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.
| 7101. |
Angle between the line \[\mathbf{r}=(\mathbf{i}+2\mathbf{j}-\mathbf{k})+\lambda (\mathbf{i}-\mathbf{j}+\mathbf{k})\] and the normal to the plane \[\mathbf{r}\,.\,(2\mathbf{i}-\mathbf{j}+\mathbf{k})=4\] is [MP PET 1997] |
| A. | \[{{\sin }^{-1}}\,\left( \frac{2\sqrt{2}}{3} \right)\] |
| B. | \[{{\cos }^{-1}}\,\left( \frac{2\sqrt{2}}{3} \right)\] |
| C. | \[{{\tan }^{-1}}\,\left( \frac{2\sqrt{2}}{3} \right)\] |
| D. | \[{{\cot }^{-1}}\,\left( \frac{2\sqrt{2}}{3} \right)\] |
| Answer» B. \[{{\cos }^{-1}}\,\left( \frac{2\sqrt{2}}{3} \right)\] | |
| 7102. |
The acute angle between the lines \[y=3\] and \[y=\sqrt{3}x+9\] is [RPET 1984, 87, 88] |
| A. | \[{{30}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{45}^{o}}\] |
| D. | \[{{90}^{o}}\] |
| Answer» C. \[{{45}^{o}}\] | |
| 7103. |
In a box of 10 electric bulbs, two are defective. Two bulbs are selected at random one after the other from the box. The first bulb after selection being put back in the box before making the second selection. The probability that both the bulbs are without defect is [MP PET 1987] |
| A. | \[\frac{9}{25}\] |
| B. | \[\frac{16}{25}\] |
| C. | \[\frac{4}{5}\] |
| D. | \[\frac{8}{25}\] |
| Answer» C. \[\frac{4}{5}\] | |
| 7104. |
The area bounded by the \[x-\]axis and the curve \[y=\sin x\] and \[x=0,\] \[x=\pi \] is [Kerala (Engg.) 2002] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 7105. |
The vector equation of the plane containing the lines \[\mathbf{r}=(\mathbf{i}+\mathbf{j})+\lambda (\mathbf{i}+2\mathbf{j}-\mathbf{k})\] and \[\mathbf{r}=(\mathbf{i}+\mathbf{j})+\mu (-\mathbf{i}+\mathbf{j}-2\mathbf{k})\] is |
| A. | \[\mathbf{r}.(\mathbf{i}+\mathbf{j}+\mathbf{k})=0\] |
| B. | \[\mathbf{r}.(\mathbf{i}-\mathbf{j}-\mathbf{k})=0\] |
| C. | \[\mathbf{r}.(\mathbf{i}+\mathbf{j}+\mathbf{k})=3\] |
| D. | None of these |
| Answer» C. \[\mathbf{r}.(\mathbf{i}+\mathbf{j}+\mathbf{k})=3\] | |
| 7106. |
In a simultaneous toss of four coins, what is the probability of getting exactly three heads [AI CBSE 1979] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{4}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7107. |
If the lines represented by the equation \[2{{x}^{2}}-3xy+{{y}^{2}}=0\] make angles \[\alpha \]and \[\beta \] with x-axis, then \[{{\cot }^{2}}\alpha +{{\cot }^{2}}\beta \]= |
| A. | 0 |
| B. | 3/2 |
| C. | 7/4 |
| D. | 5/4 |
| Answer» E. | |
| 7108. |
If the given lines \[y={{m}_{1}}x+{{c}_{1}},y={{m}_{2}}x+{{c}_{2}}\] and \[y={{m}_{3}}x+{{c}_{3}}\] be concurrent, then |
