] |
| Answer» C. \[\frac{1-x}{x}\] | |
| 766. |
The normal to the curve \[x=a\text{ }(1+\cos \theta ),\,y=a\sin \theta \]at \['\theta '\] always passes through the fixed point [AIEEE 2004] |
| A. | (a, a) |
| B. | (0, a) |
| C. | (0, 0) |
| D. | (a, 0) |
| Answer» E. | |
| 767. |
A bag contains 3 red, 4 white and 5 black balls. Three balls are drawn at random. The probability of being their different colours is [RPET 1999] |
| A. | \[\frac{3}{11}\] |
| B. | \[\frac{2}{11}\] |
| C. | \[\frac{8}{11}\] |
| D. | None of these |
| Answer» B. \[\frac{2}{11}\] | |
| 768. |
The solution of the equation \[\frac{dy}{dx}={{(x+y)}^{2}}\] is |
| A. | \[x+y+\tan (x+c)=0\] |
| B. | \[x-y+\tan (x+c)=0\] |
| C. | \[x+y-\tan (x+c)=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 769. |
The angle between curves \[{{y}^{2}}=4x\] and \[{{x}^{2}}+{{y}^{2}}=5\]at (1, 2) is [Karnataka CET 1999] |
| A. | \[{{\tan }^{-1}}(3)\] |
| B. | \[{{\tan }^{-1}}(2)\] |
| C. | \[\frac{\pi }{2}\] |
| D. | \[\frac{\pi }{4}\] |
| Answer» B. \[{{\tan }^{-1}}(2)\] | |
| 770. |
Let A, B, C be the events. If the probability of occurring exactly one event out of A and B is 1-a. out of B and C and A is 1-a and that of occurring three events simultaneously is \[{{a}^{2}}\], then the probability that at least one out of A, B, C will occur is |
| A. | ½ |
| B. | Greater than ½ |
| C. | Less than ½ |
| D. | \[Greater\text{ }than\,\,{\scriptscriptstyle 3\!/\!{ }_4}\] |
| Answer» C. Less than ½ | |
| 771. |
The probability that the birth days of six different persons will fall in exactly two calendar months is |
| A. | \[\frac{1}{6}\] |
| B. | \[^{12}{{C}_{2}}\times \frac{{{2}^{6}}}{{{12}^{6}}}\] |
| C. | \[^{12}{{C}_{2}}\times \frac{{{2}^{6}}-1}{{{12}^{6}}}\] |
| D. | \[\frac{341}{{{12}^{5}}}\] |
| Answer» E. | |
| 772. |
An aircraft has three engines A, B, and C. The aircraft crashes if all the three engines fail. The probability of failure are \[0.06,0.02\] and \[0.05\] for engines A, B and C respectively. What is the probability that the aircraft will not crash? |
| A. | \[0.00003\] |
| B. | \[0.90\] |
| C. | \[0.99997\] |
| D. | \[0.90307\] |
| Answer» D. \[0.90307\] | |
| 773. |
\[{{10}^{n}}+3({{4}^{n+2}})+5\] is divisible by \[(n\in N)\] |
| A. | 7 |
| B. | 5 |
| C. | 9 |
| D. | 17 |
| Answer» D. 17 | |
| 774. |
The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then \[P(X=1)\] is [AIEEE 2003] |
| A. | 1/32 |
| B. | 1/16 |
| C. | 1/8 |
| D. | ¼ |
| Answer» B. 1/16 | |
| 775. |
A vector perpendicular to both of the vectors \[i+j+k\] and \[i+j\] is [RPET 2000] |
| A. | i + j |
| B. | i ? j |
| C. | \[c(i-j)\], c is a scalar |
| D. | None of these |
| Answer» D. None of these | |
| 776. |
If a particle moves such that the displacement is proportional to the square of the velocity acquired, then its acceleration is [Kerala (Engg.) 2005] |
| A. | Proportion to\[{{s}^{2}}\] |
| B. | Proportional to \[1/{{s}^{2}}\] |
| C. | Proportional to s |
| D. | Proportional to \[1/s\] |
| E. | A constant |
| Answer» F. | |
| 777. |
20 teachers of a school either teach mathematics or physics. 12 of them teach mathematics while 4 teach both the subjects. Then the number of teachers teaching physics only is |
| A. | 12 |
| B. | 8 |
| C. | 16 |
| D. | None of these |
| Answer» C. 16 | |
| 778. |
