28278 + Interview Questions in Maths in Class 12 Page 44 InterviewSolution

2151.	Find the equation of the circle with centre C and radius r where C = (a,-b) , r= a+b
Answer» ANSWER :`X ^(2) + y^(2) -2ax +2by-2ab =0 `

Discussion

2152.	Definite integration as the limit of a sum : lim_(ntooo)(1)/(n)sum_(r=n+1)^(2n)log(1+(r)/(n))=.............
Answer» `log((27)/(4E))` `log((27)/(e^(2)))` `log((4)/(e))` NONE of these Answer :A

Discussion

2153.	If f and g are not derivable at x_0then f+g is not derivable at x_0.
Answer» ANSWER :F

Discussion

2154.	The radius of the circle which has the lines x+y-1=0, x+y-9=0 as tangents is
Answer» `SQRT(2)` `2sqrt(2)` `3sqrt(2)` `4sqrt(2)` ANSWER :B

Discussion

2155.	Let I_(n)=int_(0)^(pi//4) tan^(n)x dx. Statement-1: (1)/(n+1)lt 2I_(n) lt (1)/(n-1) for all n=2,3,4,….. Statement-2: I_(n)+I_(n-2)=(1)/(n-1),n=3,4,5,…...
Answer» Statement-1 is true, Statement-2 is True,Statement-2 is a correct explanation for Statement-1. Statement-1 is True, Statement-2 is not a correct explanation for Statement-1. Statement-1 is True, Statement-2 is FALSE. Statement-1 is False, Statement-2 is True. Solution :We have, `I_(n)+I_(n-2)=UNDERSET(0)overset(PI//4)int tan^(n)x dx+underset(0)overset(pi//4)int tan^(n-2)x dx` `rArr I_(n)-I_(n-2)=underset(0)overset(pi//4)int tan^(n-2)x sec^(2)x dx=[(tan^(n-1)x)/(n-1)]_(0)^(pi//4)=(1)/(n-1)` So, statement-2 is true. We know that `0 lt tan xlt1` for ll `x in (0,(pi)/(4))` `rArr tan^(n+2)xlt tan^(n-2)x` for all `x in (0,(pi)/(4))` `rArr underset(0)overset(pi//4)int tan^(n+2)x dx lt underset(0)overset(pi//4)int tan^(n-2)x dx` `rArr I_(n+2)lt I_(n)lt I_(n-2)` `rArr I_(n)+I_(n+2)lt 2I_(n)+I_(n-2)` `rArr (1)/(n+1)ltI_(n)lt(1)/(n-1)""`[Using statement-2] So, statement-1 is true and statement-2 is a correct explanation for statement-1.

Discussion

2156.	For a normal distribution if the mean is M, mode is M_(0) and median is M_(d), then
Answer» `M GT M_(d) gt M_(0)` `M LT M_(d) lt M_(0)` `M=M_(d)M_(0)` `M=M_(d)=M_(0)` SOLUTION :It is OBVIOUS.

Discussion

2157.	Show that the relation R in the set {1,2,3} given by R = {(1,2),(2,1)} is symmetric but neither reflexive nor transitive.
Answer» SOLUTION :N/A

Discussion

2158.	(cos 13^(@) - sin 13^(@))/(cos 13^(@) + sin 13^(@)) + (1)/(cot 148^(@)) is equal to
Answer» A.1 B.`-1` C.0 D.`(1)/(2)` ANSWER :c

Discussion

2159.	If the equation (x + m)^(2) - (x + n)^(2) = ( m - n)^(2) where m , n are non- zero constants and m^(2) ne n^(2) , satisfied by x = pm + pn , then the ordered pair (p , q) is equal to
Answer» (0 , -1) (-1 , 0) (1 , 0) (0, 1) ANSWER :A

Discussion

2160.	The sum of two numbers is 13, and their product is 30. What is the sum of the squares of the two numbers?
Answer» `-229` `-109` `139` `109` ANSWER :D

Discussion

2161.	State with reason,"Collection of all residents of Odisha who will live for more than 100 years " is set or not ?
Answer» Solution :It is not t set, as we do not KNOW, that who will LIVE for more than 100 YEARS.

