28278 + Interview Questions in Maths in Class 12 Page 23 InterviewSolution

1101.	The vector equationm of the line (x-5)/(3)=(y+4)/(7)=(z-6)/(2) is
Answer» `barr=3hati-7hatj-2hatk+lambda(5hati-4hatj+6hatk)` `barr=5hati+4hatj+6hatk+lambda(3hati-7hatj+2hatk)` `barr=3hati+7hatj+2hatk+lambda(5hati-4hatj+6hatk)` `barr=5hati-4hatj+6hatk+lambda(3hati+7hatj+2hatk)` ANSWER :D

Discussion

1102.	For the LPP Min z=x_(1)+x_(2) such that inequalities 5x_(1)+10x_(2)ge0,x_(1)+x_(2)le1,x_(2)le4 and x-_(1),x_(2)ge0
Answer» There is a baunded SOLUTION THEREIS no solution There are INFINITE solutions None of the above Solution :

Discussion

1103.	A has 3 shares in a lottery where there are 3 prizes and 6 blanks, B has one share in another, where there is but 1 prize and 2 blanks. Show that A has a better chance of winning a prize than B, in the ratio of 16 to 7.
Answer» ANSWER :HENCE A has a BETTER chance of winning a prize than B.

Discussion

1104.	Show that the equation of the common tangent to the circle x^(2) + y^(2) =2a^(2) and the parabola y^(2) = 8ax is y= pm ( x +2 a)
Answer» Answer :The EQUATION of the COMMON TANGENT (1) & (2) are `y = pm x pm 2a rArr y= pm ( x+2a)`

Discussion

1105.	According to Newton's law of cooling, the body cools from 100^(@)Cto60^(@)C in 20 minutes. The temperature of the surrounding being 20^(@)C The body cool down to 30^(@)C in
Answer» 40 minutes 50 minutes 90 minutes 60 minutes Answer :D

Discussion

1106.	If veca and vecb are unit vectors such that vecaxxvecb is a unit vector, then the angle between veca and vecb is ____
Answer» of any MEASURE `PI/4` `pi/2` `pi` ANSWER :C

Discussion

1107.	Differentiate from definitione^(3x)
Answer» Solution :LET `y=e^(3X)` `lim_(deltaxto0)(e^(3x)(e^(3delta)-1))/(DELTAX)` `=lim_(deltaxto0)e^(3x).3.(e^(3delta)-1)/(3deltax)` `3e^(3x).`lim_(deltaxto0)(e^(3delta)-1)/(3deltax)`=3e^(3x)` [`thereforelim_(thetato0)(e^theta-1)/theta=1`

Discussion

1108.	Determine the truth of falsity of thea in {(a)} propositions with reasons.
Answer» SOLUTION :`a in{{a}}`.It is FALSE as .a. is not an ELEMENT of the SET {(a)}.

Discussion

1109.	int_(1)^(e) ((ln x )^(3))/(x) dx=
Answer» `1/2` `1/3` `1/4` 1 Answer :C

Discussion

1110.	Integrate the following functions. int(dx)/(2+3cosx)
Answer» ANSWER :`(1)/(sqrt5)log\|(sqrt5+tan""(x)/(2))/(sqrt5-tan""(x)/(2))\|+C`

Discussion

1111.	Cards are drawn from pack of 52 cards one by one with replacement. Find the probability that exactly 10 cards will be drawn before the first ace.
Answer» ANSWER :`(12^(9))/(13^(10))`

Discussion

1112.	Normals are drawn from the external point (h,k) to the rectangular hyperbola xy=c^(2). If circle are drawn through the feet of these normals taken three at a time then centre of circle lies on another hyperbola whose centre and eccentricity is
Answer» `(h/2, k/2)` `(h,k)` `SQRT(2)` `sqrt(2)+1` Solution :EQUATION of normal to hyperbola `xy=c^(2)` at `(ct, c/t)` which passes through `(h,k)` is `ct^(4)-ht^(3)+kt-c=0` Roots of this equation is `t_(1),t_(2),t_(3)` and `t_(4)` Let equation of circle be `x^(2)+y^(2)-2gx-2fy+p=0` If `(ct, c/t)` lies on this `c^(2)t^(4)-2gct^(3)+pt^(2)-2fct+c^(2)=0` It roots are `t_(1), t_(2), t_(3)` and `t_(4)` We get `t_(4)=-t_(4)` also `c/(t_(4))-c/(t_(4))=k-2f` So locus of centre is `4C^(2)=(h-2g)(k-2f)` Centre lies on hyperbola `(x-h/2)(y-k/2)=c^(2)` `c(h/2,k/2)` and `c=sqrt(2)`

