8666 + Mcqs in Mathematics Page 139 McqOptions

6901.	Equation of curve passing through (3, 9) which satisfies the differential equation \[\frac{dy}{dx}=x+\frac{1}{{{x}^{2}}}\], is [WB JEE 1986]
A.	\[6xy=3{{x}^{2}}-6x+29\]
B.	\[6xy=3{{x}^{3}}-29x+6\]
C.	\[6xy=3{{x}^{3}}+29x-6\]
D.	None of these
Answer» D. None of these

Discussion

6902.	Angles made by the lines represented by the equation \[xy+y=0\]with \[y-\]axis are
A.	\[{{0}^{o}}\]and \[{{90}^{o}}\]
B.	\[{{0}^{o}}\]and \[{{30}^{o}}\]
C.	\[{{30}^{o}}\]and \[{{60}^{o}}\]
D.	\[{{30}^{o}}\]and \[{{90}^{o}}\]
Answer» B. \[{{0}^{o}}\]and \[{{30}^{o}}\]

Discussion

6903.	The angle between the two straight lines \[2{{x}^{2}}-5xy+2{{y}^{2}}-3x+3y+1=0\] is
A.	\[{{45}^{o}}\]
B.	\[{{60}^{o}}\]
C.	\[{{\tan }^{-1}}\frac{4}{3}\]
D.	\[{{\tan }^{-1}}\frac{3}{4}\]
Answer» E.

Discussion

6904.	The equation of the line passing through the points \[{{a}_{1}}\mathbf{i}+{{a}_{2}}\mathbf{j}+{{a}_{3}}\mathbf{k}\] and \[{{b}_{1}}\mathbf{i}+{{b}_{2}}\mathbf{j}+{{b}_{3}}\mathbf{k}\]is [RPET 2002]
A.	\[({{a}_{1}}\mathbf{i}+{{a}_{2}}\mathbf{j}+{{a}_{3}}\mathbf{k})+t({{b}_{1}}\mathbf{i}+{{b}_{2}}\mathbf{j}+{{b}_{3}}\mathbf{k})\]
B.	\[({{a}_{1}}\mathbf{i}+{{a}_{2}}\mathbf{j}+{{a}_{3}}\mathbf{k})-t({{b}_{1}}\mathbf{i}+{{b}_{2}}\mathbf{j}+{{b}_{3}}\mathbf{k})\]
C.	\[{{a}_{1}}(1-t)\mathbf{i}+{{a}_{2}}(1-t)\mathbf{j}+{{a}_{3}}(1-t)\mathbf{k}+({{b}_{1}}\mathbf{i}+{{b}_{2}}\mathbf{j}+{{b}_{3}}\mathbf{k})t\]
D.	None of these
Answer» D. None of these

Discussion

6905.	The sum of first \[n\] natural numbers is [MP PET 1984; RPET 1995]
A.	\[n\,(n-1)\]
B.	\[\frac{n\,(n-1)}{2}\]
C.	\[n\,(n+1)\]
D.	\[\frac{n\,(n+1)}{2}\]
Answer» E.

Discussion

6906.	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. \[12\pi \]

Discussion

6907.	The line of intersection of the planes \[\mathbf{r}.(\mathbf{i}-3\mathbf{j}+\mathbf{k})=1\] and \[\mathbf{r}.(2\mathbf{i}+5\mathbf{j}-3\mathbf{k})=2\] is parallel to the vector
A.	\[-4\mathbf{i}+5\mathbf{j}+11\mathbf{k}\]
B.	\[4\mathbf{i}+5\mathbf{j}+11\mathbf{k}\]
C.	\[4\mathbf{i}-5\mathbf{j}+11\mathbf{k}\]
D.	\[4\mathbf{i}-5\mathbf{j}-11\mathbf{k}\]
Answer» C. \[4\mathbf{i}-5\mathbf{j}+11\mathbf{k}\]

Discussion

6908.	For a biased die the probabilities for different faces to turn up are given below Face : 1 2 3 4 5 6 Probability : 0.1 0.32 0.21 0.15 0.05 0.17 The die is tossed and you are told that either face 1 or 2 has turned up. Then the probability that it is face 1, is [IIT 1981]
A.	\[\frac{5}{21}\]
B.	\[\frac{5}{22}\]
C.	\[\frac{4}{21}\]
D.	None of these
Answer» B. \[\frac{5}{22}\]

