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Questions >> JEEMAIN and NEET >> Mathematics

Mathematics

Limit, Continuity and Differentiability

Sets, Relations and Functions

The points $(5,0,2),\:(2,-6,0),\:(4,-9,6)\:and\:(7,-3,8)$ represent vertices of a ?

asked Jan 11, 2014 by rvidyagovindarajan_1

1 answer

A line segment of length $21$ has $d.r.=(2,-3,6)$ and makes obtuse angle with $x\:axis$ , then the components of the line segment (vector) are?

asked Jan 10, 2014 by rvidyagovindarajan_1

1 answer

If $P(2,3,4)\;and\:Q(1,b,1)$ are two points and $O$ is origin such that $OP$ is $\perp$ to $OQ$ , then $b=?$

asked Jan 10, 2014 by rvidyagovindarajan_1

1 answer

The point which divides the line joining the points $(2,4,5)\:\:and\:\:(3,5,-4)$ in the ratio $2:3$ externaly lies on the plane?

asked Jan 10, 2014 by rvidyagovindarajan_1

1 answer

If the plane $x-2y+3z=0$ is rotated through a right angle about its line of intersection with the plane $2x+3y-4z-5=0$ , then the eqn. of the plane in its new position is ?

asked Jan 9, 2014 by rvidyagovindarajan_1

1 answer

The angle between the lines $x=1,\:y=2$ and $y=-1,\:z=0$ is ?

asked Jan 9, 2014 by rvidyagovindarajan_1

1 answer

The angle between the line formed by $3x-7y-5z=1$ and $8x-11y+2z=0$ and the line formed by $5x-13y+3z+2=0$ and $8x-11y+2z=0$

asked Jan 9, 2014 by rvidyagovindarajan_1

1 answer

A and B throw a dice each. The probability that A's throw is not greater than B's throw is

asked Jan 9, 2014 by thanvigandhi_1

1 answer

A is targetting to B, b and C are targetting to A. probability of hitting the target by A,B and C are $\large\frac{2}{3}, \large\frac{1}{2} \: and \: \large\frac{1}{3}$ respectively. If A is hit then the probability that B hits the target and C does not is

asked Jan 9, 2014 by thanvigandhi_1

1 answer

Ordinary dice are rolled. The probability that at least half of them will show at least 3 is

asked Jan 9, 2014 by thanvigandhi_1

1 answer

A fair coin is tossed 100 times. The probability of getting tails on odd number of times is

asked Jan 9, 2014 by thanvigandhi_1

1 answer

A coin is tossed 7 times. The probability that he wins the toss on more occasions is

asked Jan 9, 2014 by thanvigandhi_1

1 answer

In a binomial distribution $B \bigg( n, P = \large\frac{1}{4} \bigg)$ If the probability of at least one success is greater than or equal to $\large\frac{9}{10}$ then $n$ is greater than

asked Jan 9, 2014 by thanvigandhi_1

1 answer

It is given that the events A and B are such that $P(A) = \large\frac{1}{4}\: \: P \bigg( \large\frac{A}{B} \bigg) \large\frac{1}{2}\: and \: P \bigg( \large\frac{B}{A} \bigg) = \large\frac{2}{3}$ Then $P(B)$ is

asked Jan 9, 2014 by thanvigandhi_1

1 answer

If X is binomial variate with parameters $n$ and $p$ where $0 < P < 1$ such that $\large\frac{P(x=r)}{P(x=n-r)}$ is independent of n and r then p equals.

asked Jan 9, 2014 by thanvigandhi_1

1 answer

Equation of the line through the point $(2,-1,-1)$ , which is parallel to the plane $4x+y+z+2=0$ ans is $\perp$ to the line $x=\large\frac{y}{-2}=$ $z-5$ is ?

asked Jan 8, 2014 by rvidyagovindarajan_1

1 answer

The probability that $\sin^{-1} ( \sin \: x)+ \cos^{-1} ( \cos\: y)$ is an integer $x,y \in \{ 1,2,3,4 \}$ is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

Let A and B be two independent events such that $P(A) = \large\frac{1}{5} \: P( A \cup B ) = \large\frac{7}{10}$ . Ten $P(\overline B)$ is equal to

asked Jan 8, 2014 by thanvigandhi_1

1 answer

The equation of projection of the line $\large\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-3}{3}$ on the plane $x+y+z=1$ is given by ?

asked Jan 8, 2014 by rvidyagovindarajan_1

1 answer

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form $7^m+7^n$ is divisible by 5 equals.

asked Jan 8, 2014 by thanvigandhi_1

1 answer

The direction cosine of a line which is $\perp$ to two perpendicular lines whose direction cosines are $(l_1,m_1,n_1)\:\:and\:\:(l_2,m_2,n_2)$ is ?

asked Jan 8, 2014 by rvidyagovindarajan_1

1 answer

A box contains 3 white and 2 red balls. If we draw one ball and without replacing the first ball, the probability of drawing red ball in the second draw is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

The mean and variance of a binomial variate X are 2 and 1 respectively. The probability that X takes a value greater than 1 is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

A and B are two independent events. The probability that both A and B occur is $\large\frac{1}{6}$ and the probability that neither of them occurs is $\large\frac{1}{3}$ . Then the probability of the two events are respectively

asked Jan 8, 2014 by thanvigandhi_1

1 answer

A pair of dice is rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals

asked Jan 8, 2014 by thanvigandhi_1

2 answers

A box contains 24 identical bals of which 12 are white and remaining black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

A fair die is tossed until a number greater than 4 appears. The probability that an even number of tosses shall be required is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

If the probability for A to fail in an examination is 0.2 and that for B is 0.3 then the probability that either A or B fails is

asked Jan 8, 2014 by thanvigandhi_1

1 answer

An unbiased die with faces marked 1,2,3,4,5 and 6 is rolled four times out of four values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is :

asked Jan 8, 2014 by thanvigandhi_1

1 answer

The equation of the plane that meets the coordinate axes at the points $A,B,C$ respectively and the centroid of the $\Delta\:ABC$ is $(2,1,5)$ is ?