Discussion

2162.	Integrate the following functions : int(2x+5)/(x^(2)+5x+9)dx
Answer» ANSWER :`log\|x^(2)+5x+9\|+c`

Discussion

2163.	Let A=[(0,2),(0,3)] and B=[(2,3),(0,0)], then AB equals :
Answer» `[(0,6),(0,0)]` `[(0,4),(0,0)]` `[(0,6),(0,4)]` `[(0,0),(0,0)]` ANSWER :D

Discussion

2164.	If the coefficient of x^(3) is 1140 in the expansion of (1+2x+kx^(2)), then the value of k is______.
Answer» ANSWER :A

Discussion

2165.	Find the order and degree (if defined) of the following differential equations. y' + 5y = 0
Answer» Solution :The HIGHEST ORDER DERIVATIVE in the differential equation is y. . Order of the differential equation = !, The degree of y. is 1. `therefore` The degree of the differential equation = 1.

Discussion

2166.	Find the angles between the pair of lines whose slopes are , sqrt3,-1 .
Answer» SOLUTION :LET `m_1=sqrt3,m_2=-1` `THEREFORE` `TANTHETA=(m_2-m_1)/(1+m_1m_2)=(-1-sqrt3)/(1-sqrt3)` =`((sqrt3+1)/(1+sqrt3))=(sqrt3+1)/(sqrt3-1)=tan75^@ ` `therefore` `theta=75^@`.

Discussion

2167.	int(3x)/(1+2x^(4)) dx
Answer» ANSWER :`3/(2sqrt2)tan^(-1)sqrt2x^(2)+C`

Discussion

2168.	If sum_(i=1)^(4)a_(i)^(2)x^(2)-2sum_(i=1)^(4)a_(i)a_(i+1)x+sum_(i=1)^(4)a_(i)^(2)+1) le 0, " where " a_(i) gt 0 and all are distinct. Then,
Answer» `a_(1)+a_(5) GT 2a_(3)` `SQRT(a_(1)a_(5))=a_(3)` `2/sqrt(a_(1)a_(4)) gt 1/a_(1)+1/a_(4)` `prod_(i=1)^(5)a_(i)=a_(3)^(5)` Answer :A::B::C

Discussion

2169.	The point P(alpha,alpha +1) will lie inside the triangle whose vertices are A(0,3), B(-2,0) and C(6,1) if
Answer» `alpha =- 1` `alpha =- (1)/(2)` `alpha = (1)/(2)` `-(6)/(7) lt alpha lt (3)/(2)` Solution :We have `A(0,3), B(-2,0)` and `C(6,1)` Equation of AC is `X +3y - 9 =0` Equation of BC is `x - 8y +2 = 0` `P (alpha, alpha +1)` lies on the line `y = x +1` whichcuts BC at `D(-(6)/(7),(1)/(7))` and AC at `E ((3)/(2),(5)/(2))` `:. alpha` must lie between `-(6)/(7)`and `(3)/(2)`.

Discussion

2170.	Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr.(hati-hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6
Answer» ANSWER :`THEREFORE VECR=(hati+2hatj-4hatk)+LAMBDA(-3hati+5hatj+4hatk)`

Discussion

2171.	Find the unit vector in the direction of the vector 2hati-2hatj+hatk.
Answer» Answer :`(2)/(3)hati-(2)/(3)hatj+(1)/(3)HATK`

Discussion

2172.	If sum_(i=1)^(15)x_(i)=45,A=sum_(i=1)^(15)(x_(i)-2)^(2) B=sum_(i=1)^(15)(x_(i)-3)^(2) and C=sum_(i=1)^(15)(x_(i)-5)^(2) then Statement 1: min(A,B,C)=A Statement 2: The sum of squares of deviations is least when taken from man.
Answer» Statement 1: is TRUE, Statement 2 is True , Statement 2 ISA correct explanation for statement 1 Statement 1 is True, Statement 2 is True Statement 2 is NOT a correct explanation for Statement 1 Statement 1 is True, Statement 2 is False Statement 1 is False, Statement 2 is True Solution :`sum_(i=1)^(n)(x_(i)-barx)^(2)` `implies "min" (A,B,C)=B`