Discussion

6909.	The distance in seconds, described by a particle in t seconds is given by \[s=a{{e}^{t}}+\frac{b}{{{e}^{t}}}\]. Then acceleration of the particle at time t is
A.	Proportional to t
B.	Proportional to s
C.	s
D.	Constant
Answer» D. Constant

Discussion

6910.	The position vectors of points A and B are \[\mathbf{i}-\mathbf{j}+3\mathbf{k}\] and \[3\mathbf{i}+3\mathbf{j}+3\mathbf{k}\] respectively. The equation of a plane is \[\mathbf{r}.(5\mathbf{i}+2\mathbf{j}-7\mathbf{k})+9=0\]. The points A and B
A.	Lie on the plane
B.	Are on the same side of the plane
C.	Are on the opposite side of the plane
D.	None of these
Answer» D. None of these

Discussion

6911.	In a Boolean Algebra B, for all x in B, \[x\wedge x=\]
A.	0
B.	1
C.	x
D.	None of these
Answer» D. None of these

Discussion

6912.	In a triangle\[ABC\], if \[b=2,\,B=30{}^\circ \]then the area of circumcircle of triangle ABC in square units is [Karnataka CET 2004]
A.	\[\pi \]
B.	\[2\pi \]
C.	\[4\pi \]
D.	\[6\pi \]
Answer» D. \[6\pi \]

Discussion

6913.	The lines represented by the equation \[9{{x}^{2}}+24xy+16{{y}^{2}}+21x+28y+6=0\] are
A.	Parallel
B.	Coincident
C.	Perpendicular
D.	None of these
Answer» B. Coincident

Discussion

6914.	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

Discussion

6915.	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.

Discussion

6916.	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

Discussion

6917.	The equation of motion of a car is \[s={{t}^{2}}-2t\], where t is measured in hours and s in kilometers. When the distance travelled by the car is \[15\,km\], the velocity of the car is
A.	\[2\,km/h\]
B.	\[4\,km/h\]
C.	\[2\,km/h\]
D.	\[8\,km/h\]
Answer» E.

Discussion

6918.	If both the roots of \[k(6{{x}^{2}}+3)+rx+2{{x}^{2}}-1=0\] and \[6k(2{{x}^{2}}+1)+px+4{{x}^{2}}-2=0\] are common, then \[2r-p\] is equal to [MNR 1983]
A.	-1
B.	0
C.	1
D.	2
Answer» C. 1

Discussion

6919.	The value of \[\|z-5\|\]if \[z=x+iy\], is [RPET 1995]
A.	\[\sqrt{{{(x-5)}^{2}}+{{y}^{2}}}\]
B.	\[{{x}^{2}}+\sqrt{{{(y-5)}^{2}}}\]
C.	\[\sqrt{{{(x-y)}^{2}}+{{5}^{2}}}\]
D.	\[\sqrt{{{x}^{2}}+{{(y-5)}^{2}}}\]
Answer» B. \[{{x}^{2}}+\sqrt{{{(y-5)}^{2}}}\]

Discussion

6920.	The distance between the chords of contact of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]from the origin and the point \[(g,f)\]is
A.	\[\frac{1}{2}\left( \frac{{{g}^{2}}+{{f}^{2}}-c}{\sqrt{{{g}^{2}}+{{f}^{2}}}} \right)\]
B.	\[\left( \frac{{{g}^{2}}+{{f}^{2}}-c}{\sqrt{{{g}^{2}}+{{f}^{2}}}} \right)\]
C.	\[\frac{1}{2}\left( \frac{{{g}^{2}}+{{f}^{2}}-c}{{{g}^{2}}+{{f}^{2}}} \right)\]
D.	None of these
Answer» B. \[\left( \frac{{{g}^{2}}+{{f}^{2}}-c}{\sqrt{{{g}^{2}}+{{f}^{2}}}} \right)\]

Discussion

6921.	If \[n\] be odd or even, then the sum of \[n\] terms of the series \[1-2+\] \[3-\]\[4+5-6+......\] will be
A.	\[-\frac{n}{2}\]
B.	\[\frac{n-1}{2}\]
C.	\[\frac{n+1}{2}\]
D.	\[\frac{2n+1}{2}\]
Answer» D. \[\frac{2n+1}{2}\]

Discussion

6922.	The four arithmetic means between 3 and 23 are [MP PET 1985]
A.	5, 9, 11, 13
B.	7, 11, 15, 19
C.	5, 11, 15, 22
D.	7, 15, 19, 21
Answer» C. 5, 11, 15, 22

Discussion

6923.	If the middle point of a chord of the circle \[{{x}^{2}}+{{y}^{2}}+x-y-1=0\]be (1, 1), then the length of the chord is
A.	4
B.	2
C.	5
D.	None of these
Answer» E.