| A. | \[{{m}_{1}}({{c}_{2}}-{{c}_{3}})+{{m}_{2}}({{c}_{3}}-{{c}_{1}})+{{m}_{3}}({{c}_{1}}-{{c}_{2}})=0\] |
| B. | \[{{m}_{1}}({{c}_{2}}-{{c}_{1}})+{{m}_{2}}({{c}_{3}}-{{c}_{2}})+{{m}_{3}}({{c}_{1}}-{{c}_{3}})=0\] |
| C. | \[{{c}_{1}}({{m}_{2}}-{{m}_{3}})+{{c}_{2}}({{m}_{3}}-{{m}_{1}})+{{c}_{3}}({{m}_{1}}-{{m}_{2}})=0\] |
| D. | None of these |
| Answer» B. \[{{m}_{1}}({{c}_{2}}-{{c}_{1}})+{{m}_{2}}({{c}_{3}}-{{c}_{2}})+{{m}_{3}}({{c}_{1}}-{{c}_{3}})=0\] | |
| 7109. |
pth term of the series\[\left( 3-\frac{1}{n} \right)+\left( 3-\frac{2}{n} \right)+\left( 3-\frac{3}{n} \right)+....\] will be |
| A. | \[\left( 3+\frac{p}{n} \right)\] |
| B. | \[\left( 3-\frac{p}{n} \right)\] |
| C. | \[\left( 3+\frac{n}{p} \right)\] |
| D. | \[\left( 3-\frac{n}{p} \right)\] |
| Answer» C. \[\left( 3+\frac{n}{p} \right)\] | |
| 7110. |
The area bounded by the straight lines \[x=0,x=2\]and the curves \[y={{2}^{x}},y=2x-{{x}^{2}}\]is [AMU 2001] |
| A. | \[\frac{4}{3}-\frac{1}{\log 2}\] |
| B. | \[\frac{3}{\log 2}+\frac{4}{3}\] |
| C. | \[\frac{4}{\log 2}-1\] |
| D. | \[\frac{3}{\log 2}-\frac{4}{3}\] |
| Answer» E. | |
| 7111. |
The area bounded by the parabola \[{{y}^{2}}=4ax,\] its axis and two ordinates \[x=4,\] \[x=9\] is |
| A. | \[4{{a}^{2}}\] |
| B. | \[4{{a}^{2}}.4\] |
| C. | \[4{{a}^{2}}(9-4)\] |
| D. | \[\frac{152\sqrt{a}}{3}\] |
| Answer» E. | |
| 7112. |
If the sum of the series \[2+5+8+11............\]is 60100, then the number of terms are [MNR 1991; DCE 2001] |
| A. | 100 |
| B. | 200 |
| C. | 150 |
| D. | 250 |
| Answer» C. 150 | |
| 7113. |
The equation of the chord of contact, if the tangents are drawn from the point (5, ?3) to the circle \[{{x}^{2}}+{{y}^{2}}=10\], is |
| A. | \[5x-3y=10\] |
| B. | \[5x+3y=10\] |
| C. | \[3x+5y=10\] |
| D. | \[3x-5y=10\] |
| Answer» B. \[5x+3y=10\] | |
| 7114. |
A tetrahedron has vertices at \[O(0,\,0,\,0)\], \[A(1,\,2,\,1),B(2,\,1,\,3)\] and \[C(-1,\,1,\,2)\]. Then the angle between the faces \[OAB\]and \[ABC\]will be [MNR 1994; UPSEAT 2000; AIEEE 2003] |
| A. | \[{{\cos }^{-1}}\left( \frac{19}{35} \right)\] |
| B. | \[{{\cos }^{-1}}\left( \frac{17}{31} \right)\] |
| C. | \[30{}^\circ \] |
| D. | \[90{}^\circ \] |
| Answer» B. \[{{\cos }^{-1}}\left( \frac{17}{31} \right)\] | |
| 7115. |
\[{{\left( \frac{a}{a+x} \right)}^{\frac{1}{2}}}+{{\left( \frac{a}{a-x} \right)}^{\frac{1}{2}}}=\] [DCE 1994; Pb. CET 2002; AIEEE 2002] |
| A. | \[2+\frac{3{{x}^{2}}}{4{{a}^{2}}}+....\] |
| B. | \[1+\frac{3{{x}^{2}}}{8{{a}^{2}}}+....\] |
| C. | \[2+\frac{x}{a}+\frac{3{{x}^{2}}}{4{{a}^{2}}}+....\] |
| D. | \[2-\frac{x}{a}+\frac{3{{x}^{2}}}{4{{a}^{2}}}\]+...... |