Discussion

2173.	Express in polar form (mod-Amplitude form) -2 + 2isqrt3
Answer» ANSWER :B::C::D

Discussion

2174.	A slip of paper is given to a person A who marks it either with a plus sign or a minus sign. The probability of his writing a plus sign is 1//3. A passes the slip to B, who may either leave it alone or change the sign before passing it to C. Next C passes the slip to D after perhaps changing the sign. Finally D passes it to a refere after perhaps changing the sign. B,C,D each change the sign with probability 2//3. The probability that the referee observes a plus sign on the slip if it is known that A wrote a plus sign is
Answer» `14//27` `16//27` `13//27` `17//27` SOLUTION :`(c )` Let `E_(1)=` Event that `A` WROTE a plus SIGN `E_(1)=` Event that `B` wrote a plus sign `E=` Event that the REFEREE observes a plus sign. Given `P(E_(1))=(1)/(3)impliesP(E_(2))=(2)/(3)` `P(E//E_(1))=` PROBABILITY that none of `B`, `C`, `D` change sign `+` Probability that exactly two of `B,C,D` change sign `=(1)/(27)+3((1)/(3)xx(2)/(3)xx(2)/(3))=(13)/(27)` `P(E//E_(2))=` Probability that all of `B,c,d` change sign `+` Probability that exactly one of `B,C,D` changes sign ,brgt `=(8)/(27)+3((2)/(3)xx(1)/(3)xx(1)/(3))=(14)/(27)` `:.P(E_(1)//E)=(13)/(41)` (Using Bayes' Theorem)

Discussion

2175.	A slip of paper is given to a person A who marks it either with a plus sign or a minus sign. The probability of his writing a plus sign is 1//3. A passes the slip to B, who may either leave it alone or change the sign before passing it to C. Next C passes the slip to D after perhaps changing the sign. Finally D passes it to a refere after perhaps changing the sign. B,C,D each change the sign with probability 2//3. If the refree observes a plus sign on the slip then the probability that A originally wrote a plus sign is
Answer» `13//41` `19//27` `17//25` `21//37` Solution :`(a)` Let `E_(1)=` Event that `A` wrote a plus sign `E_(1)=` Event that `B` wrote a plus sign `E=` Event that the referee observes a plus sign. Given `P(E_(1))=(1)/(3)impliesP(E_(2))=(2)/(3)` `P(E//E_(1))=` Probability that none of `B`, `C`, `D` change sign `+` Probability that exactly two of `B,C,D` change sign `=(1)/(27)+3((1)/(3)XX(2)/(3)xx(2)/(3))=(13)/(27)` `P(E//E_(2))=` Probability that all of `B,c,d` change sign `+` Probability that exactly one of `B,C,D` changes sign ,brgt `=(8)/(27)+3((2)/(3)xx(1)/(3)xx(1)/(3))=(14)/(27)` `:.P(E_(1)//E)=(13)/(41)` (USING BAYES' Theorem)

Discussion

2176.	Match the following. {:( "I." C_0 + 3.C_1 + 5. C_2 + …...(2n + 1). C_n=,"a)" (n+1)2^(n)),( "II." 3. C_0+7. C_1 + 11. C_2 + ….+ (4n+3). C_n=,"b)" (2n+3)2^(n)),( "III." C_0 + 4. C_1 + 7. C_2 + …. (n+1) "terms" =, "c)" (2n+3) 2^(n-1)),( "IV." (3n+2)^(n) C_0 + (3n - 1) ^n C_1+ (3n-4)^n C_2 + .......+ (""^n C_n)=,"d)" (3n+4) 2^(n-1)):}
Answer» a, b, C, d d, c, b, a a, c, d, b d, a, b, c Answer :A

Discussion

2177.	Let abs(a)=sqrt(3), abs(b)=5, b*c=10, angle between b and c is equal to pi//3. If a is perpendicular to b times c, " then "abs(a times (b times c))=_________
Answer» ANSWER :30

Discussion

2178.	Let A, B, C be three events and barA, barB, barC be their corresponding complementary event. If the probabilities of events B, AnnBnnbarC and barA nnB nnbarC are (5)/(6),(1)/(2) and (1)/(4) respectively, then the probability of the event BnnC is
Answer» `(1)/(12)` `(1)/(4)` `(1)/(6)` `(1)/(3)` ANSWER :A

Discussion

2179.	What is the correct order of nitration of the following compounds? {:(C_(6)H_(5)CH_(3),C_(6)H_(6),C_(6)D_(6),C_(6)T_(6),C_(6)H_(5)Br,C_(6)H_(5)overset(+)NR_(3),C_(6)H_(5)NMe_(2)),("a","b"," c"," d","e","f","g"):}
Answer» `G GT a gt b gt c gt d gt e gt F` `g gt b gt c gt d gt e gt a gt f` `g gt a gt b = c = d gt e gt f` `g gt a gt b gt c = d gt e gt f` Solution :r.d.s of NITRATION does not involve (C-H) bond cleavage `:. C_(6)H_(6)=C_(6)D_(6)=C_(6)T_(6)`