Discussion

6924.	The lines represented by the equation \[{{x}^{2}}+2\sqrt{3}xy+3{{y}^{2}}-3x-3\sqrt{3}y-4=0\], are
A.	Perpendicular to each other
B.	Parallel
C.	Inclined at \[{{45}^{o}}\]to each other
D.	None of these
Answer» C. Inclined at \[{{45}^{o}}\]to each other

Discussion

6925.	The first term of an A.P. of consecutive integers is \[{{p}^{2}}+1\] The sum of \[(2p+1)\] terms of this series can be expressed as
A.	\[{{(p+1)}^{2}}\]
B.	\[{{(p+1)}^{3}}\]
C.	\[(2p+1){{(p+1)}^{2}}\]
D.	\[{{p}^{3}}+{{(p+1)}^{3}}\]
Answer» E.

Discussion

6926.	If \[x,y,z\] are in A.P. and \[{{\tan }^{-1}}x,{{\tan }^{-1}}y\]and \[{{\tan }^{-1}}z\] are also in A.P., then [Kerala (Engg.) 2005]
A.	\[x=y=z\]
B.	\[x=y=-z\]
C.	\[x=1;y=2;z=3\]
D.	\[x=2;y=4;z=6\]
E.	\[x=2y=3z\]
Answer» B. \[x=y=-z\]

Discussion

6927.	The difference between an integer and its cube is divisible by [MP PET 1999]
A.	4
B.	6
C.	9
D.	None of these
Answer» C. 9

Discussion

6928.	The area of the region bounded by \[y=\,\,\|x-1\|\] and \[y=1\] is [IIT Screening 1994]
A.	2
B.	1
C.	\[\frac{1}{2}\]
D.	None of these
Answer» C. \[\frac{1}{2}\]

Discussion

6929.	The value of C for which \[P\,(X=k)=C{{k}^{2}}\]can serve as the probability function of a random variable X that takes 0, 1, 2, 3, 4 is [EAMCET 1994]
A.	\[\frac{1}{30}\]
B.	\[\frac{1}{10}\]
C.	\[\frac{1}{3}\]
D.	\[\frac{1}{15}\]
Answer» B. \[\frac{1}{10}\]

Discussion

6930.	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. \[{{150}^{o}}\]

Discussion

6931.	If \[a,b,c\] are real numbers such that \[a+b+c=0,\] then the quadratic equation \[3a{{x}^{2}}+2bx+c=0\]has [MNR 1992; DCE 1999]
A.	At least one root in [0, 1]
B.	At least one root in [1, 2]
C.	At least one root in \[[-1,\,0]\]
D.	None of these
Answer» B. At least one root in [1, 2]

Discussion

6932.	If \[\bar{E}\] and \[\bar{F}\] are the complementary events of events E and F respectively and if \[0
A.	\[P\,(E/F)+P\,(\bar{E}/F)=1\]
B.	\[P\,(E/F)+P\,(E/\bar{F})=1\]
C.	\[P\,(\bar{E}/F)+P\,(E/\bar{F})=1\]
D.	\[P\,(E/\bar{F})+P\,(\bar{E}/\bar{F})=1\]
Answer» B. \[P\,(E/F)+P\,(E/\bar{F})=1\]

Discussion

6933.	The displacement of a particle in time t is given by \[s=2{{t}^{2}}-3t+1\]. The acceleration is
A.	1
B.	3
C.	4
D.	5
Answer» D. 5

Discussion

6934.	If \[{{z}_{1}}.{{z}_{2}}........{{z}_{n}}=z,\] then \[arg\,{{z}_{1}}+arg\,{{z}_{2}}+....\]+\[arg\,{{z}_{n}}\] and \[arg\]\[z\] differ by a
A.	Multiple of \[\pi \]
B.	Multiple of\[\frac{\pi }{2}\]
C.	Greater than \[\pi \]
D.	Less than \[\pi \]
Answer» B. Multiple of\[\frac{\pi }{2}\]

Discussion

6935.	A population p(t) of 1000 bacteria introduced into nutrient medium grows according to the relation \[p(t)=1000+\frac{1000t}{100+{{t}^{2}}}\]. The maximum size of this bacterial population is [Karnataka CET 2005]
A.	1100
B.	1250
C.	1050
D.	5250
Answer» D. 5250

