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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.
| 7151. |
For a biased die, the probabilities for different faces to turn up are Face : 1 2 3 4 5 6 Probability : 0.2 0.22 0.11 0.25 0.05 0.17 The die is tossed and you are told that either face 4 or face 5 has turned up. The probability that it is face 4 is |
| A. | \[\frac{1}{6}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{5}{6}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7152. |
The equation of the chord of the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]having \[({{x}_{1}},{{y}_{1}})\]as its mid-point is [IIT 1983; MP PET 1986; Pb. CET 2003] |
| A. | \[x{{y}_{1}}+y{{x}_{1}}={{a}^{2}}\] |
| B. | \[{{x}_{1}}+{{y}_{1}}=a\] |
| C. | \[x{{x}_{1}}+y{{y}_{1}}=x_{1}^{2}+y_{1}^{2}\] |
| D. | \[x{{x}_{1}}+y{{y}_{1}}={{a}^{2}}\] |
| Answer» D. \[x{{x}_{1}}+y{{y}_{1}}={{a}^{2}}\] | |
| 7153. |
The sum of the series \[1+\frac{1.3}{6}+\frac{1.3.5}{6.8}+....\infty \]is [UPSEAT 2001] |
| A. | 1 |
| B. | 0 |
| C. | \[\infty \] |
| D. | 4 |
| Answer» E. | |
| 7154. |
The sixth term of an A.P. is equal to 2, the value of the common difference of the A.P. which makes the product \[{{a}_{1}}{{a}_{4}}{{a}_{5}}\] least is given by |
| A. | \[x=\frac{8}{5}\] |
| B. | \[x=\frac{5}{4}\] |
| C. | \[x=2/3\] |
| D. | None of these |
| Answer» D. None of these | |
| 7155. |
\[n\] gentlemen can be made to sit on a round table in [MP PET 1982] |
| A. | \[\frac{1}{2}(n+1)\ !\] ways |
| B. | \[(n-1)\ !\] ways |
| C. | \[\frac{1}{2}(n-1)\ !\] ways |
| D. | \[(n+1)\ !\] ways |
| Answer» C. \[\frac{1}{2}(n-1)\ !\] ways | |
| 7156. |
The polars drawn from (-1, 2) to the circles \[{{S}_{1}}\equiv {{x}^{2}}+{{y}^{2}}+6y+7=0\]and \[{{S}_{2}}\equiv {{x}^{2}}+{{y}^{2}}+6x+1=0\], are [RPET 2002] |
| A. | Parallel |
| B. | Equal |
| C. | Perpendicular |
| D. | Intersect at a point |
| Answer» E. | |
| 7157. |
The lines \[2x+y-1=0,ax+3y-3=0\] and \[3x+2y-2=0\] are concurrent for [EAMCET 1994] |
| A. | All a |
| B. | \[a=4\]only |
| C. | \[-1\le a\le 3\] |
| D. | \[a>0\]only |
| Answer» B. \[a=4\]only | |
| 7158. |
The length of the chord joining the points in which the straight line \[\frac{x}{3}+\frac{y}{4}=1\]cuts the circle \[{{x}^{2}}+{{y}^{2}}=\frac{169}{25}\]is [Orissa JEE 2003] |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | 8 |
| Answer» C. 4 | |
| 7159. |
Angle between the lines \[2x-y-15=0\] and \[3x+y+4=0\]is [RPET 2003] |
| A. | \[{{90}^{o}}\] |
| B. | \[{{45}^{o}}\] |
| C. | \[{{180}^{o}}\] |
| D. | \[{{60}^{o}}\] |
| Answer» B. \[{{45}^{o}}\] | |
| 7160. |
The point of intersection of the lines represented by equation \[2{{(x+2)}^{2}}+3(x+2)(y-2)-2{{(y-2)}^{2}}=0\] is |