Discussion

2180.	lim_(xto0) {(1)/(x3sqrt(8+x)-(1)/(2x))} is equal to
Answer» `(1)/(12)` `(-4)/(3)` `(-16)/(3)` `(-1)/(48)` ANSWER :D

Discussion

2181.	Amar and Bimal are two contestants for an election, probability that Amar will win is 1/4 and that Bimal will win the election is 1/5, then what is probability that either Amar or Bimal will win the election.
Answer» `13//20` `9//20` `11//20` NONE of these Answer :B

Discussion

2182.	Find the number of ways of forming a committee of 5 members out of 6 Indians and 5 Americans so that always the Indians will be in majority in the committee.
Answer» ANSWER :281

Discussion

2183.	The volume of the parallelepiped whose coterminous edges are represented by the vectors 8vec(b)xxvec(c),3vec(c)xxvec(a)and4vec(a)xxvec(b), where vec(a)=(1+sintheta)hat(i)+costhetahat(j)+sin2thetahat(k), vec(b)=sin(theta+(2pi)/(3))hat(i)+cos(theta+(2pi)/(3))hat(j)+sin(2theta+(4pi)/(3))hat(k), vec(c)=sin(theta-(2pi)/(3))hat(i)+cos(theta-(2pi)/(3))hat(j)+sin(2theta-(4pi)/(3))hat(k) is 18 cubic units, then the values of theta, in the interval (0,(pi)/(2))," is/are"
Answer» `(pi)/(9)` `(2PI)/(9)` `(pi)/(3)` `(4PI)/(9)` ANSWER :A::B::D

Discussion

2184.	If A+B+C+D= 2pi , " then " -4 cos""((A+B)/(2)) sin""((A+C)/(2)) cos""((A-D)/(2))=
Answer» `SIN A + sin B+ sin C-sin D ` `sin A - sin B + sin C - sin D ` `sin A + sin B + sin C + sin D ` `sin A - sin B +sin C + sin D ` ANSWER :B

Discussion

2185.	int(Inx)/x^5dx
Answer» Solution :`int(INX)/x^5dx=int1nx.x^-5dx` [TAKE 1n x as FIRST and `x^-5` as second function] =`1nx.x^-4/-4-int1/x.x^-4/-4dx` =`-(1n x)/(4x^4) +1/4intx^-5dx` =`-(1nx)/(4x^4)+1/4 x^-4/-4+C` =`-(1nx)/(4x^4)-1/(16x^4)+C`

Discussion

2186.	Correct order of indicated bond length is/are:
Answer» `CH_(2)OVERSET(a)=CH-O"Me" lt O_(2)N-CH_(2)overset(b)=CH-O"Me"` `CH_(3)CH_(2)ul(a)Cl lt CH_(2) =CH-CH_(2)ul(b)Cl` `CH_(3)-UNDERSET(O)underset(\|\|)CUL(a)OH lt CH_(3)-underset(O)underset(\|\|)Cul(b) O^(Ѳ)` Answer :A::B::C

Discussion

2187.	If a^(2)-3(b-\|d\|) lt 0 prove that f(x) = x^(3) + ax^(2) + bx +dsinx is an increasing function in the set of real number R.
Answer»

Discussion

2188.	If A, B and C are three sets such that A nn B=A nn C and AuuB=AuuC, then
Answer» A = C B = C `AnnB=Phi` 0 Answer :B

Discussion

2189.	If int(2x^(2)+5)/(x^(2)+a)dx=f(x), where f(x) is a polynomial or ratio of polynomials, then the number of possible value(s) of a isequal to
Answer» 0 1 2 3 Answer :C

Discussion

2190.	Find the value of k if the following equations have equal roots i) x^(2)–2(1+3k)x+7(3+2k)= 0 ii) x^(2) -15 - k(2x – 8) = 0 iii) (3k+1)x^(2)+2(k+1)x+k=0 iv) x^(2)+2(k+2)x+9k=0
Answer» Answer :i) `(-10)/(9)`, 2 ii) 3, 5 iii) `(-1)/(2)`, 1 IV) 1, 4

Discussion

2191.	Let P(n) be a statement such that truth of P(n)impliesthe truth of P(n + 1)[ n inN, then P(n) is true
Answer» `AA N GT 1` `AA n` Nothingcan besaid `AAn gt k`( k issomefixedpositiveinteger ) ANSWER :C

