28278 + Interview Questions in Maths in Class 12 Page 185 InterviewSolution

9201.	Which of the following reagents or process are suitable to distinguish MeOH & EtOH ?
Answer» `NAOI` anhydrous `ZnCl_(2)+conc.HCl` Victor Mayor's process Solution :ETOH GIVES + ve test with NaOI (i.e. haloform) but not `CH_(3)OH`. Only MeOH gives + ve test with SALICYLIC acid and form winter oil green.

Discussion

9202.	Integrate the following intx(sqrt(x^2+3)dx (x^2+3=v)
Answer» SOLUTION :`intxsqrt(x^2+3)DX` [PUT`x^2+3=r^2`then 2xdx=2tdt or xdx=tdt] `intsqrt(t^2)tcdot t =intt^2dt=(1/3)t^3+C` `(1/3)(x^2+3)^(3/2)+C`

Discussion

9203.	If x_1,x_2,x_3 are three non-zero real numbers such that(x_1^(2) +x_2^(2)) (x_2^(2) +x_3^(2)) le (x_1x_2+x_2x_3)^(2)then the G.M.Of x_1 ,x_2 ,x_3 is
Answer» `x_1` ` x_2` ` x_3` ` (x_1x_2x_3)/( 3)` ANSWER :B

Discussion

9204.	underset(x to 0+)"Lt" [x] sin"" 1/x=
Answer» 0 1 `-1` does not exist Answer :A

Discussion

9205.	Integration by partial fraction : int(3sinx+2 cosx)/(3 cosx+ 2 sinx)dx=...
Answer» `(12)/(13)x-(5)/(13)LOG(3 cosx+2 sinx)` `(12)/(13)x+(5)/(13)log(3 cosx+2 sinx)` `(13)/(12)x+(5)/(13)log(3 cosx+2 sinx)` None of these Answer :A

Discussion

9206.	Let alpha, beta , gamma be the roots of x^(3)+x+10=0. Write alpha_(1)=(alpha+beta)/(alpha^(2)),beta_(1)=(beta+gamma)/(alpha^(2)), gamma_(1)=(gamma+alpha)/(beta^(2)). Then the value of (alpha_(1)^(3)+beta_(1)^(3)+gamma_(1)^(3))-(1)/(10)(alpha_(1)^(2)+beta_(1)^(2)+gamma_(1)^(2)) is
Answer» `(1)/(10)` `1/5` `3/10` `1/2` ANSWER :C

Discussion

9207.	5 Indian and 5 Russian couples meet at a party and shake hands. The probability that no wife shakes hands with her husband and no Indian wife shakes hands with a male is
Answer» `23/38` `27/38` `9/19` `3/5` ANSWER :B

Discussion

9208.	int(3x^2)/(x^2+1)dx
Answer» SOLUTION :`INT(3x^2)/(x^2+1)DX` =`3int((x^2+1)-1)/(x^2-1)dx` =`3int{1-1/(x^2+1)}dx` =`3{x-tna^-1x}+C`

Discussion

9209.	Let A and B be sets. Show that f: A xxB rarr B xxA such that f(a,b) = (b,a) is bijecive function.
Answer» SOLUTION :N/A

Discussion

9210.	The locus of the point of intersection of two perpendicular tangents to the circle x^(2)+y^(2)=a^(2)is
Answer» `x^(2)+y^(2)=SQRT(2)a^(2)` `x^(2)+y^(2)=3A^(2)` `x^(2)+y^(2)=4a^(2)` `x^(2)+y^(2)=2A^(2)` Answer :D

Discussion

9211.	lim_(x rarr 0) ((1 + tan x)/(1 - tan x))^(1//x) is :
Answer» 0 1 `E^(2)` None of these ANSWER :C

Discussion

9212.	Evaluation of definite integrals by subsitiution and properties of its : g(x)=int_(0)^(x)f(t)dt where (1)/(2)lef(t)le1,tin[0,1] and 0lef(t)le(1)/(2),tin(1,2] then ………..
Answer» `-(3)/(2)LEG(2)lt(1)/(2)` `0leg(2)lt2` `(3)/(2)LTG(2)LE(5)/(2)` `2ltg(2)lt4` Answer :B

Discussion

9213.	Which of the following options is the only correct combination ?
Answer» <P>(IV)(i)(S) (II)(iii)(P) (III)(ii)(R ) (I)(i)(S) Answer :D

Discussion

9214.	Which of the following options is the only correct combination ?
Answer» (III)(i)(R ) (I)(iii)(Q) (IV)(II)(P) (II)(iii)(S) Answer :C

Discussion

9215.	Which of the following options is the only correct combination ?
Answer» (III)(iii)(Q) (I)(ii)(Q) (III)(IV)(P) (IV)(ii)(R ) ANSWER :A

Discussion

9216.	A: In a Delta ABC, Delta =a^2-(b-c)^2 then tan""A/2=1/2 R: In a Delta ABC, tan""A/2= Delta/((s-b)(s-c))
Answer» A is TRUE, R is true and R is CORRECT explanation of A A is true, R is true and R is not correct explanation of A A is true, R is false A is false, R is true Answer :D

Discussion

9217.	The sum of the series ""^20C_0 - ""^20C_1 + ""^20C_2 - ""^20C_3 +…….""^20C_10 is
Answer» `""^20C_10` `- (""^20C_10)` `1/2. (""^20C_10)` `0` ANSWER :C