| A. | (2, 2) |
| B. | (-2, -2) |
| C. | (- 2, 2) |
| D. | (2, -2) |
| Answer» D. (2, -2) | |
| 7161. |
The area of the region bounded by the curve \[y=x|x|\], x-axis and the ordinates \[x=1,\,\,x=-1\]is given by [Pb. CET 2004] |
| A. | Zero |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{2}{3}\] |
| D. | 1 |
| Answer» D. 1 | |
| 7162. |
The line through \[\mathbf{i}+3\mathbf{j}+2\mathbf{k}\] and perpendicular to the lines \[\mathbf{r}=(\mathbf{i}+2\mathbf{j}-\mathbf{k})+\lambda (2\mathbf{i}+\mathbf{j}+\mathbf{k})\] and \[\mathbf{r}=(2\mathbf{i}+6\mathbf{j}+\mathbf{k})+\mu (\mathbf{i}+2\mathbf{j}+3\mathbf{k})\] is |
| A. | \[\mathbf{r}=(\mathbf{i}+2\mathbf{j}-\mathbf{k})+\lambda (-\mathbf{i}+5\mathbf{j}-3\mathbf{k})\] |
| B. | \[\mathbf{r}=\mathbf{i}+3\mathbf{j}+2\mathbf{k}+\lambda (\mathbf{i}-5\mathbf{j}+3\mathbf{k})\] |
| C. | \[\mathbf{r}=\mathbf{i}+3\mathbf{j}+2\mathbf{k}+\lambda (\mathbf{i}+5\mathbf{j}+3\mathbf{k})\] |
| D. | \[\mathbf{r}=\mathbf{i}+3\mathbf{j}+2\mathbf{k}+\lambda (-\mathbf{i}+5\mathbf{j}-3\mathbf{k})\] |
| Answer» E. | |
| 7163. |
If sum of \[n\] terms of an A.P. is \[3{{n}^{2}}+5n\] and \[{{T}_{m}}=164\] then \[m=\] [RPET 1991, 95; DCE 1999] |
| A. | 26 |
| B. | 27 |
| C. | 28 |
| D. | None of these |
| Answer» C. 28 | |
| 7164. |
If \[\bar{z}\] be the conjugate of the complex number \[z\], then which of the following relations is false [MP PET 1987] |
| A. | \[|z|\,=\,|\bar{z}|\] |
| B. | \[z.\,\bar{z}=|\bar{z}{{|}^{2}}\] |
| C. | \[\overline{{{z}_{1}}+{{z}_{2}}}=\overline{{{z}_{1}}}+\overline{{{z}_{2}}}\] |
| D. | \[arg\,z=arg\,\bar{z}\] |
| Answer» E. | |
| 7165. |
Area bounded by the parabola \[{{y}^{2}}=2x\] and the ordinates \[x=1,x=4\] is |
| A. | \[\frac{4\sqrt{2}}{3}sq.\,unit\] |
| B. | \[\frac{28\sqrt{2}}{3}sq.\,unit\] |
| C. | \[\frac{56}{3}\text{ }sq. unit\] |
| D. | None of these |
| Answer» C. \[\frac{56}{3}\text{ }sq. unit\] | |
| 7166. |
If \[\alpha \] and \[\beta \], \[\alpha \] and \[\gamma \], \[\alpha \] and \[\delta \] are the roots of the equations \[a{{x}^{2}}+2bx+c=0\], \[2b{{x}^{2}}+cx+a=0\] and \[c{{x}^{2}}+ax+2b=0\] respectively, where \[a,b\] and \[c\] are positive real numbers, then \[\alpha +{{\alpha }^{2}}\]= [Kerala (Engg.) 2005] |
| A. | -1 |
| B. | 0 |
| C. | abc |
| D. | \[a+2b+c\] |
| E. | abc |
| Answer» C. abc | |
| 7167. |
Let z be a complex number (not lying on X-axis of maximum modulus such that \[\left| z+\frac{1}{z} \right|=1\]. Then |
| A. | \[\operatorname{Im}(z)=0\] |
| B. | \[\operatorname{Re}(z)=0\] |
| C. | \[amp(z)=\pi \] |
| D. | None of these |
| Answer» C. \[amp(z)=\pi \] | |
| 7168. |
If \[z=3+5i,\,\,\text{then }\,{{z}^{3}}+\bar{z}+198=\] [EAMCET 2002] |
| A. | \[-3-5i\] |
| B. | \[-3+5i\] |