Discussion

2192.	Computethe shortestdistancebetweenthe lines vec(r )=(hat(i) -hat(j)) + lambda (2hat(i) -hat(k))" and" vec(r ) =(2hat(i) -hat(j))+ mu (hat(i) - hat(j) -hat(k)) Determinewhether theselinesintersect of not.
Answer» ANSWER :`SD =(SQRT(14))/(14) NE 0`the givenlinesdo notintersect

Discussion

2193.	Assertion (A) : The remainder of x^(3)+2x^(2)-5x-3 which is divided by x-2 is 3. Reason (R) : The remainder of the polynomial f(x) when divided by x-a is f(a)
Answer» Both A & R are TRUE and R is CORRECT EXPLANATION of A Both A & R are true and R is not correct explanation of A A is true but R is false A is false but R is true Answer :A

Discussion

2194.	Fundamental theorem of definite integral : int_(a)^(b)(logx)/(x)dx=...... (where a binR^(+) )
Answer» `(1)/(2)LOGAB` `LOG((b)/(a))` `2log((b)/(a))` `(1)/(2)log(AB)log((b)/(a))` Answer :D

Discussion

2195.	Determine the truth of falsity of the{1,2} in {1,2,3} propositions with reasons.
Answer» SOLUTION :`{1,2} in {1,2,3}` is FALSE, as {1,2} is not an ELEMENT of {1,2,3} but it is a SUBSET.

Discussion

2196.	In a bivariate distribution the regression equation of y on x is 8x – 10y + 66 = 0. If barx= 13, find bary
Answer» ANSWER :`bary=17`

Discussion

2197.	Show that a function p is a polynomial function is continuous.
Answer» <P> ANSWER :HENCE, p is a CONTINUOUS FUNCTION.

Discussion

2198.	Line L has intercepts a and b on the axes of co ordinates. When the axes are rotatedthrough a givenn angle, keeping the origin fixed, the straight line L has intercpets p and q on the transformed axes. Prove that1/(a^(2))+1/(b^(2))=1/(p^(2))+1/(q^(2)).
Answer» SOLUTION :NA

Discussion

2199.	Contraction of muscles results from :-
Answer» A contraction of MYOSIN filaments. The SLIDING of the ACTIN over myosin. The formation of PEPTIDE bonds that link actin and myosin. Contraction of actin. Answer :A

Discussion

2200.	If three dice are thrown, the probability that they show the numbers in A.P.is
Answer» `(1)/(36)` `(1)/(12)` `(2)/(9)` `(5)/(18)` Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

Find the equation of the circle with centre C and radius r where C = (a,-b) , r= a+b

Definite integration as the limit of a sum : lim_(ntooo)(1)/(n)sum_(r=n+1)^(2n)log(1+(r)/(n))=.............

If f and g are not derivable at x_0then f+g is not derivable at x_0.

The radius of the circle which has the lines x+y-1=0, x+y-9=0 as tangents is

Let I_(n)=int_(0)^(pi//4) tan^(n)x dx. Statement-1: (1)/(n+1)lt 2I_(n) lt (1)/(n-1) for all n=2,3,4,….. Statement-2: I_(n)+I_(n-2)=(1)/(n-1),n=3,4,5,…...

For a normal distribution if the mean is M, mode is M_(0) and median is M_(d), then

Show that the relation R in the set {1,2,3} given by R = {(1,2),(2,1)} is symmetric but neither reflexive nor transitive.

(cos 13^(@) - sin 13^(@))/(cos 13^(@) + sin 13^(@)) + (1)/(cot 148^(@)) is equal to

If the equation (x + m)^(2) - (x + n)^(2) = ( m - n)^(2) where m , n are non- zero constants and m^(2) ne n^(2) , satisfied by x = pm + pn , then the ordered pair (p , q) is equal to

The sum of two numbers is 13, and their product is 30. What is the sum of the squares of the two numbers?

State with reason,"Collection of all residents of Odisha who will live for more than 100 years " is set or not ?

Integrate the following functions : int(2x+5)/(x^(2)+5x+9)dx

Let A=[(0,2),(0,3)] and B=[(2,3),(0,0)], then AB equals :

If the coefficient of x^(3) is 1140 in the expansion of (1+2x+kx^(2)), then the value of k is______.

