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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.
| 451. |
A line L intersects the three sides BC. CA and AB of a\[\Delta ABC\]at P, Q and R respectively. Then, \[\frac{BP}{PC}.\frac{CQ}{QA}.\frac{AR}{RB}\] is equal to |
| A. | 1 |
| B. | 0 |
| C. | -1 |
| D. | None of these |
| Answer» D. None of these | |
| 452. |
The area bounded by the curve \[y=f(x)\], x-axis and ordinates x = 1 and \[x=b\]is \[\frac{5}{24}\pi \], then \[f(x)\] is [RPET 2000] |
| A. | \[3(x-1)\cos (3x+4)+\sin (3x+4)\] |
| B. | \[(b-1)\sin (3x+4)+3\cos (3x+4)\] |
| C. | \[(b-1)\cos (3x+4)+3\sin (3x+4)\] |
| D. | None of these |
| Answer» B. \[(b-1)\sin (3x+4)+3\cos (3x+4)\] | |
| 453. |
Area under the curve \[y=\sqrt{3x+4}\] between \[x=0\] and \[x=4,\] is [AI CBSE 1979, 80] |
| A. | \[\frac{56}{9}\] sq. unit |
| B. | \[\frac{64}{9}\] sq. unit |
| C. | 8 sq. unit |
| D. | None of these |
| Answer» E. | |
| 454. |
For \[-\pi |
| A. | \[\pm \frac{\pi }{3},\pm \frac{2\pi }{3}\] |
| B. | \[\frac{\pi }{3},\frac{2\pi }{4}\] |
| C. | \[\frac{\pi }{4},\frac{3\pi }{4}\] |
| D. | None of these |
| Answer» B. \[\frac{\pi }{3},\frac{2\pi }{4}\] | |
| 455. |
The locus of a point, such that the sum of the squares of its distances from the planes \[x+y+z=0,\]\[x-z=0\] And \[x-2y+z=0\]is 9, is |
| A. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=3\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=6\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=9\] |
| D. | \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=12\] |
| Answer» D. \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=12\] | |
| 456. |
The value of integral \[\int_{0}^{1}{\frac{{{x}^{b}}-1}{\log x}}\,dx\] is |
| A. | \[\log b\] |
| B. | \[2\log (b+1)\] |
| C. | \[3\log b\] |
| D. | None of these |
| Answer» E. | |
| 457. |
The line \[y=x+c\]will intersect the circle \[{{x}^{2}}+{{y}^{2}}=1\]in two coincident points, if |
| A. | \[c=\sqrt{2}\] |
| B. | \[c=-\sqrt{2}\] |
| C. | \[c=\pm \sqrt{2}\] |
| D. | None of these |
| Answer» D. None of these | |
| 458. |
If the system of equations \[x-ky-z=0\], \[kx-y-z=0\] and \[x+y-z=0\] has a non zero solution, then the possible value of k are [IIT Screening 2000] |
| A. | - 1, 2 |
| B. | 1, 2 |
| C. | 0, 1 |
| D. | - 1, 1 |
| Answer» E. | |
| 459. |
If \[\sin A+\sin 2A=x\] and \[\cos A+\cos 2A=y,\] then \[({{x}^{2}}+{{y}^{2}})({{x}^{2}}+{{y}^{2}}-3)=\] |
| A. | \[2y\] |
| B. | \[y\] |
| C. | \[3y\] |
| D. | None of these |
| Answer» B. \[y\] | |
| 460. |
If \[\sin x+\sin y=a\] and \[cos\text{ }x+cos\,y=b,\]then \[{{\tan }^{2}}\left( \frac{x+y}{2} \right)+{{\tan }^{2}}\left( \frac{x-y}{2} \right)\] is equal to |
| A. | \[\frac{{{a}^{4}}+{{b}^{4}}+4{{b}^{2}}}{{{a}^{2}}{{b}^{2}}+{{b}^{4}}}\] |
| B. | \[\frac{{{a}^{4}}-{{b}^{4}}+4{{b}^{2}}}{{{a}^{2}}{{b}^{2}}+{{b}^{4}}}\] |