Discussion

1113.	Negation of pharr q is
Answer» <P>`(p ^^ Q) VV (p ^^ q)` `(p ^^ ~q) vv (q ^^ ~p)` `(~p ^^ q) vv (q ^^ p)` `(p ^^ q) vv (~q ^^ p)` ANSWER :B

Discussion

1114.	If A,B are two events such that P(A)=0.3, P(B)=0.4,P(AcupB)=0.6 Find P(B \| A^c)
Answer» <P> SOLUTION :`P(B\|A^c)=(P(B capA^c))/(P(A^c))=(P(B-A))/(1-P(A))=(P(B)-P(ACAPB))/(1-0.3)=(0.4-0.1)/0.7=0.3/0.7=3/7`

Discussion

1115.	Solvetheequationx^3 -6x^2+7x+2=0onerootbeing2 + sqrt(5)
Answer» ANSWER :`2,2 +-SQRT(5)`

Discussion

1116.	(1+isqrt3)^(9)=
Answer» `-2^6` `-2^8` `-2^9` `-2^(12)` ANSWER :C

Discussion

1117.	The value of [a-b b-c c-a] is equal to
Answer» 0 1 2 3 Solution :`[(a-b,b-C,c-a)]` `={(a-b)XX(b-c)}.(c-a)` `=(AXXB-axxc-bxxb+bxxc).(c-a)` `=(axxb+cxxa+bxxc).(c-a)` `=(axxb).c-(bxxc).a` `=[ABC]-[abc]=0`

Discussion

1118.	Find the integrals of the functions sin x sin 2x sin 3x
Answer» ANSWER :`pi/2log1/2`

Discussion

1119.	Find the derivative of sqrt(x)+sqrt(y) = 9 " at "(4,9).
Answer» ANSWER :`(-3)/(2)`

Discussion

1120.	Match the items given in List-I with those of the items of List - II The correct answer is
Answer» `{:(A,B,C,D),("(v)","(III)","(i)","(II)"):}` `{:(A,B,C,D),("(iv)","(ii)","(i)","(iii)"):}` `{:(A,B,C,D),("(iv)","(i)","(ii)","(iii)"):}` `{:(A,B,C,D),("(i)","(iii)","(iv)","(ii)"):}` Answer :C

Discussion

1121.	Solve system of linear equations , using matrix method if exists 5x-7=2 7x-5y=3
Answer» ANSWER :`X=(9/5),y=(48/25)'

Discussion

1122.	Prove that if the sequence {a_n//b_n} {b_n gt 0} is monotonic, then the sequence. {(a_(1)+a_(2)+.....+a_(n))/(b_1+b_2+.....+b_n)} will also be monotonic.
Answer» Answer :If the SEQUENCES `a_n/b_n` INCREASES, then `a_i/b_i LT (a_(N+1))/(a_(n+1)) ie, b_(n+1) a_(i) lt a_(n+1) b(i=,2,...n)`

Discussion

1123.	Let f(x) bedifferentiablefunction and g(x) be twicedifferentiableZeros of f(x) ,g(x) be a,b respectively (a ltb) Showthat there existsat leat one rootof requation f(x) g(x) +f(x) g''(x) =0 on (a,b)
Answer»

Discussion

1124.	If x = (1 ^(2))/(1) =+ (2 ^(2))/( 3) + (3 ^(2))/( 5) +.....+ (1001 ^(2))/( 2001) , y = (1^(2))/(3) + (2 ^(2))/( 5) + (3 ^(2))/(7) + .....+ (1001 ^(2))/(2003),then([x -y])/(10) is equal to where [.] denotes greatest integer function)
Answer» ANSWER :50

Discussion

1125.	Two events A and B will be independent, if
Answer» <P>A and B are MUTUALLY EXCLUSIVE `P(A^(')B^('))=[1-P(A)][1-P(B)]` P(A) = P(B) P(A) + P(B) = 1 Answer :B

Discussion

1126.	Let A and B be events with P(A)= 3/8, P(B)= 1/2 andP(A cap B) = 1/4,Find P(A^c cap B^c)
Answer» <P> ANSWER :`P(A)=3/8,P(B)=1/2,P(ACAPB)=1/4` `P(A^CcapB^C)=P(ACUPB)^C=1-(AcupB)` `1-5/8=3/8`

Discussion

1127.	If equation of plane passing through (2,1,3),(3,2,1)and(1,3,2) is ax+by+cz=1 then a+b+c is equal to _________
Answer» ANSWER :`0.50`