| Answer» B. \[1+\frac{3{{x}^{2}}}{8{{a}^{2}}}+....\] | |
| 7116. |
A pair has two children. If one of them is boy, then the probability that other is also a boy, is |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{1}{3}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7117. |
The number of straight lines which is equally inclined to both the axes is [RPET 2002] |
| A. | 4 |
| B. | 2 |
| C. | 3 |
| D. | 1 |
| Answer» C. 3 | |
| 7118. |
A point moves in a straight line during the time \[t=0\] to \[t=3\]according to the law \[s=15t-2{{t}^{2}}\]. The average velocity is [MP PET 1992] |
| A. | 3 |
| B. | 9 |
| C. | 15 |
| D. | 27 |
| Answer» C. 15 | |
| 7119. |
Modulus of \[\left( \frac{3+2i}{3-2i} \right)\] is [RPET 1996] |
| A. | 1 |
| B. | 44228 |
| C. | 2 |
| D. | \[\sqrt{2}\] |
| Answer» B. 44228 | |
| 7120. |
If \[|{{z}_{1}}|\,=\,|{{z}_{2}}|\] and \[amp\,{{z}_{1}}+amp\,\,{{z}_{2}}=0\], then [MP PET 1999] |
| A. | \[{{z}_{1}}={{z}_{2}}\] |
| B. | \[{{\bar{z}}_{1}}={{z}_{2}}\] |
| C. | \[{{z}_{1}}+{{z}_{2}}=0\] |
| D. | \[{{\bar{z}}_{1}}={{\bar{z}}_{2}}\] |
| Answer» C. \[{{z}_{1}}+{{z}_{2}}=0\] | |
| 7121. |
The modulus and amplitude of \[\frac{1+2i}{1-{{(1-i)}^{2}}}\] are [Karnataka CET 2005] |
| A. | \[\sqrt{2}\text{ and }\frac{\pi }{6}\] |
| B. | 1 and 0 |
| C. | 1 and \[\frac{\pi }{3}\] |
| D. | 1 and \[\frac{\pi }{4}\] |
| Answer» C. 1 and \[\frac{\pi }{3}\] | |
| 7122. |
If the equation \[12{{x}^{2}}+7xy-p{{y}^{2}}-18x+qy+6=0\] represents a pair of perpendicular straight lines, then [Kurukshetra CEE 2002] |
| A. | \[p=12,q=1\] |
| B. | \[p=1,q=12\] |
| C. | \[p=-1,q=12\] |
| D. | \[p=1,q=-12\] |
| Answer» B. \[p=1,q=12\] | |
| 7123. |
Area bounded by the curve \[y=x{{e}^{{{x}^{2}}}},\] \[x-\]axis and the ordinates \[x=0,\,\,x=a\] |
| A. | \[\frac{{{e}^{{{a}^{2}}}}+1}{2}\]sq. unit |
| B. | \[\frac{{{e}^{{{a}^{2}}}}-1}{2}\]sq. unit |
| C. | \[{{e}^{{{a}^{2}}}}+1\]sq. unit |
| D. | \[{{e}^{{{a}^{2}}}}-1\]sq. unit |
| Answer» C. \[{{e}^{{{a}^{2}}}}+1\]sq. unit | |
| 7124. |
A coin is tossed 3 times. The probability of obtaining at least two heads is or Three coins are tossed all together. The probability of getting at least two heads is [MP PET 1995] |
| A. | \[\frac{1}{8}\] |
| B. | \[\frac{3}{8}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{2}{3}\] |
| Answer» D. \[\frac{2}{3}\] | |
| 7125. |
Angle between the lines \[\frac{x}{a}+\frac{y}{b}=1\] and \[\frac{x}{a}-\frac{y}{b}=1\] is [MP PET 1995] |
| A. | \[2{{\tan }^{-1}}\frac{b}{a}\] |
| B. | \[{{\tan }^{-1}}\frac{2ab}{{{a}^{2}}+{{b}^{2}}}\] |