| C. | \[\frac{{{a}^{4}}-{{b}^{4}}+4{{a}^{2}}}{{{a}^{2}}{{b}^{2}}+{{a}^{4}}}\] |
| D. | None of the above |
| Answer» C. \[\frac{{{a}^{4}}-{{b}^{4}}+4{{a}^{2}}}{{{a}^{2}}{{b}^{2}}+{{a}^{4}}}\] | |
| 461. |
The line \[y=mx+c\]intersects the circle \[{{x}^{2}}+{{y}^{2}}={{r}^{2}}\]at two real distinct points, if |
| A. | \[-r\sqrt{1+{{m}^{2}}}<c\le 0\] |
| B. | \[0\le c<r\sqrt{1+{{m}^{2}}}\] |
| C. | (a) and (b) both |
| D. | \[-c\sqrt{1-{{m}^{2}}}<r\] |
| Answer» D. \[-c\sqrt{1-{{m}^{2}}}<r\] | |
| 462. |
The coordinates of the points O, A and B are (0,0), (0,4) and (6,0) respectively. If a points P moves such that the area of \[\Delta POA\]is always twice the area of \[\Delta POB\], then the equation to both parts of the locus of P is [IIT 1964] |
| A. | \[(x-3y)(x+3y)=0\] |
| B. | \[(x-3y)(x+y)=0\] |
| C. | \[(3x-y)(3x+y)=0\] |
| D. | None of these |
| Answer» B. \[(x-3y)(x+y)=0\] | |
| 463. |
If a line makes \[\alpha ,\beta ,\gamma \] with the positive direction of \[x,\ y\] and z-axis respectively. Then, \[{{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma \] is [Orissa JEE 2002] |
| A. | ½ |
| B. | ?1/2 |
| C. | ?1 |
| D. | 1 |
| Answer» E. | |
| 464. |
A rectangle ABCD, where A(0, 0), B(4, 0), C(4, 2), D(0, 2), undergoes the following transformations successively: i. \[{{f}_{1}}(x,y)\to (y,x)\] ii. \[{{f}_{2}}(x,y)\to (x+3y,y)\] iii. \[{{f}_{3}}(x,y)\to ((x-y)/2,(x+y)/2)\] The final figure will be |
| A. | A square |
| B. | A rhombus |
| C. | A rectangle |
| D. | A parallelogram |
| Answer» E. | |
| 465. |
If the vectors a and b are mutually perpendicular, then \[\mathbf{a}\times \{\mathbf{a}\times \{\mathbf{a}\times (\mathbf{a}\times \mathbf{b})\}\}\] is equal to |
| A. | \[|\mathbf{a}{{|}^{2}}\mathbf{b}\] |
| B. | \[|\mathbf{a}{{|}^{3}}\mathbf{b}\] |
| C. | \[|\mathbf{a}{{|}^{4}}\mathbf{b}\] |
| D. | None of these |
| Answer» D. None of these | |
| 466. |
If A = {x, y} then the power set of A is [Pb. CET 2004, UPSEAT 2000] |
| A. | \[\{{{x}^{x}},\,{{y}^{y}}\}\] |
| B. | {f, x, y} |
| C. | {f, {x}, {2y}} |
| D. | {f, {x}, {y}, {x, y}} |
| Answer» E. | |
| 467. |
The locus of centre of a circle passing through (a, b) and cuts orthogonally to circle \[{{x}^{2}}+{{y}^{2}}={{p}^{2}}\], is [IIT 1988; AIEEE 2005] |
| A. | \[2ax+2by-({{a}^{2}}+{{b}^{2}}+{{p}^{2}})=0\] |
| B. | \[2ax+2by-({{a}^{2}}-{{b}^{2}}+{{p}^{2}})=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-3ax-4by+({{a}^{2}}+{{b}^{2}}-{{p}^{2}})=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-2ax-3by+({{a}^{2}}-{{b}^{2}}-{{p}^{2}})=0\] |
| Answer» B. \[2ax+2by-({{a}^{2}}-{{b}^{2}}+{{p}^{2}})=0\] | |
| 468. |
The most general value of \[\theta \]satisfying the equations \[\sin \theta =\sin \alpha \]and \[\cos \theta =\cos \alpha \]is [IIT 1971; Karnataka CET 1993; DCE 1999] |
| A. | \[2n\pi +\alpha \] |