Discussion

6936.	The conjugate of the complex number \[\frac{2+5i}{4-3i}\] is [MP PET 1994]
A.	\[\frac{7-26i}{25}\]
B.	\[\frac{-7-26i}{25}\]
C.	\[\frac{-7+26i}{25}\]
D.	\[\frac{7+26i}{25}\]
Answer» C. \[\frac{-7+26i}{25}\]

Discussion

6937.	If a dice is thrown twice, the probability of occurrence of 4 at least once is [UPSEAT 2003]
A.	\[\frac{11}{36}\]
B.	\[\frac{7}{12}\]
C.	\[\frac{35}{36}\]
D.	None of these
Answer» B. \[\frac{7}{12}\]

Discussion

6938.	Equation of angle bisector between the lines \[3x+4y-7=0\] and \[12x+5y+17=0\]are [RPET 1995]
A.	\[\frac{3x+4y-7}{\sqrt{25}}=\pm \frac{12x+5y+17}{\sqrt{169}}\]
B.	\[\frac{3x+4y+7}{\sqrt{25}}=\frac{12x+5y+17}{\sqrt{169}}\]
C.	\[\frac{3x+4y+7}{\sqrt{25}}=\pm \frac{12x+5y+17}{\sqrt{169}}\]
D.	None of these
Answer» B. \[\frac{3x+4y+7}{\sqrt{25}}=\frac{12x+5y+17}{\sqrt{169}}\]

Discussion

6939.	The records of a hospital show that 10% of the cases of a certain disease are fatal. If 6 patients are suffering from the disease, then the probability that only three will die is [MP PET 1998]
A.	\[1458\times {{10}^{-5}}\]
B.	\[1458\times {{10}^{-6}}\]
C.	\[41\times {{10}^{-6}}\]
D.	\[8748\times {{10}^{-5}}\]
Answer» B. \[1458\times {{10}^{-6}}\]

Discussion

6940.	The locus of midpoint of the chords of the circle \[{{x}^{2}}+{{y}^{2}}-2x-2y-2=0\]which makes an angle of \[120{}^\circ \] at the centre is [MNR 1994]
A.	\[{{x}^{2}}+{{y}^{2}}-2x-2y+1=0\]
B.	\[{{x}^{2}}+{{y}^{2}}+x+y-1=0\]
C.	\[{{x}^{2}}+{{y}^{2}}-2x-2y-1=0\]
D.	None of these
Answer» B. \[{{x}^{2}}+{{y}^{2}}+x+y-1=0\]

Discussion

6941.	If the bisectors of the angles between the pairs of lines given by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] and \[a{{x}^{2}}+2hxy+b{{y}^{2}}+\lambda ({{x}^{2}}+{{y}^{2}})=0\] be coincident, then \[\lambda =\]
A.	a
B.	b
C.	\[h\]
D.	Any real number
Answer» E.

Discussion

6942.	In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together [EAMCET 1990; MP PET 2001; DCE 2001; UPSEAT 2002;Pb. CET 2000]
A.	\[{{(7\,!)}^{2}}\]
B.	\[7\,!\,\times \,6\,!\]
C.	\[{{(6\,!)}^{2}}\]
D.	\[7\,!\]
Answer» C. \[{{(6\,!)}^{2}}\]

Discussion

6943.	A particle is moving in a straight line according as \[s=45\,t+11{{t}^{2}}-{{t}^{3}}\]then the time when it will come to rest, is
A.	? 9 seconds
B.	\[\frac{5}{3}\]seconds
C.	9 seconds
D.	\[-\frac{5}{3}\]seconds
Answer» D. \[-\frac{5}{3}\]seconds

Discussion

6944.	If \[\|x\|
A.	n
B.	\[n+1\]
C.	1
D.	-1
Answer» D. -1

Discussion

6945.	If the ratio of the sum of \[n\] terms of two A.P.'s be \[(7n+1):(4n+27)\], then the ratio of their \[{{11}^{th}}\] terms will be [AMU 1996]
A.	\[2:3\]
B.	\[3:4\]
C.	\[4:3\]
D.	\[5:6\]
Answer» D. \[5:6\]

Discussion

6946.	The lines \[15x-18y+1=0,\] \[12x+10y-3=0\] and \[6x+66y-11=0\] are [AMU 1978]
A.	Parallel
B.	Perpendicular
C.	Concurrent
D.	None of these
Answer» D. None of these

Discussion

6947.	If \[\tan \,n\theta =\tan m\theta \], then the different values of will be in [Karnataka CET 1998]
A.	A.P.
B.	G.P.
C.	H.P.
D.	None of these
Answer» B. G.P.