| C. | \[{{\tan }^{-1}}\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\] |
| D. | None of these |
| Answer» B. \[{{\tan }^{-1}}\frac{2ab}{{{a}^{2}}+{{b}^{2}}}\] | |
| 7126. |
If the lengths of the chords intercepted by the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy=0\]from the co-ordinate axes be 10 and 24 respectively, then the radius of the circle is |
| A. | 17 |
| B. | 9 |
| C. | 14 |
| D. | 13 |
| Answer» E. | |
| 7127. |
The solution of\[{{\log }_{\sqrt{3}}}x+{{\log }_{\sqrt[4]{3}}}x+{{\log }_{\sqrt[6]{3}}}x+.........+{{\log }_{\sqrt[16]{3}}}x=36\] is |
| A. | \[x=3\] |
| B. | \[x=4\sqrt{3}\] |
| C. | \[x=9\] |
| D. | \[x=\sqrt{3}\] |
| Answer» E. | |
| 7128. |
The sum of the series \[1+2x+3{{x}^{2}}+4{{x}^{3}}+.........\]upto \[n\] terms is |
| A. | \[\frac{1-(n+1){{x}^{n}}+n{{x}^{n+1}}}{{{(1-x)}^{2}}}\] |
| B. | \[\frac{1-{{x}^{n}}}{1-x}\] |
| C. | \[{{x}^{n+1}}\] |
| D. | None of these |
| Answer» B. \[\frac{1-{{x}^{n}}}{1-x}\] | |
| 7129. |
If \[x\] is real, the function \[\frac{(x-a)(x-b)}{(x-c)}\] will assume all real values, provided [IIT 1984; Karnataka CET 2002] |
| A. | \[a>b>c\] |
| B. | \[a<b<c\] |
| C. | \[a>c<b\] |
| D. | \[a<c<b\] |
| Answer» E. | |
| 7130. |
If A and B are two independent events, then \[P\,\left( \frac{A}{B} \right)=\] |
| A. | 0 |
| B. | 1 |
| C. | \[P\,(A)\] |
| D. | \[P\,(B)\] |
| Answer» D. \[P\,(B)\] | |
| 7131. |
If the equation \[{{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+....+{{a}_{1}}x=0\], \[{{a}_{1}}\ne 0\], \[\,n\ge 2\], has a positive root \[x=\alpha \], then the equation \[n{{a}_{n}}{{x}^{n-1}}+(n-1){{a}_{n-1}}{{x}^{n-2}}+....+{{a}_{1}}=0\] has a positive root, which is [AIEEE 2005] |
| A. | Greater than or equal to a |
| B. | Equal to \[\alpha \] |
| C. | Greater than \[\alpha \] |
| D. | Smaller than \[\alpha \] |
| Answer» E. | |
| 7132. |
If \[{{z}_{1}},{{z}_{2}}\in C\], then \[amp\,\left( \frac{{{\text{z}}_{\text{1}}}}{{{{\text{\bar{z}}}}_{\text{2}}}} \right)=\] |
| A. | \[amp\,({{z}_{1}}{{\overline{z}}_{2}})\] |
| B. | \[amp\,({{\overline{z}}_{1}}{{z}_{2}})\] |
| C. | \[amp\,\left( \frac{{{z}_{2}}}{{{{\bar{z}}}_{1}}} \right)\] |
| D. | \[amp\,\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)\] |
| Answer» D. \[amp\,\left( \frac{{{z}_{1}}}{{{z}_{2}}} \right)\] | |
| 7133. |
The parabolas \[{{y}^{2}}=4x\] and \[{{x}^{2}}=4y\] divide the square region bounded by the lines \[x=4\], \[y=4\]and the coordinate axes. If \[{{S}_{1}},{{S}_{2}},{{S}_{3}}\] are respectively the areas of these parts numbered from top to bottom, then \[{{S}_{1}}:{{S}_{2}}:{{S}_{3}}\] is [AIEEE 2005] |