| B. | \[2n\pi -\alpha \] |
| C. | \[n\pi +\alpha \] |
| D. | \[n\pi -\alpha \] |
| Answer» B. \[2n\pi -\alpha \] | |
| 469. |
Which pairs of function is identical? |
| A. | \[f(x)=\sqrt{{{x}^{2}}},\] \[g(x)=x\] |
| B. | \[f(x)={{\sin }^{2}}x+{{\cos }^{2}}x;\,g(x)=1\] |
| C. | \[f(x)=\frac{x}{x},\,\,g(x)=1\] |
| D. | None of these |
| Answer» C. \[f(x)=\frac{x}{x},\,\,g(x)=1\] | |
| 470. |
If A is a skew-symmetric matrix of order n, and C is a column matrix of order \[n\times 1\], then \[{{C}^{T}}\]AC is [AMU 2005] |
| A. | A Identity matrix of order n |
| B. | A unit matrix of order one |
| C. | A zero matrix of order one |
| D. | None of these |
| Answer» D. None of these | |
| 471. |
By examining the chest X-ray, the probability that TB is detected when a person is actually suffering is 0.99. The probability of an healthy person diagnosed to have TB is 0.001. in a certain city, 1 in 1000 people suffers from TB, A person is selected at random and is diagnosed to have TB. Then, the probability that the person actually has TB is |
| A. | \[\frac{110}{221}\] |
| B. | \[\frac{2}{223}\] |
| C. | \[\frac{110}{223}\] |
| D. | \[\frac{1}{221}\] |
| Answer» B. \[\frac{2}{223}\] | |
| 472. |
If X and Y are two sets such that \[(X\cup Y)\] has 60 elements, X has 38 elements and Y has 42 elements, how many elements does \[(X\cap Y)\]have? |
| A. | 11 |
| B. | 20 |
| C. | 13 |
| D. | None of these |
| Answer» C. 13 | |
| 473. |
The value of \[\int_{a}^{a+(\pi /2)}{({{\sin }^{4}}x+{{\cos }^{4}}x)\,dx}\] is |
| A. | Independent of \[a\] |
| B. | \[a\,{{\left( \frac{\pi }{2} \right)}^{2}}\] |
| C. | \[\frac{3\pi }{8}\] |
| D. | \[\frac{3\pi {{a}^{2}}}{8}\] |
| Answer» D. \[\frac{3\pi {{a}^{2}}}{8}\] | |
| 474. |
In a \[\Delta ABC;\] if \[2\Delta ={{a}^{2}}-{{(b-c)}^{2}}\] then value of \[\tan A=\] |
| A. | \[-\frac{4}{3}\] |
| B. | \[\frac{4}{3}\] |
| C. | \[\frac{8}{15}\] |
| D. | \[\frac{4}{15}\] |
| Answer» C. \[\frac{8}{15}\] | |
| 475. |
\[\frac{{{\sin }^{2}}A-{{\sin }^{2}}B}{\sin A\cos A-\sin B\cos B}=\] [MP PET 1993] |
| A. | \[\tan (A-B)\] |
| B. | \[\tan (A+B)\] |
| C. | \[\cot (A-B)\] |
| D. | \[\cot (A+B)\] |
| Answer» C. \[\cot (A-B)\] | |
| 476. |
There are 10 bags \[{{B}_{1}},{{B}_{2}},{{B}_{3}},...,{{B}_{10}},\]which contain 21, 22? 30 different articles respectively. The total number of ways to bring out 10 articles from a bag is |
| A. | \[^{31}{{C}_{20}}{{-}^{21}}{{C}_{10}}\] |
| B. | \[^{31}{{C}_{21}}\] |
| C. | \[^{31}{{C}_{20}}\] |
| D. | None of these |
| Answer» B. \[^{31}{{C}_{21}}\] | |
| 477. |
A line makes angles of \[45{}^\circ \]and\[60{}^\circ \] with the positive axes of X and Y respectively. The angle made by the same line with the positive axis of Z, is [MP PET 1997] |
| A. | \[30{}^\circ \]or \[60{}^\circ \] |
| B. | \[60{}^\circ \]or \[90{}^\circ \] |
| C. | \[90{}^\circ \]or \[120{}^\circ \] |