Discussion

1128.	A cubical die is thrown. Find the Mean and variance of X, giving the number on the face that shows up.
Answer» ANSWER :`=(35)/(12)`

Discussion

1129.	The straight lines x + y = 0, 3x + y = 4, x + 3y – 4 = 0 form a triangle which is
Answer» isosceles equilateral right angled obtuse angled Answer :A

Discussion

1130.	Solve sqrt(2x+1)+sqrt(3x+2)=sqrt(5x+3)
Answer» ANSWER :`X= -1 // 2`

Discussion

1131.	Considera triangle ABC such that cotA+cotB+cotC=cot theta. Now answer the following : Q.The possible value of theta is :
Answer» `60^(@)` `25^(@)` `35^(@)` `45^(@)` Answer :B

Discussion

1132.	Consider the sequence 4,4,8,0,2,2,4,6,0,….. where the nth term is the units place of the sum of the previous two terms for n ge 3. If S _(n) is the sum to n terms of this sequence then the smallest 'n' for which S _(n) gt 2010 is:
Answer» ANSWER :503

Discussion

1133.	The values of {:("=-"),(z+z):} is …………….. .
Answer» `2 Re (Z)` `Re(z)` `IM(z)` `2Im(z)` ANSWER :A

Discussion

1134.	Show that -a is the inverse of a for the addition opertion '+' on R and 1/a is the inverse of a ne 0 for the multiplication opertion 'x' on R.
Answer» ANSWER :`1/a`

Discussion

1135.	Of the students in a college,. it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hosteler?
Answer» ANSWER :`(9)/(13)`

Discussion

1136.	Find all the integral values of a for which the quadratic equation (x - a) (x - 10) + 1 = 0 has integral roots.
Answer» ANSWER :a=12,8

Discussion

1137.	If the area enclosed by y^(2)=2x and x^(2)+4+4x=4y^(2) is k square units, then the value of 3k is equal to
Answer» ANSWER :4

Discussion

1138.	The vector equation of the line passing through (2, 1, -1) and parallel to hati+2hatj+hatk is
Answer» `barr=hati+2hatj+hatk+lambda(2hati+hatj-hatk)` `barr=2hati+hatj-hatk+lambda(hati+2hatj+hatk)` `barr=-hati-2hatj-hatk+lambda(-2hati-hatj+hatk)` `barr=-2hati-hatj+hatk+lambda(-hati-2hatj-hatk)` ANSWER :B

Discussion

1139.	Ifz=re^(itheta), then \|e^(iz)\|is equal to
Answer» `E^(-rcostheta)` `e^(rcostheta)` `e^(rsintheta)` `e^(-rsintheta)` SOLUTION :`because z=re^(itheta)=R(costheta+isintheta)` `IMPLIES IZ=r(-sintheta+icostheta)` `=e^(iz)=e^(-rsintheta).e^(ircostheta)` `implies\|e^(iz)\|=e^(-rsintheta)`

Discussion

1140.	A circle passes through the points (3,4) and cuts the circlex^(2) + y^(2) = a^(2) orthogonally, the locus of its centre is a straight line . If the distance of this straight line from the origin is 25 , thena^(2) =
Answer» 250 225 100 25 Answer :B

Discussion

1141.	if f, g, andh aredifferentiablefunction of x and Delta (x)=\|{:(f,,g,,h),((xf)',,(xg)',,(xh)'),((x^(2)f)'',,(x^(2) g)'',,(x^(2)h)''):}\| " prove that" Delta (x)=\|{:(f,,g,,h),(f',,g,,h),((x^(3)f'')',,(x^(3) g'')',,(x^(3)h'')'):}\| " where prime"(') denotes thederivatives .
Answer» Solution :` (xf) =xf' +f "and " (X^(2)f)''` `=[2xf+ x^(2) f]'` ` =2f +4xf'+ x^(2) f''` `rArr Delta =\| {:( f,,g,,h),(xf+f,,xg'+g,,XH'+h),(2f+4xf+x^(2)f'',,2g+4xg'+x^(2)g'',,2h+4xh+x^(2)h''):}\| ` `R_(2) to R_(2) -R_(1) " ANDTHEN " R_(3) toR_(3) -4R_(2) -2R_(1)` `rArr Delta = \|{:(f,,g,,h),(xf,,xg,,xh),(x^(2)f,,x^(2)g,,x^(2)h):}\|` `Delta = \|{:(f,,g,,h),(xf,,xg,,xh),(x^(3)f,,x^(3)g,,x^(3)h):}\|` `rArr (dDelta)/(dx) = \|{:(f',,g',,h'),(f',,g',,h'),(x^(3)f'',,x^(3)g'',,x^(3) h''):}\|+\|{:(f,,g,,h),(f'',,g'',,h''),(x^(3)f'',,x^(3)g'',,x^(3)h''):}\|` `+\|{:(f,,g,,h),(f',,g',,h'),((x^(3)f'')',,(x^(3)g'')',,(x^(3)h'')'):}\|` `=0+0+ \|{:(f,,g,,h),(f',,g',,h'),((x^(3)f'')',,(x^(3)g'')',,(x^(3)h'')'):}\|`