| C. | \[3+5i\] |
| D. | \[3-5i\] |
| Answer» C. \[3+5i\] | |
| 7169. |
The equation of the curve which passes through the point (1, 1) and whose slope is given by \[\frac{2y}{x}\], is [Roorkee 1987] |
| A. | \[y={{x}^{2}}\] |
| B. | \[{{x}^{2}}-{{y}^{2}}=0\] |
| C. | \[2{{x}^{2}}+{{y}^{2}}=3\] |
| D. | None of these |
| Answer» B. \[{{x}^{2}}-{{y}^{2}}=0\] | |
| 7170. |
The area bounded by the curves \[{{y}^{2}}=8x\] and \[y=x\] is |
| A. | \[\frac{128}{3}\] sq. unit |
| B. | \[\frac{32}{3}\] sq. unit |
| C. | \[\frac{64}{3}\] sq. unit |
| D. | 32 sq. unit |
| Answer» C. \[\frac{64}{3}\] sq. unit | |
| 7171. |
The equation of the curve through the point (1,0) and whose slope is \[\frac{y-1}{{{x}^{2}}+x}\]is |
| A. | \[(y-1)(x+1)+2x=0\] |
| B. | \[2x(y-1)+x+1=0\] |
| C. | \[x(y-1)(x+1)+2=0\] |
| D. | None of these |
| Answer» B. \[2x(y-1)+x+1=0\] | |
| 7172. |
The area bounded by the curve \[y={{x}^{3}},\] \[x-\]axis and two ordinates \[x=1\] to \[x=2\] equal to [MP PET 1999] |
| A. | \[\frac{15}{2}\] sq. unit |
| B. | \[\frac{15}{4}\] sq. unit |
| C. | \[\frac{17}{2}\] sq. unit |
| D. | \[\frac{17}{4}\] sq. unit |
| Answer» C. \[\frac{17}{2}\] sq. unit | |
| 7173. |
The equations of motion of two stones thrown vertically upwards simultaneously are \[s=19.6\,t-4.9\,{{t}^{2}}\] and \[s=9.8\,t-4.9\,{{t}^{2}}\] respectively and the maximum height attained by the first one is h. When the height of the first stone is maximum, the height of the second stone will be |
| A. | h/3 |
| B. | 2h |
| C. | h |
| D. | 0 |
| Answer» E. | |
| 7174. |
The coefficient of \[{{x}^{n}}\] in \[\frac{{{(1+x)}^{2}}}{{{(1-x)}^{3}}}\]is |
| A. | \[3{{n}^{2}}+2n+1\] |
| B. | \[2{{n}^{2}}+2n+1\] |
| C. | \[{{n}^{2}}+n+1\] |
| D. | \[2{{n}^{2}}-2n+1\] |
| Answer» C. \[{{n}^{2}}+n+1\] | |
| 7175. |
The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two female are not seated together is [Roorkee 1999] |
| A. | 480 |
| B. | 600 |
| C. | 720 |
| D. | 840 |
| Answer» B. 600 | |
| 7176. |
If the angle between the lines represented by the equation \[{{y}^{2}}+kxy-{{x}^{2}}\]\[{{\tan }^{2}}A=0\]be \[2A\], then \[k=\] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | \[\tan A\] |
| Answer» B. 1 | |
| 7177. |
A die is tossed twice. Getting a number greater than 4 is considered a success. Then the variance of the probability distribution of the number of successes is [AISSE 1979] |
| A. | \[\frac{2}{9}\] |
| B. | \[\frac{4}{9}\] |
| C. | \[\frac{1}{3}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{3}\] | |
| 7178. |
The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is [AIEEE 2003] |
| A. | \[a\cot \left( \frac{\pi }{n} \right)\] |
| B. | \[\frac{a}{2}\cot \left( \frac{\pi }{2n} \right)\] |