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

The equation of the plane which makes double the intercepts of the plane $3x+6y-z+12=0$ is ?

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow r\times\overrightarrow b=\overrightarrow c\times\overrightarrow b$ and $\overrightarrow r.\overrightarrow a=0$ , where $\overrightarrow a=2\hat i+3\hat j-\hat k,\:\overrightarrow b=3\hat i-\hat i+\hat k\:and\:\:\overrightarrow c=\hat i+\hat j+3\hat k$ , then $\overrightarrow r=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=(-1,1,1)\:\:\overrightarrow b=(2,0,1)\:and\:\overrightarrow x$ is vector such that $\overrightarrow x.\overrightarrow a=7,\:\overrightarrow x.\overrightarrow b=0$ and $\overrightarrow a,\overrightarrow b,\overrightarrow x$ are coplanar, then $\overrightarrow x=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

In a rt. angled triangle $ABC$ if hypotenuse, $AB=p$ , then $\overrightarrow {AB}.\overrightarrow {AC}+\overrightarrow {BC}.\overrightarrow {BA}+\overrightarrow {CA}.\overrightarrow {CB}$ = ?

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

A vector $a\hat i+b\hat j+c\hat k$ is such that its magnitude is $|a|+|b|+|c|$ . This is possible only if

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $P$ is point whose position vector is $\overrightarrow r=x\hat i+y\hat j+z\hat k$ where $x,y,z \in N$ and $\overrightarrow a=\hat i+\hat j+\hat k$ , then the number of possible points $P$ for which $\overrightarrow r.\overrightarrow a=10$ is ?

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=\hat i+\hat j+\hat k,\:\:\overrightarrow c=\hat j-\hat k$ and $\overrightarrow b$ is such that $\overrightarrow a\times\overrightarrow b=\overrightarrow c\:\:and\:\:\overrightarrow a.\overrightarrow b=3$ then $\overrightarrow b=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a=2\hat i+\hat j-2\hat k\:\;and\:\:\overrightarrow b=\hat i+\hat j$ and $\overrightarrow c$ is such that $\overrightarrow c.\overrightarrow a=|\overrightarrow c|$ , $|\overrightarrow c-\overrightarrow a|=2\sqrt 2$ and the angle between $\overrightarrow a\times\overrightarrow b$ and $\overrightarrow c$ is $30^{\circ}$ , then $|(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c|=?$

asked Jan 7, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b$ are mutually $\perp$ unit vectors and the vectors $x\overrightarrow a+x\overrightarrow b+z(\overrightarrow a\times\overrightarrow b ),\:\:\overrightarrow a+(\overrightarrow a\times\overrightarrow b),\:\:and\:\:z\overrightarrow a+z\overrightarrow b+y(\overrightarrow a\times\overrightarrow b)$ lie in a plane then $Z$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

The probability that a number selected at random from the set of numbers { 1,2,3,.....100} is a cube is

asked Jan 6, 2014 by thanvigandhi_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are unit vectors and $\overrightarrow a+\overrightarrow b+\overrightarrow c$ is also a unit vector and $\alpha,\beta,\gamma$ are angles between $\overrightarrow a\:and\:\overrightarrow b,\:\:\overrightarrow b\:and\:\overrightarrow c\:\:\overrightarrow c\:and\:\overrightarrow a$ respectively, then among the three angles,

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are any three vectors such that $\overrightarrow a=\overrightarrow b+\overrightarrow c$ and $\overrightarrow b$ is $\perp$ to $\overrightarrow c$ , then ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

For a poisson variate X if $P(X=0) = 0.2$ then its variance is

asked Jan 6, 2014 by thanvigandhi_1

1 answer

If S is a sample space $P(A) = \large\frac{1}{3} P(B)\: and \: S = A \cup B$ where A,B are two mutually exclusive events, then $P(A)=$

asked Jan 6, 2014 by thanvigandhi_1

1 answer

A line makes angle $\theta$ with both $x\:axis$ and $z\:axis$ . If it makes angle $\alpha$ with $y\:axis$ and $\sin^2\alpha=2 \sin^2\theta$ then $\cot^2\theta=?$

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

A tetrahedron has vertices $O(0,0,0),\:A(1,2,1)\:B(2,1,3)\:C(-1,1,2)$ . The angle between the faces $OAB$ and $ABC$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

The value of $k$ for which the line $\overrightarrow r=(4\hat i+2\hat j-\hat k)+\lambda(\hat i-k\hat j+2\hat k)$ lies on the plane $2x-4y+z=3$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

The value of $k$ for which the line $\large\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ to lie on the plane $2x-4y+3z=6$ is ?

asked Jan 6, 2014 by rvidyagovindarajan_1

1 answer

If $E_1$ denotes the event of coming sum 6 in throwing two dice and $E_2$ be the event of coming 2 in any one of the two, then $P(E_2/E_1)$ is

asked Jan 6, 2014 by thanvigandhi_1

1 answer

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