| D. | \[60{}^\circ \]or \[120{}^\circ \] |
| Answer» E. | |
| 478. |
The line, \[\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}\] intersects the curve \[xy={{c}^{2}},z=0\] if c is equal to |
| A. | \[\pm 1\] |
| B. | \[\pm \frac{1}{3}\] |
| C. | \[\pm \sqrt{5}\] |
| D. | None |
| Answer» D. None | |
| 479. |
Let \[{{\vec{r}}_{1}},{{\vec{r}}_{2}},{{\vec{r}}_{3}},.....{{\vec{r}}_{n}},\] be the position vectors of points \[{{P}_{1}},{{P}_{2}},{{P}_{3}},....,{{P}_{n}}\] relative to the origin O. If the vector equation \[{{a}_{1}}{{\vec{r}}_{1}}+{{a}_{2}}{{\vec{r}}_{2}}+....+{{a}_{n}}{{\vec{r}}_{n}}=0\] holds, then a similar equation will also hold w.r.t. to any other origin provided |
| A. | \[{{a}_{1}}+{{a}_{2}}+....+{{a}_{n}}=n\] |
| B. | \[{{a}_{1}}+{{a}_{2}}+....+{{a}_{n}}=1\] |
| C. | \[{{a}_{1}}+{{a}_{2}}+....+{{a}_{n}}=0\] |
| D. | \[{{a}_{1}}={{a}_{2}}={{a}_{3}}=....={{a}_{n}}=0\] |
| Answer» D. \[{{a}_{1}}={{a}_{2}}={{a}_{3}}=....={{a}_{n}}=0\] | |
| 480. |
If \[A=\left[ \begin{matrix} 3 & 2 \\ 1 & 4 \\ \end{matrix} \right]\], then \[A(adj\,A)=\] [MP PET 1995; RPET 1997] |
| A. | \[\left[ \begin{matrix} 10 & 0 \\ 0 & 10 \\ \end{matrix} \right]\] |
| B. | \[\left[ \begin{matrix} 0 & 10 \\ 10 & 0 \\ \end{matrix} \right]\] |
| C. | \[\left[ \begin{matrix} 10 & 1 \\ 1 & 10 \\ \end{matrix} \right]\] |
| D. | None of these |
| Answer» B. \[\left[ \begin{matrix} 0 & 10 \\ 10 & 0 \\ \end{matrix} \right]\] | |
| 481. |
Let \[\overset{\to }{\mathop{a}}\,,\overset{\to }{\mathop{b}}\,,\overset{\to }{\mathop{c}}\,\] be non-coplanar vectors and\[\overset{\to }{\mathop{p}}\,=\frac{\overset{\to }{\mathop{b}}\,\times \overset{\to }{\mathop{c}}\,}{[\overset{\to }{\mathop{a}}\,\overset{\to }{\mathop{b}}\,\overset{\to }{\mathop{c}}\,]},\,\,\,\overset{\to }{\mathop{q}}\,=\frac{\overset{\to }{\mathop{c}}\,\times \overset{\to }{\mathop{a}}\,}{[\overset{\to }{\mathop{a}}\,\overset{\to }{\mathop{b}}\,\overset{\to }{\mathop{c}}\,]},\,\,\,\overset{\to }{\mathop{r}}\,=\frac{\overset{\to }{\mathop{a}}\,\times \overset{\to }{\mathop{b}}\,}{[\overset{\to }{\mathop{a}}\,\overset{\to }{\mathop{b}}\,\overset{\to }{\mathop{c}}\,]}.\] What is the value of\[(\vec{a}-\vec{b}-\vec{c}).\vec{p}+(\vec{b}-\vec{c}-\vec{a}).\vec{q}+(\vec{c}-\vec{a}-\vec{b}).\vec{r}\]? |
| A. | 0 |
| B. | -3 |
| C. | 3 |
| D. | -9 |
| Answer» D. -9 | |
| 482. |
The value of \[\cos 52{}^\circ +\cos 68{}^\circ +\cos 172{}^\circ \] is [MP PET 1997; Pb. CET 1995, 99] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | \[\frac{3}{2}\] |
| Answer» B. 1 | |
| 483. |
Let f be a function on R given by \[f(x)={{x}^{2}}\] and let \[E=\{x\in R:-1\le x\le 0\}\] And \[F=\{x\in R:0\le x\le 1\}\] then which of the following is false? |
| A. | \[f(E)=f(F)\] |
| B. | \[E\cap F\subset f(E)\cap f(F)\] |
| C. | \[E\cup F\subset f(E)\cup f(F)\] |