| A. | \[2:1:2\] |
| B. | \[1:1:1\] |
| C. | \[1:2:1\] |
| D. | \[1:2:3\] |
| Answer» C. \[1:2:1\] | |
| 7134. |
\[\left| \frac{1}{2}({{z}_{1}}+{{z}_{2}})+\sqrt{{{z}_{1}}{{z}_{2}}} \right|+\left| \frac{1}{2}({{z}_{1}}+{{z}_{2}})-\sqrt{{{z}_{1}}{{z}_{2}}} \right|\] = |
| A. | \[|{{z}_{1}}+{{z}_{2}}|\] |
| B. | \[|{{z}_{1}}-{{z}_{2}}|\] |
| C. | \[|{{z}_{1}}+{{z}_{2}}|\] |
| D. | \[|{{z}_{1}}|-|{{z}_{2}}|\] |
| Answer» D. \[|{{z}_{1}}|-|{{z}_{2}}|\] | |
| 7135. |
The solution of the equation \[|z|-z=1+2i\] is [MP PET 1993] |
| A. | \[2-\frac{3}{2}i\] |
| B. | \[\frac{3}{2}+2i\] |
| C. | \[\frac{3}{2}-2i\] |
| D. | \[-2+\frac{3}{2}i\] |
| Answer» D. \[-2+\frac{3}{2}i\] | |
| 7136. |
Area bounded by curve \[y={{x}^{3}},\] \[x-\]axis and ordinates \[x=1\] and \[x=4,\] is |
| A. | 64 sq. unit |
| B. | 27 sq. unit |
| C. | \[\frac{127}{4}\]sq. unit |
| D. | \[\frac{255}{4}\]sq. unit |
| Answer» E. | |
| 7137. |
Integral curve satisfying \[y'=\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}},\ y(1)=2\] has the slope at the point (1, 0) of the curve, equal to [MP PET 2000] |
| A. | ? 5/3 |
| B. | ? 1 |
| C. | 1 |
| D. | 5/3 |
| Answer» D. 5/3 | |
| 7138. |
A die is tossed thrice. If getting a four is considered a success, then the mean and variance of the probability distribution of the number of successes are [DSSE 1987] |
| A. | \[\frac{1}{2},\,\frac{1}{12}\] |
| B. | \[\frac{1}{6},\,\frac{5}{12}\] |
| C. | \[\frac{5}{6},\,\frac{1}{2}\] |
| D. | None of these |
| Answer» E. | |
| 7139. |
The sum of all two digit numbers which, when divided by 4, yield unity as a remainder is |
| A. | 1190 |
| B. | 1197 |
| C. | 1210 |
| D. | None of these |
| Answer» D. None of these | |
| 7140. |
The equation of the line which bisects the obtuse angle between the lines \[x-2y+4=0\] and \[4x-3y+2=0\], is [IIT 1979] |
| A. | \[(4-\sqrt{5})x-(3-2\sqrt{5})y+(2-4\sqrt{5})=0\] |
| B. | \[(4+\sqrt{5})x-(3+2\sqrt{5})y+(2+4\sqrt{5})=0\] |
| C. | \[(4+\sqrt{5})x+(3+2\sqrt{5})y+(2+4\sqrt{5})=0\] |
| D. | None of these |
| Answer» B. \[(4+\sqrt{5})x-(3+2\sqrt{5})y+(2+4\sqrt{5})=0\] | |
| 7141. |
If a root of the equations \[{{x}^{2}}+px+q=0\] and \[{{x}^{2}}+\alpha x+\beta =0\] is common, then its value will be (where \[p\ne \alpha \] and \[q\ne \beta \]) [IIT 1974, 1976; RPET 1997] |
| A. | \[\frac{q-\beta }{\alpha -p}\] |
| B. | \[\frac{p\beta -\alpha q}{q-\beta }\] |
| C. | \[\frac{q-\beta }{\alpha -p}\]or \[\frac{p\beta -\alpha q}{q-\beta }\] |
| D. | None of these |
| Answer» D. None of these | |
| 7142. |