| C. | \[a\cot \left( \frac{\pi }{2n} \right)\] |
| D. | \[\frac{a}{2}\cot \left( \frac{\pi }{2n} \right)\] |
| Answer» C. \[a\cot \left( \frac{\pi }{2n} \right)\] | |
| 7179. |
The area bounded by the curve \[y={{(x+1)}^{2}},\,y={{(x-1)}^{2}}\] and the line \[y=\frac{1}{4}\] is [IIT Screening 2005] |
| A. | 1/6 |
| B. | 2/3 |
| C. | 1/4 |
| D. | 1/3 |
| Answer» E. | |
| 7180. |
Let \[z\] be a complex number, then the equation \[{{z}^{4}}+z+2=0\] cannot have a root, such that |
| A. | \[|z|\,<1\] |
| B. | \[|z|\,=1\] |
| C. | \[|z|\,>1\] |
| D. | None of these |
| Answer» B. \[|z|\,=1\] | |
| 7181. |
If z is a complex number, then \[z.\,\overline{z}=0\] if and only if |
| A. | \[z=0\] |
| B. | \[\operatorname{Re}(z)=0\] |
| C. | \[\operatorname{Im}\,(z)=0\] |
| D. | None of these |
| Answer» B. \[\operatorname{Re}(z)=0\] | |
| 7182. |
If \[{{(r+1)}^{th}}\] term is the first negative term in the expansion of \[{{(1+x)}^{7/2}}\], then the value of r is |
| A. | 5 |
| B. | 6 |
| C. | 4 |
| D. | 7 |
| Answer» B. 6 | |
| 7183. |
For any complex number \[z,\bar{z}=\left( \frac{1}{z} \right)\]if and only if [RPET 1985] |
| A. | \[z\] is a pure real number |
| B. | \[|z|=1\] |
| C. | \[z\]is a pure imaginary number |
| D. | \[z=1\] |
| Answer» C. \[z\]is a pure imaginary number | |
| 7184. |
The angle between the lines represented by the equation \[{{x}^{2}}-2pxy+{{y}^{2}}=0\], is |
| A. | \[{{\sec }^{-1}}p\] |
| B. | \[{{\cos }^{-1}}p\] |
| C. | \[{{\tan }^{-1}}p\] |
| D. | None of these |
| Answer» B. \[{{\cos }^{-1}}p\] | |
| 7185. |
Let \[\alpha ,\beta \] be the roots of \[{{x}^{2}}+(3-\lambda )x-\lambda =0.\] The value of \[\lambda \] for which \[{{\alpha }^{2}}+{{\beta }^{2}}\] is minimum, is [AMU 2002] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» D. 3 | |
| 7186. |
If the \[{{p}^{th}}\] term of an A.P. be \[\frac{1}{q}\] and \[{{q}^{th}}\] term be\[\frac{1}{p}\], then the sum of its \[p{{q}^{th}}\]terms will be |
| A. | \[\frac{pq-1}{2}\] |
| B. | \[\frac{1-pq}{2}\] |
| C. | \[\frac{pq+1}{2}\] |
| D. | \[-\frac{pq+1}{2}\] |
| Answer» D. \[-\frac{pq+1}{2}\] | |
| 7187. |
The straight lines represented by the equation \[9{{x}^{2}}-12xy+4{{y}^{2}}=0\] are |
| A. | Coincident |
| B. | Perpendicular |
| C. | Parallel |
| D. | Inclined at an angle of\[{{45}^{o}}\] |
| Answer» B. Perpendicular | |
| 7188. |
Three lines \[3x-y=2,\,\,5x+ay=3\] and \[2x+y=3\] are concurrent, then a = [MP PET 1996] |
| A. | 2 |
| B. | 3 |
| C. | -1 |
| D. | -2 |
| Answer» E. | |
| 7189. |
The pole of the straight line \[x+2y=1\]with respect to the circle \[{{x}^{2}}+{{y}^{2}}=5\]is [RPET 2000, 01] |
| A. | (5, 5) |
| B. | (5, 10) |
| C. | (10, 5) |
| D. | (10, 10) |
| Answer» C. (10, 5) | |
| 7190. |