Discussion

6948.	Area bounded by parabola \[{{y}^{2}}=x\] and straight line \[2y=x\] is [MP PET 1996]
A.	\[\frac{4}{3}\]
B.	1
C.	\[\frac{2}{3}\]
D.	\[\frac{1}{3}\]
Answer» B. 1

Discussion

6949.	One bisector of the angle between the lines given by \[a{{(x-1)}^{2}}+2h\,(x-1)y+b{{y}^{2}}=0\] is \[2x+y-2=0\]. The other bisector is
A.	\[x-2y+1=0\]
B.	\[2x+y-1=0\]
C.	\[x+2y-1=0\]
D.	\[x-2y-1=0\]
Answer» E.

Discussion

6950.	In a certain town, 40% of the people have brown hair, 25% have brown eyes and 15% have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes, is [MNR 1988]
A.	\[\frac{1}{5}\]
B.	\[\frac{3}{8}\]
C.	\[\frac{1}{3}\]
D.	\[\frac{2}{3}\]
Answer» C. \[\frac{1}{3}\]

Discussion

Explore topic-wise MCQs in Joint Entrance Exam - Main (JEE Main).

Equation of curve passing through (3, 9) which satisfies the differential equation \[\frac{dy}{dx}=x+\frac{1}{{{x}^{2}}}\], is [WB JEE 1986]

Angles made by the lines represented by the equation \[xy+y=0\]with \[y-\]axis are

The angle between the two straight lines \[2{{x}^{2}}-5xy+2{{y}^{2}}-3x+3y+1=0\] is

The equation of the line passing through the points \[{{a}_{1}}\mathbf{i}+{{a}_{2}}\mathbf{j}+{{a}_{3}}\mathbf{k}\] and \[{{b}_{1}}\mathbf{i}+{{b}_{2}}\mathbf{j}+{{b}_{3}}\mathbf{k}\]is [RPET 2002]

The sum of first \[n\] natural numbers is [MP PET 1984; RPET 1995]

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]

The line of intersection of the planes \[\mathbf{r}.(\mathbf{i}-3\mathbf{j}+\mathbf{k})=1\] and \[\mathbf{r}.(2\mathbf{i}+5\mathbf{j}-3\mathbf{k})=2\] is parallel to the vector

For a biased die the probabilities for different faces to turn up are given below Face : 1 2 3 4 5 6 Probability : 0.1 0.32 0.21 0.15 0.05 0.17 The die is tossed and you are told that either face 1 or 2 has turned up. Then the probability that it is face 1, is [IIT 1981]

The distance in seconds, described by a particle in t seconds is given by \[s=a{{e}^{t}}+\frac{b}{{{e}^{t}}}\]. Then acceleration of the particle at time t is

The position vectors of points A and B are \[\mathbf{i}-\mathbf{j}+3\mathbf{k}\] and \[3\mathbf{i}+3\mathbf{j}+3\mathbf{k}\] respectively. The equation of a plane is \[\mathbf{r}.(5\mathbf{i}+2\mathbf{j}-7\mathbf{k})+9=0\]. The points A and B

In a Boolean Algebra B, for all x in B, \[x\wedge x=\]

In a triangle\[ABC\], if \[b=2,\,B=30{}^\circ \]then the area of circumcircle of triangle ABC in square units is [Karnataka CET 2004]

The lines represented by the equation \[9{{x}^{2}}+24xy+16{{y}^{2}}+21x+28y+6=0\] are

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]

If a particle moves such that the displacement is proportional to the square of the velocity acquired, then its acceleration is [Kerala (Engg.) 2005]

The solution of equations \[x+y=10,2x+y=18\] and \[4x-3y=26\] will be [DCE 2005]

The equation of motion of a car is \[s={{t}^{2}}-2t\], where t is measured in hours and s in kilometers. When the distance travelled by the car is \[15\,km\], the velocity of the car is

If both the roots of \[k(6{{x}^{2}}+3)+rx+2{{x}^{2}}-1=0\] and \[6k(2{{x}^{2}}+1)+px+4{{x}^{2}}-2=0\] are common, then \[2r-p\] is equal to [MNR 1983]

The value of \[|z-5|\]if \[z=x+iy\], is [RPET 1995]