Find the order and degree (if defined) of the following differential equations. y' + 5y = 0

Find the angles between the pair of lines whose slopes are , sqrt3,-1 .

int(3x)/(1+2x^(4)) dx

If sum_(i=1)^(4)a_(i)^(2)x^(2)-2sum_(i=1)^(4)a_(i)a_(i+1)x+sum_(i=1)^(4)a_(i)^(2)+1) le 0, " where " a_(i) gt 0 and all are distinct. Then,

The point P(alpha,alpha +1) will lie inside the triangle whose vertices are A(0,3), B(-2,0) and C(6,1) if

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr.(hati-hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6

Find the unit vector in the direction of the vector 2hati-2hatj+hatk.

If sum_(i=1)^(15)x_(i)=45,A=sum_(i=1)^(15)(x_(i)-2)^(2) B=sum_(i=1)^(15)(x_(i)-3)^(2) and C=sum_(i=1)^(15)(x_(i)-5)^(2) then Statement 1: min(A,B,C)=A Statement 2: The sum of squares of deviations is least when taken from man.

Express in polar form (mod-Amplitude form) -2 + 2isqrt3

Let abs(a)=sqrt(3), abs(b)=5, b*c=10, angle between b and c is equal to pi//3. If a is perpendicular to b times c, " then "abs(a times (b times c))=_________

Let A, B, C be three events and barA, barB, barC be their corresponding complementary event. If the probabilities of events B, AnnBnnbarC and barA nnB nnbarC are (5)/(6),(1)/(2) and (1)/(4) respectively, then the probability of the event BnnC is

What is the correct order of nitration of the following compounds? {:(C_(6)H_(5)CH_(3),C_(6)H_(6),C_(6)D_(6),C_(6)T_(6),C_(6)H_(5)Br,C_(6)H_(5)overset(+)NR_(3),C_(6)H_(5)NMe_(2)),("a","b"," c"," d","e","f","g"):}

lim_(xto0) {(1)/(x3sqrt(8+x)-(1)/(2x))} is equal to

Amar and Bimal are two contestants for an election, probability that Amar will win is 1/4 and that Bimal will win the election is 1/5, then what is probability that either Amar or Bimal will win the election.

Find the number of ways of forming a committee of 5 members out of 6 Indians and 5 Americans so that always the Indians will be in majority in the committee.

If A+B+C+D= 2pi , " then " -4 cos""((A+B)/(2)) sin""((A+C)/(2)) cos""((A-D)/(2))=

int(Inx)/x^5dx

Correct order of indicated bond length is/are:

If a^(2)-3(b-|d|) lt 0 prove that f(x) = x^(3) + ax^(2) + bx +dsinx is an increasing function in the set of real number R.

If A, B and C are three sets such that A nn B=A nn C and AuuB=AuuC, then

If int(2x^(2)+5)/(x^(2)+a)dx=f(x), where f(x) is a polynomial or ratio of polynomials, then the number of possible value(s) of a isequal to

Find the value of k if the following equations have equal roots i) x^(2)–2(1+3k)x+7(3+2k)= 0 ii) x^(2) -15 - k(2x – 8) = 0 iii) (3k+1)x^(2)+2(k+1)x+k=0 iv) x^(2)+2(k+2)x+9k=0

Let P(n) be a statement such that truth of P(n)impliesthe truth of P(n + 1)[ n inN, then P(n) is true

Computethe shortestdistancebetweenthe lines vec(r )=(hat(i) -hat(j)) + lambda (2hat(i) -hat(k))" and" vec(r ) =(2hat(i) -hat(j))+ mu (hat(i) - hat(j) -hat(k)) Determinewhether theselinesintersect of not.

Assertion (A) : The remainder of x^(3)+2x^(2)-5x-3 which is divided by x-2 is 3. Reason (R) : The remainder of the polynomial f(x) when divided by x-a is f(a)

Fundamental theorem of definite integral : int_(a)^(b)(logx)/(x)dx=...... (where a binR^(+) )

Determine the truth of falsity of the{1,2} in {1,2,3} propositions with reasons.

In a bivariate distribution the regression equation of y on x is 8x – 10y + 66 = 0. If barx= 13, find bary

Show that a function p is a polynomial function is continuous.

Line L has intercepts a and b on the axes of co ordinates. When the axes are rotatedthrough a givenn angle, keeping the origin fixed, the straight line L has intercpets p and q on the transformed axes. Prove that1/(a^(2))+1/(b^(2))=1/(p^(2))+1/(q^(2)).

Contraction of muscles results from :-

If three dice are thrown, the probability that they show the numbers in A.P.is