In four schools \[{{B}_{1}},{{B}_{2}},{{B}_{3}},{{B}_{4}}\] the percentage of girls students is 12, 20, 13, 17 respectively, From a school selected at random, one student is pick up at random and it is found that the student is girl, the probability that the school selected is \[{{B}_{2,}}\]is |
| A. | \[\frac{6}{31}\] |
| B. | \[\frac{10}{31}\] |
| C. | \[\frac{13}{62}\] |
| D. | \[\frac{17}{62}\] |
| Answer» C. \[\frac{13}{62}\] | |
| 779. |
Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals. |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{7}{15}\] |
| C. | \[\frac{2}{15}\] |
| D. | \[\frac{1}{3}\] |
| Answer» C. \[\frac{2}{15}\] | |
| 780. |
A box contains 10 identical electronic components of which 4 are defective. If 3 components are selected at random form the box, in succession, without replacing the units already drawn, what is the probability that two of the selected components are defective? |
| A. | 44317 |
| B. | 45413 |
| C. | 44472 |
| D. | 14611 |
| Answer» D. 14611 | |
| 781. |
The solution of equations \[x+y=10,2x+y=18\] and \[4x-3y=26\] will be [DCE 2005] |
| A. | Only one solution |
| B. | No Solution |
| C. | Infinite solution |
| D. | None of these |
| Answer» B. No Solution | |
| 782. |
The inverse of a matrix \[A=\left( \begin{matrix} a & b \\ c & d \\ \end{matrix} \right)\]is [AMU 2001] |
| A. | \[\left( \begin{matrix} d & -b \\ -c & a \\ \end{matrix} \right)\] |
| B. | \[\frac{1}{(ad-bc)}\left( \begin{matrix} d & -b \\ -c & a \\ \end{matrix} \right)\] |
| C. | \[\frac{1}{|A|}\left( \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right)\] |
| D. | \[\left( \begin{matrix} b & -a \\ d & -c \\ \end{matrix} \right)\] |
| Answer» C. \[\frac{1}{|A|}\left( \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right)\] | |
| 783. |
In a skew symmetric matrix, the diagonal elements are all [MP PET 1987] |
| A. | Different from each other |
| B. | Zero |
| C. | One |
| D. | None of these |
| Answer» C. One | |
| 784. |
The equation of the line bisecting the line segment joining the points (a, b) and \[({a}',\ {b}')\]at right angle, is |
| A. | \[2(a-{a}')x+2(b-{b}')y={{a}^{2}}+{{b}^{2}}-{{{a}'}^{2}}-{{{b}'}^{2}}\] |
| B. | \[(a-{a}')x+(b-{b}')y={{a}^{2}}+{{b}^{2}}-{{{a}'}^{2}}-{{{b}'}^{2}}\] |
| C. | \[2(a-{a}')x+2(b-{b}')y={{{a}'}^{2}}+b{{'}^{2}}-{{a}^{2}}-{{b}^{2}}\] |
| D. | None of these |
| Answer» B. \[(a-{a}')x+(b-{b}')y={{a}^{2}}+{{b}^{2}}-{{{a}'}^{2}}-{{{b}'}^{2}}\] | |
| 785. |
The roots of the equation \[{{x}^{4}}-8{{x}^{2}}-9=0\] are |
| A. | \[\pm 3,\ \pm 1\] |
| B. | \[\pm 3,\ \pm i\] |
| C. | \[\pm 2,\ \pm i\] |
| D. | None of these |
| Answer» C. \[\pm 2,\ \pm i\] | |
| 786. |
The equation of the line passing through (1, 1) and parallel to the line \[2x+3y-7=0\] is [RPET 1996] |
| A. | \[2x+3y-5=0\] |
| B. | \[3x+2y-5=0\] |
| C. | \[3x-2y-7=0\] |
| D. | \[2x+3y+5=0\] |
| Answer» B. \[3x+2y-5=0\] | |
| 787. |
If \[f:R\to S,\]defined by \[f(x)=sinx-\sqrt{3}\cos x+1,\] is onto, then the interval of S is |
| A. | \[[-1,3]\] |
| B. | \[[-1,1]\] |
| C. | \[[0,1]\] |
| D. | \[[0,3]\] |
| Answer» B. \[[-1,1]\] | |
| 788. |
The area of a parallelogram whose two adjacent sides are represented by the vector \[3\mathbf{i}-\mathbf{k}\] and \[\mathbf{i}+2\mathbf{j}\] is [MNR 1981] |
| A. | \[\frac{1}{2}\sqrt{17}\] |
| B. | \[\frac{1}{2}\sqrt{14}\] |
| C. | \[\sqrt{41}\] |
| D. | \[\frac{1}{2}\sqrt{7}\] |
| Answer» D. \[\frac{1}{2}\sqrt{7}\] | |