| D. | \[f(E\cap F)=\{0\}\] |
| Answer» D. \[f(E\cap F)=\{0\}\] | |
| 484. |
If \[f(x)=4x-{{x}^{2}},x\in R,\] then \[f(a+1)-f(a-1)\] is equal to |
| A. | \[2(4-a)\] |
| B. | \[4(2-a)\] |
| C. | \[4(2+a)\] |
| D. | \[2(4+a)\] |
| Answer» C. \[4(2+a)\] | |
| 485. |
The number of values of \[\theta \] in [0, 2p] satisfying the equation \[2{{\sin }^{2}}\theta =4+3\]\[\cos \theta \]are [MP PET 1989] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» B. 1 | |
| 486. |
Locus of midpoint of the portion between the axes of \[x\cos \alpha +y\sin \alpha =p\] where p is constant is |
| A. | \[{{x}^{2}}+{{y}^{2}}=\frac{4}{{{p}^{2}}}\] |
| B. | \[{{x}^{2}}+{{y}^{2}}=4{{p}^{2}}\] |
| C. | \[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}=\frac{2}{{{p}^{2}}}\] |
| D. | \[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}=\frac{4}{{{p}^{2}}}\] |
| Answer» E. | |
| 487. |
Area of the triangle formed by the line \[x+y=3\]and the angle bisectors of the pairs of straight lines \[{{x}^{2}}-{{y}^{2}}+2y=1\] is |
| A. | 2 sq. units |
| B. | 4 sq. units |
| C. | 6 sq. units |
| D. | 8 sq. units |
| Answer» B. 4 sq. units | |
| 488. |
If the angle between the two lines represented by \[2{{x}^{2}}+5xy+3{{y}^{2}}+6x+7y+4=0\] is \[{{\tan }^{-1}}m.\] then m is equal to: |
| A. | \[\frac{1}{5}\] |
| B. | 1 |
| C. | \[\frac{7}{5}\] |
| D. | 7 |
| Answer» B. 1 | |
| 489. |
The least integer k which makes the roots of the equation \[{{x}^{2}}+5x+k=0\] imaginary is [Kerala (Engg.) 2002] |
| A. | 4 |
| B. | 5 |
| C. | 6 |
| D. | 7 |
| Answer» E. | |
| 490. |
The locus of a point P which moves in such a way that the segment OP, where O is the origin, has slope \[\sqrt{3}\] is |
| A. | \[x-\sqrt{3}y=0\] |
| B. | \[x+\sqrt{3}y=0\] |
| C. | \[\sqrt{3}x+y=0\] |
| D. | \[\sqrt{3}x-y=0\] |
| Answer» E. | |
| 491. |
The value of 'x' for which the angle between the vectors \[\overset{\to }{\mathop{a}}\,=2{{x}^{2}}\hat{i}+4x\hat{j}+\hat{k}\] and \[\overset{\to }{\mathop{b}}\,=7\hat{i}-2\hat{j}+x\hat{k}\] is obtuse are |
| A. | \[\operatorname{x} < 0\] |
| B. | \[x>\frac{1}{2}\] |
| C. | \[0<x<\frac{1}{2}\] |
| D. | \[x\in R\] |
| Answer» D. \[x\in R\] | |
| 492. |
Let \[\vec{r}=(\vec{a}\times \vec{b})\sin \,x+(\vec{b}\times \vec{c})\cos \,y+2(\vec{c}\times \vec{a})\] where \[\vec{a},\vec{b},\vec{c}\]three non-coplanar vectors are. If \[\vec{r}\] is perpendicular to \[\vec{a}+\vec{b}+\vec{c},\] the minimum value of \[{{x}^{2}}+{{y}^{2}}\] is |
| A. | \[{{\pi }^{2}}\] |
| B. | \[\frac{{{\pi }^{2}}}{4}\] |
| C. | \[\frac{5{{\pi }^{2}}}{4}\] |
| D. | None of these |
| Answer» D. None of these | |
| 493. |
Let \[\vec{a},\vec{b}\] and \[\vec{c}\] be three non-zero vectors such that no two of these are collinear. If the vector \[\vec{a}+2\vec{b}\] is collinear with \[\vec{c}\] and \[\vec{b}+3\vec{c}\] is collinear with \[\vec{a}\] (\[\lambda \] being some non-zero scalar) then \[\vec{a}+2\vec{b}+6\vec{c}\] equals |