\[y=mx\] is a chord of a circle of radius a and the diameter of the circle lies along x-axis and one end of this chord in origin .The equation of the circle described on this chord as diameter is [MP PET 1990] |
| A. | \[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})-2ax=0\] |
| B. | \[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})-2a(x+my)=0\] |
| C. | \[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})+2a(x+my)=0\] |
| D. | \[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})-2a(x-my)=0\] |
| Answer» C. \[(1+{{m}^{2}})({{x}^{2}}+{{y}^{2}})+2a(x+my)=0\] | |
| 7143. |
If area bounded by the curves \[{{y}^{2}}=4ax\] and \[y=mx\] is \[{{a}^{2}}/3,\], then the value of \[m\] is |
| A. | 2 |
| B. | \[-2\] |
| C. | \[\frac{1}{2}\] |
| D. | None of these |
| Answer» B. \[-2\] | |
| 7144. |
The straight lines \[x+2y-9=0,\] \[3x+5y-5=0\] and \[ax+by-1=0\] are concurrent, if the straight line \[35x-22y+1=0\] passes through the point |
| A. | \[(a,b)\] |
| B. | \[(b,a)\] |
| C. | \[(-a,-b)\] |
| D. | None of these |
| Answer» B. \[(b,a)\] | |
| 7145. |
The velocity of a particle at time t is given by the relation \[v=6t-\frac{{{t}^{2}}}{6}\]. The distance traveled in 3 seconds is, if \[s=0\]at \[t=0\] |
| A. | \[\frac{39}{2}\] |
| B. | \[\frac{57}{2}\] |
| C. | \[\frac{51}{2}\] |
| D. | \[\frac{33}{2}\] |
| Answer» D. \[\frac{33}{2}\] | |
| 7146. |
A coin is tossed three times in succession. If E is the event that there are at least two heads and F is the event in which first throw is a head, then \[P\,\left( \frac{E}{F} \right)=\] [MP PET 1996] |
| A. | \[\frac{3}{4}\] |
| B. | \[\frac{3}{8}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{1}{8}\] |
| Answer» B. \[\frac{3}{8}\] | |
| 7147. |
Amplitude of \[\left( \frac{1-i}{1+i} \right)\] is [RPET 1996] |
| A. | #NAME? |
| B. | p/2 |
| C. | p/4 |
| D. | p/6 |
| Answer» B. p/2 | |
| 7148. |
\[{{n}^{th}}\] term of the series \[3.8+6.11+\] \[9.14+12.17+.....\]will be |
| A. | \[3n(3n+5)\] |
| B. | \[3n(n+5)\] |
| C. | \[n(3n+5)\] |
| D. | \[n(n+5)\] |
| Answer» B. \[3n(n+5)\] | |
| 7149. |
The area of the region (in the square unit) bounded by the curve \[{{x}^{2}}=4y,\] line \[x=2\] and x-axis is [MP PET 2002] |
| A. | 1 |
| B. | \[\frac{2}{3}\] |
| C. | \[\frac{4}{3}\] |
| D. | \[\frac{8}{3}\] |
| Answer» C. \[\frac{4}{3}\] | |
| 7150. |
The equation of the bisector of that angle between the lines \[x+2y-11=0\], \[3x-6y-5=0\]which contains the point (1, ?3) is |
| A. | \[3x=19\] |
| B. | \[3y=7\] |
| C. | \[3x=19\]and \[3y=7\] |
| D. | None of these |
| Answer» B. \[3y=7\] | |