The distance between the chords of contact of the tangents to the circle \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\]from the origin and the point \[(g,f)\]is

If \[n\] be odd or even, then the sum of \[n\] terms of the series \[1-2+\] \[3-\]\[4+5-6+......\] will be

The four arithmetic means between 3 and 23 are [MP PET 1985]

If the middle point of a chord of the circle \[{{x}^{2}}+{{y}^{2}}+x-y-1=0\]be (1, 1), then the length of the chord is

The lines represented by the equation \[{{x}^{2}}+2\sqrt{3}xy+3{{y}^{2}}-3x-3\sqrt{3}y-4=0\], are

The first term of an A.P. of consecutive integers is \[{{p}^{2}}+1\] The sum of \[(2p+1)\] terms of this series can be expressed as

If \[x,y,z\] are in A.P. and \[{{\tan }^{-1}}x,{{\tan }^{-1}}y\]and \[{{\tan }^{-1}}z\] are also in A.P., then [Kerala (Engg.) 2005]

The difference between an integer and its cube is divisible by [MP PET 1999]

The area of the region bounded by \[y=\,\,|x-1|\] and \[y=1\] is [IIT Screening 1994]

The value of C for which \[P\,(X=k)=C{{k}^{2}}\]can serve as the probability function of a random variable X that takes 0, 1, 2, 3, 4 is [EAMCET 1994]

The obtuse angle between the lines \[y=-\ 2\] and \[y=x+2\] is [RPET 1984]

If \[a,b,c\] are real numbers such that \[a+b+c=0,\] then the quadratic equation \[3a{{x}^{2}}+2bx+c=0\]has [MNR 1992; DCE 1999]

If \[\bar{E}\] and \[\bar{F}\] are the complementary events of events E and F respectively and if \[0

The displacement of a particle in time t is given by \[s=2{{t}^{2}}-3t+1\]. The acceleration is

If \[{{z}_{1}}.{{z}_{2}}........{{z}_{n}}=z,\] then \[arg\,{{z}_{1}}+arg\,{{z}_{2}}+....\]+\[arg\,{{z}_{n}}\] and \[arg\]\[z\] differ by a

A population p(t) of 1000 bacteria introduced into nutrient medium grows according to the relation \[p(t)=1000+\frac{1000t}{100+{{t}^{2}}}\]. The maximum size of this bacterial population is [Karnataka CET 2005]

The conjugate of the complex number \[\frac{2+5i}{4-3i}\] is [MP PET 1994]

If a dice is thrown twice, the probability of occurrence of 4 at least once is [UPSEAT 2003]

Equation of angle bisector between the lines \[3x+4y-7=0\] and \[12x+5y+17=0\]are [RPET 1995]

The records of a hospital show that 10% of the cases of a certain disease are fatal. If 6 patients are suffering from the disease, then the probability that only three will die is [MP PET 1998]

The locus of midpoint of the chords of the circle \[{{x}^{2}}+{{y}^{2}}-2x-2y-2=0\]which makes an angle of \[120{}^\circ \] at the centre is [MNR 1994]

If the bisectors of the angles between the pairs of lines given by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] and \[a{{x}^{2}}+2hxy+b{{y}^{2}}+\lambda ({{x}^{2}}+{{y}^{2}})=0\] be coincident, then \[\lambda =\]

In how many ways 7 men and 7 women can be seated around a round table such that no two women can sit together [EAMCET 1990; MP PET 2001; DCE 2001; UPSEAT 2002;Pb. CET 2000]

A particle is moving in a straight line according as \[s=45\,t+11{{t}^{2}}-{{t}^{3}}\]then the time when it will come to rest, is

If \[|x|

If the ratio of the sum of \[n\] terms of two A.P.'s be \[(7n+1):(4n+27)\], then the ratio of their \[{{11}^{th}}\] terms will be [AMU 1996]

The lines \[15x-18y+1=0,\] \[12x+10y-3=0\] and \[6x+66y-11=0\] are [AMU 1978]

If \[\tan \,n\theta =\tan m\theta \], then the different values of will be in [Karnataka CET 1998]

Area bounded by parabola \[{{y}^{2}}=x\] and straight line \[2y=x\] is [MP PET 1996]

One bisector of the angle between the lines given by \[a{{(x-1)}^{2}}+2h\,(x-1)y+b{{y}^{2}}=0\] is \[2x+y-2=0\]. The other bisector is

In a certain town, 40% of the people have brown hair, 25% have brown eyes and 15% have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes, is [MNR 1988]