| 789. |
If \[f:R\to R,f(x)=\left\{ \begin{matrix} x\left| x \right|-4,x\in Q \\ x\left| x \right|-\sqrt{3}\,x\notin Q \\ \end{matrix}, \right.\] then \[f(x)\] is |
| A. | one to one and onto |
| B. | Many to one and onto |
| C. | one to one and into |
| D. | Many to one and into |
| Answer» E. | |
| 790. |
Let \[f:\{x,y,z\}\to \{1,2,3\}\] be a one-one mapping such that only one of the following three statements is true and remaining two are false: \[f(x)\ne 2,f(y)=2,f(z)\ne 1\], then |
| A. | \[f(x)>f(y)>f(z)\] |
| B. | \[f(x)<f(y)<f(z)\] |
| C. | \[f(y)<f(x)<f(z)\] |
| D. | \[f(y)<f(z)<f(x)\] |
| Answer» D. \[f(y)<f(z)<f(x)\] | |
| 791. |
A box contains 10 red balls and 15 green balls. If two balls are drawn in succession then the probability that one is red and other is green, is |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{4}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{4}\] | |
| 792. |
From three non- collinear points we can draw [MP PET 1984; BIT Ranchi 1990] |
| A. | Only one circle |
| B. | Three circle |
| C. | Infinite circles |
| D. | No circle |
| Answer» B. Three circle | |
| 793. |
Two numbers a and b are chosen at random from the set of first 30 natural numbers. The probability that \[{{a}^{2}}-{{b}^{2}}\]is divisible by 3 is |
| A. | \[\frac{9}{87}\] |
| B. | \[\frac{12}{87}\] |
| C. | \[\frac{15}{87}\] |
| D. | \[\frac{47}{87}\] |
| Answer» E. | |
| 794. |
If \[aN=\{ax:x\in N\},\] then the set \[3N\cap 7N\] is |
| A. | 21 N |
| B. | 10 N |
| C. | 4 N |
| D. | None of these |
| Answer» B. 10 N | |
| 795. |
The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is |
| A. | 2 |
| B. | 3 |
| C. | \[\frac{3}{2}\] |
| D. | -1 |
| Answer» B. 3 | |
| 796. |
The obtuse angle between the lines \[y=-\ 2\] and \[y=x+2\] is [RPET 1984] |
| A. | \[{{120}^{o}}\] |
| B. | \[{{135}^{o}}\] |
| C. | \[{{150}^{o}}\] |
| D. | \[{{160}^{o}}\] |
| Answer» C. \[{{150}^{o}}\] | |
| 797. |
The value of \[k\] for which the quadratic equation,\[k{{x}^{2}}+1=\]\[kx+3x-11{{x}^{2}}\] has real and equal roots are [BIT Ranchi 1993] |
| A. | \[-11,-3\] |
| B. | \[5,\,7\] |
| C. | \[5,-7\] |
| D. | None of these |
| Answer» D. None of these | |
| 798. |
The equation of tangent at \[(-4,\,-4)\] on the curve \[{{x}^{2}}=-4y\] is [Karnataka CET 2001: Pb. CET 2000] |
| A. | \[2x+y+4=0\] |
| B. | \[2x-y-12=0\] |
| C. | \[2x+y-4=0\] |
| D. | \[2x-y+4=0\] |
| Answer» E. | |
| 799. |
If \[P=\left[ \begin{matrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \\ \end{matrix} \right],\,A=\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right]\] and \[Q=PA{{P}^{T}}\], then \[P({{Q}^{2005}}){{P}^{T}}\] equal to [IIT Screening 2005] |
| A. | \[\left[ \begin{matrix} 1 & 2005 \\ 0 & 1 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} \sqrt{3}/2 & 2005 \\ 1 & 0 \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} 1 & 2005 \\ \sqrt{3}/2 & 1 \\ \end{matrix} \right]\] |
| D. | \[\left[ \begin{matrix} 1 & \sqrt{3}/2 \\ 0 & 2005 \\ \end{matrix} \right]\] |
| Answer» B. \[\left[ \begin{matrix} \sqrt{3}/2 & 2005 \\ 1 & 0 \\ \end{matrix} \right]\] | |
| 800. |
The value of x in the given equation\[{{4}^{x}}-{{3}^{x\,\ -\ \frac{1}{2}}}={{3}^{x+\frac{1}{2}}}-{{2}^{2x-1}}\]is |
| A. | \[\frac{4}{3}\] |
| B. | \[\frac{3}{2}\] |
| C. | \[\frac{2}{1}\] |
| D. | \[\frac{5}{3}\] |
| Answer» C. \[\frac{2}{1}\] | |