Discussion

1142.	If S_(n) denotes the sum of n terms of an A.P., S_(n +3) - 3S_(n + 2) + 3S_(n + 1) - S_(n) =
Answer» 3 1 `1/2` 0

Discussion

1143.	State which of the following matrices is symmetric,slew symmetric, both or not either: [[1,0,3],[0,-1,2],[3,2,1]]
Answer» SOLUTION :SYMMETRIC

Discussion

1144.	If the complex number A(z_(1)),B(z_(2)) and origin forms an isosceles triangle such thatangle(AOB) = (2pi)/3 ,then (z_(1)^(2)+z_(2)^(2) +4z_(1)z_(2))/(z_(1)z_(2)) equals ________
Answer» ANSWER :3

Discussion

1145.	lim_(x -> infty) [sqrt(x^(2) +ax +b)-x](a lt 0 lt b)
Answer» depends on both a NAD b depends only on b depends only on a does not DEPEND on a and b ANSWER :C

Discussion

1146.	sin2theta+(1)/(3)sin^(3)2theta+(1)/(5)sin^(5)2theta+....=
Answer» `log[TAN((pi)/(4)+theta)]` `log[cot((pi)/(4)+theta)]` `log tan theta` `log cot theta` ANSWER :A

Discussion

1147.	If the 7^(th) term of a H.P is (1)/(10) and the 12^(th) term is (1)/(25), then the 20^(th) term is
Answer» `(1)/(37)` `(1)/(41)` `(1)/(45)` `(1)/(49)` ANSWER :D

Discussion

1148.	a xx [a xx (a xx b)] =
Answer» `a^(2) (a XX B)` `a^(2) (b xx a)` `-a^(2) (b xx a)` `a. (b xx a)` ANSWER :B

Discussion

1149.	Find (d^(2)y)/(dx^(2)), if y= x^(3)+ tan x.
Answer» ANSWER :`= 6x+2 SEC^(2)X TAN x`.

Discussion

1150.	int (dx)/sqrt(1+4x^(2)).
Answer» ANSWER :`1/2logabs(2x+sqrt(1+4x^(2)))+C`

Discussion

Explore topic-wise InterviewSolutions in .

The vector equationm of the line (x-5)/(3)=(y+4)/(7)=(z-6)/(2) is

For the LPP Min z=x_(1)+x_(2) such that inequalities 5x_(1)+10x_(2)ge0,x_(1)+x_(2)le1,x_(2)le4 and x-_(1),x_(2)ge0

A has 3 shares in a lottery where there are 3 prizes and 6 blanks, B has one share in another, where there is but 1 prize and 2 blanks. Show that A has a better chance of winning a prize than B, in the ratio of 16 to 7.

Show that the equation of the common tangent to the circle x^(2) + y^(2) =2a^(2) and the parabola y^(2) = 8ax is y= pm ( x +2 a)

According to Newton's law of cooling, the body cools from 100^(@)Cto60^(@)C in 20 minutes. The temperature of the surrounding being 20^(@)C The body cool down to 30^(@)C in

If veca and vecb are unit vectors such that vecaxxvecb is a unit vector, then the angle between veca and vecb is ____

Differentiate from definitione^(3x)

Determine the truth of falsity of thea in {(a)} propositions with reasons.

int_(1)^(e) ((ln x )^(3))/(x) dx=

Integrate the following functions. int(dx)/(2+3cosx)

Cards are drawn from pack of 52 cards one by one with replacement. Find the probability that exactly 10 cards will be drawn before the first ace.

Normals are drawn from the external point (h,k) to the rectangular hyperbola xy=c^(2). If circle are drawn through the feet of these normals taken three at a time then centre of circle lies on another hyperbola whose centre and eccentricity is

Negation of pharr q is

If A,B are two events such that P(A)=0.3, P(B)=0.4,P(AcupB)=0.6 Find P(B | A^c)

Solvetheequationx^3 -6x^2+7x+2=0onerootbeing2 + sqrt(5)

(1+isqrt3)^(9)=

The value of [a-b b-c c-a] is equal to

Find the integrals of the functions sin x sin 2x sin 3x

Find the derivative of sqrt(x)+sqrt(y) = 9 " at "(4,9).