| A. | 0 |
| B. | \[\lambda \vec{b}\] |
| C. | \[\lambda \vec{c}\] |
| D. | \[\lambda \vec{a}\] |
| Answer» D. \[\lambda \vec{a}\] | |
| 494. |
\[{{L}_{1}}\] and \[{{L}_{2}}\] are two lines whose vector equations are \[{{L}_{1}}:\overset{\to }{\mathop{r}}\,=\lambda ((cos\,\,\theta +\sqrt{3})\hat{i}+(\sqrt{2}sin\,\,\theta )\hat{j}\]\[+(cos\theta -\sqrt{3})\hat{k}){{L}_{2}}:\overset{\to }{\mathop{r}}\,=\mu \left( a\hat{i}+b\hat{j}+c\hat{k} \right)\], where \[\lambda \] and \[\mu \] are scalars and \[\alpha \] is the acute angle between \[{{L}_{1}}\] and\[{{L}_{2}}\]. If the angle \['\alpha '\] is independent of \[\theta \] then the value of \['\alpha '\] is |
| A. | \[\frac{\pi }{6}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | \[\frac{\pi }{3}\] |
| D. | \[\frac{\pi }{2}\] |
| Answer» B. \[\frac{\pi }{4}\] | |
| 495. |
What is the equation of the plane through z-axis and parallel to the line\[\frac{x-1}{\cos \theta }=\frac{y+2}{\sin \theta }=\frac{z-3}{0}\]? |
| A. | \[x\,\,cot\,\theta +y=0\] |
| B. | \[x\,\,tan\,\,\theta -y=0\] |
| C. | \[x+y\,\,cot\,\theta =0\] |
| D. | \[x-y\,\,tan\,\theta =0\] |
| Answer» C. \[x+y\,\,cot\,\theta =0\] | |
| 496. |
Two system of rectangular axes have the same origin. If a plane cuts them at distances a, b, c and a', b', c' respectively from the origin, then\[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}+\frac{1}{{{c}^{2}}}=k\left( \frac{1}{a{{'}^{2}}}+\frac{1}{b{{'}^{2}}}+\frac{1}{c{{'}^{2}}} \right)\], where k is equal to |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | None of these |
| Answer» B. 2 | |
| 497. |
If \[U=[2\,-3\,\,4],X=[0\,\,2\,\,3],\] \[V=\left[ \begin{align} & 3 \\ & 2 \\ & 1 \\ \end{align} \right]\] and \[Y=\left[ \begin{align} & 2 \\ & 2 \\ & 4 \\ \end{align} \right]\], then \[UV+XY\]= [MP PET 1997] |
| A. | 20 |
| B. | [- 20] |
| C. | -20 |
| D. | [20] |
| Answer» E. | |
| 498. |
The value of ?n? for which \[^{n-1}{{C}_{4}}{{-}^{n-1}}{{C}_{3}}-\frac{5}{4}{{.}^{n-1}}{{P}_{2}}<0,\] Where \[n\in N\] |
| A. | \[\{5,6,7,8,9,10\}\] |
| B. | \[\{1,2,3,4,5,6,7,8,9,10\}\] |
| C. | \[\{1,4,5,6,7,8,9,10\}\] |
| D. | \[(-\infty ,2)\cup (3,11)\] |
| Answer» B. \[\{1,2,3,4,5,6,7,8,9,10\}\] | |
| 499. |
Given (i) 85 observations which are not shortest and (ii) 150 observations which are sorted and arranged in an increasing order. The median values of (i) & (ii) respectively can be found as |
| A. | (i) 43rd observation (ii) A.M. of 75th and 76th observation |
| B. | (i) 43rd observation (ii) 76th observation |
| C. | (i) cannot be found (ii) cannot be found |
| D. | None of these |
| Answer» E. | |
| 500. |
The variance of first 50 even natural numbers is |
| A. | 437 |
| B. | \[\frac{437}{4}\] |
| C. | \[\frac{833}{4}\] |
| D. | \[833\] |
| Answer» E. | |