In how many ways can 5 boys and 5 girls sit in a circle so that no two boys sit together [IIT 1975; MP PET 1987] |
| A. | \[5!\,\times 5\,!\] |
| B. | \[4\,!\,\,\times \,\,5\,!\] |
| C. | \[\frac{5\,\,!\,\,\times \,\,5\,\,!}{2}\] |
| D. | None of these |
| Answer» C. \[\frac{5\,\,!\,\,\times \,\,5\,\,!}{2}\] | |
| 7191. |
The combined equation of the bisectors of the angle between the lines represented by \[({{x}^{2}}+{{y}^{2}})\sqrt{3}=\] \[4xy\] is [MP PET 1992] |
| A. | \[{{y}^{2}}-{{x}^{2}}=0\] |
| B. | \[xy=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}=2xy\] |
| D. | \[\frac{{{x}^{2}}-{{y}^{2}}}{\sqrt{3}}=\frac{xy}{2}\] |
| Answer» B. \[xy=0\] | |
| 7192. |
The motion of stone thrown up vertically is given by \[s=13.8t-4.9{{t}^{2}}\], where s is in metre and t is in seconds. Then its velocity at \[t=1\] second is |
| A. | 3 m/s |
| B. | 5 m/s |
| C. | 4 m/s |
| D. | None of these |
| Answer» D. None of these | |
| 7193. |
The adjoining figure shows the graph of \[y=a{{x}^{2}}+bx+c\]. Then |
| A. | \[a<0\] |
| B. | \[{{b}^{2}}<4ac\] |
| C. | \[c>0\] |
| D. | a and b are of opposite signs |
| Answer» B. \[{{b}^{2}}<4ac\] | |
| 7194. |
The number of solutions of the equation \[{{z}^{2}}+\bar{z}=0\] is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» E. | |
| 7195. |
Area under the curve \[y=\sin 2x+\cos 2x\] between \[x=0\] and \[x=\frac{\pi }{4},\] is [AI CBSE 1979] |
| A. | 2 sq. unit |
| B. | 1 sq. unit |
| C. | 3 sq. unit |
| D. | 4 sq. unit |
| Answer» C. 3 sq. unit | |
| 7196. |
The area bounded by the x-axis, the curve \[y=f(x)\] and the lines \[x=1,\,x=b\] is equal to \[\sqrt{{{b}^{2}}+1}-\sqrt{2}\] for all b > 1, then \[f(x)\] is \[\] [MP PET 2000; AMU 2000] |
| A. | \[\sqrt{x-1}\] |
| B. | \[\sqrt{x+1}\] |
| C. | \[\sqrt{{{x}^{2}}+1}\] |
| D. | \[\frac{x}{\sqrt{1+{{x}^{2}}}}\] |
| Answer» E. | |
| 7197. |
If the sum of the first terms of a series be\[5{{n}^{2}}+2n\], then its second term is [MP PET 1996] |
| A. | 7 |
| B. | 17 |
| C. | 24 |
| D. | 42 |
| Answer» C. 24 | |
| 7198. |
Area bounded by the curve \[y=\log x\,,\] \[x-\]axis and the ordinates \[x=1,\,\,x=2\] is [MP PET 2004] |
| A. | \[\log 4\]sq. unit |
| B. | \[(\log 4+1)\]sq. unit |
| C. | \[(\log 4-1)\]sq. unit |
| D. | None of these |
| Answer» D. None of these | |
| 7199. |
The straight lines \[4ax+3by+c=0\]where \[a+b+c=0\], will be concurrent, if point is [RPET 2002] |
| A. | (4, 3) |
| B. | (1/4, 1/3) |
| C. | (1/2, 1/3) |
| D. | None of these |
| Answer» C. (1/2, 1/3) | |
| 7200. |
Let \[z\]be a purely imaginary number such that \[\operatorname{Im}\,(z)>0\]. Then \[arg(z)\] is equal to |
| A. | \[\pi \] |
| B. | \[\frac{\pi }{2}\] |
| C. | 0 |
| D. | \[-\frac{\pi }{2}\] |
| Answer» C. 0 | |