Match the items given in List-I with those of the items of List - II The correct answer is

Solve system of linear equations , using matrix method if exists 5x-7=2 7x-5y=3

Prove that if the sequence {a_n//b_n} {b_n gt 0} is monotonic, then the sequence. {(a_(1)+a_(2)+.....+a_(n))/(b_1+b_2+.....+b_n)} will also be monotonic.

Let f(x) bedifferentiablefunction and g(x) be twicedifferentiableZeros of f(x) ,g(x) be a,b respectively (a ltb) Showthat there existsat leat one rootof requation f(x) g(x) +f(x) g''(x) =0 on (a,b)

If x = (1 ^(2))/(1) =+ (2 ^(2))/( 3) + (3 ^(2))/( 5) +.....+ (1001 ^(2))/( 2001) , y = (1^(2))/(3) + (2 ^(2))/( 5) + (3 ^(2))/(7) + .....+ (1001 ^(2))/(2003),then([x -y])/(10) is equal to where [.] denotes greatest integer function)

Two events A and B will be independent, if

Let A and B be events with P(A)= 3/8, P(B)= 1/2 andP(A cap B) = 1/4,Find P(A^c cap B^c)

If equation of plane passing through (2,1,3),(3,2,1)and(1,3,2) is ax+by+cz=1 then a+b+c is equal to _________

A cubical die is thrown. Find the Mean and variance of X, giving the number on the face that shows up.

The straight lines x + y = 0, 3x + y = 4,﻿ x + 3y – 4 = 0 form a triangle which is﻿

Solve sqrt(2x+1)+sqrt(3x+2)=sqrt(5x+3)

Considera triangle ABC such that cotA+cotB+cotC=cot theta. Now answer the following : Q.The possible value of theta is :

Consider the sequence 4,4,8,0,2,2,4,6,0,….. where the nth term is the units place of the sum of the previous two terms for n ge 3. If S _(n) is the sum to n terms of this sequence then the smallest 'n' for which S _(n) gt 2010 is:

The values of {:("=-"),(z+z):} is …………….. .

Show that -a is the inverse of a for the addition opertion '+' on R and 1/a is the inverse of a ne 0 for the multiplication opertion 'x' on R.

Find all the integral values of a for which the quadratic equation (x - a) (x - 10) + 1 = 0 has integral roots.

If the area enclosed by y^(2)=2x and x^(2)+4+4x=4y^(2) is k square units, then the value of 3k is equal to

The vector equation of the line passing through (2, 1, -1) and parallel to hati+2hatj+hatk is

Ifz=re^(itheta), then |e^(iz)|is equal to

A circle passes through the points (3,4) and cuts the circlex^(2) + y^(2) = a^(2) orthogonally, the locus of its centre is a straight line . If the distance of this straight line from the origin is 25 , thena^(2) =

if f, g, andh aredifferentiablefunction of x and Delta (x)=|{:(f,,g,,h),((xf)',,(xg)',,(xh)'),((x^(2)f)'',,(x^(2) g)'',,(x^(2)h)''):}| " prove that" Delta (x)=|{:(f,,g,,h),(f',,g,,h),((x^(3)f'')',,(x^(3) g'')',,(x^(3)h'')'):}| " where prime"(') denotes thederivatives .

If S_(n) denotes the sum of n terms of an A.P., S_(n +3) - 3S_(n + 2) + 3S_(n + 1) - S_(n) =

State which of the following matrices is symmetric,slew symmetric, both or not either: [[1,0,3],[0,-1,2],[3,2,1]]

If the complex number A(z_(1)),B(z_(2)) and origin forms an isosceles triangle such thatangle(AOB) = (2pi)/3 ,then (z_(1)^(2)+z_(2)^(2) +4z_(1)z_(2))/(z_(1)z_(2)) equals ________

lim_(x -> infty) [sqrt(x^(2) +ax +b)-x](a lt 0 lt b)

sin2theta+(1)/(3)sin^(3)2theta+(1)/(5)sin^(5)2theta+....=

If the 7^(th) term of a H.P is (1)/(10) and the 12^(th) term is (1)/(25), then the 20^(th) term is

a xx [a xx (a xx b)] =

Find (d^(2)y)/(dx^(2)), if y= x^(3)+ tan x.

int (dx)/sqrt(1+4x^(2)).

The straight lines x + y = 0, 3x + y = 4, x + 3y – 4 = 0 form a triangle which is