Discussion

9218.	Let a, b, c in R and alpha, beta are the real roots of the equation ax2 + bx + c = 0 and if a + b + c < 0, a – b + c < 0 and c > 0 then [alpha] + [beta] is equal to (where [.] denotes the greatest integer function.)
Answer» 0 1 `-1` None Solution :`(ax-b)^2 + (bx-c)^2 + (cx-d)^2 lt 0` `b/a=c/b=d/c=x ""b^2=ac` 2 LOG 6 = log a + log c `\|{:(33,14,log a),(65,27,log b ),(97,40,log c):}\|to `APPLY `R_1 to R_1 + R_3 -2R_2` =0

Discussion

9219.	Derive the equation of a line space passing through two given points both in vector and cartesian form.
Answer» ANSWER :`(X-x_(1))/(x_(2)-x_(1))= (y-y_(1))/(y_(2)-y_(1))=(Z-z_(1))/(z_(2)-z_(1))`

Discussion

9220.	Prove that [hati""hatj""hatk]=1, Hence give geometric interpretation.
Answer» SOLUTION :N/A

Discussion

9221.	Define negative of a vector.
Answer» Answer :A VECTOR WHOSE magnitude is same as that of a GIVEN vector but direction is opposite to that of it is CALLED NEGATIVE of vector.

Discussion

9222.	((C_0 + C_1)(C_1 + C_2)(C_2 + C_3)………(C_(n-1) + C_n) )/(C_0C_1C_2…C_n)
Answer» `((N + 1)^n)/(n!)` `(n+1)/(n!)` `((n+1)^(n-1))/(n!)` `((n-1)^n)/(n!)` ANSWER :A

Discussion

9223.	Let barA, barB and barC be vectors of length 3, 4 and 5 respectively. Let barAbot(barB+barC).barb bot(barC+barA) and barCbot(barA+barB). Then (barA.barBxxbarC)/(barCxxbarA.barB)+(barB.barAxxbarC)/(barC.barAxxbarB)=…
Answer» `2SQRT2` `3SQRT3` `4sqrt2` `5sqrt2` ANSWER :D

Discussion

9224.	If f(x)=int(x^(2)dx)/((1+x^(2))(1+sqrt(1+x^(2)))) and f(0) = 0 then f(1) =
Answer» `log (1+sqrt(2))` `log(1+sqrt(2))-(PI)/(4)` `log(1+sqrt(2))+(pi)/(4)` `log(1+sqrt(2))+(pi)/(3)` ANSWER :2

Discussion

9225.	If A=[(1,5),(6,7)], the find A+A'
Answer» ANSWER :`[(2,11),(11,14)]`.

Discussion

9226.	If X follows binomial distribution with parameters n= 5, p and P(X=2)= 9 P(X=3) then p = ……….
Answer» ANSWER :`(1)/(10)`

Discussion

9227.	(i) int(x^(2) - 1/(x^(2)))^(3) dx , (ii) int(sqrt(x) -1/(sqrt(x))) dx (iii) int(sqrt(x) + 1/(sqrt(x)))^(2) dx , (iv) int((1+2x)^(3))/(x^(4)) (v) int((1+x)^(3))/(sqrt(x)) dx , (vi) int(2x^(2)+x-2)/((x-2)) dx
Answer» SOLUTION :N//A

Discussion

9228.	Let f:R rarr R defined by f(x)=cos^(-1)(-{-x}), where{x} denotes fractional part of x. Then, which of the following is/are correct?
Answer» f is MANY coe but not even function Eange of f contains TWO prime numbers f is a periodic Graph of f does not lie below x-axis ANSWER :A::B::D

Discussion

9229.	Let p,q,r in R satisfies [p q r][(1,8,7),(9,2,3),(7,7,7)] = [0 0 0] .....(i) {:(,"List-I",,"List-I"),((P),"If the point M(p.q.r) with reference to (i) lies on the curve" 2x+y+z=1 then (7p+q+r) "is equalto",(1),-2),((Q),"Let" omega(ne1) "cube root of unity with"lm(omega) gt0.If p=2 "with q and r satisfying" (i) then(3/(omega^(p))+1/(omega^(q))+3/(omega^(r))) "is equal to ",(2),7),((R),"Let q=6 with p and r satisfying"(i). ifalpha and beta"are roots of quadratic equation " px^(2)+qx+r=0 " then" Sigma_(n=0)^(oo) (1/(alpha)+1/(beta))^(n) " is equal to ",(3),6):}
Answer» Solution :(P) `p=1,Q=6,r=-7` `therefore (7p+q+r)=6` (Q) `OMEGA =(-1)/(2)+isqrt(3)/(2)` `p=2,q=12,r=-14` `implies(3)/(omega^(p))+(1)/(omega^(q))+(3)/(omega^(r))=(3)/(omega^(2))+(1)/(omega^(12))+(3)/(omega^(-14))` `= 3omega+1+3omega^(2)=-3+1=-2` (R ) `p=1,q=6,r=-7` `impliesx^(2)+6x-7=0` `OVERSET(^^^)(alpha beta)` `therefore (1)/(alpha)+(1)/(beta)=(alpha+beta)/(alphabeta)=(-6)/(-7)=(6)/(7)` `impliessum_(n-0)^(oo)` `((1)/(alpha)+(1)/(beta))^(n)=1+(6)/(7)+((6)/(7))^(2)+.....x` `=(1)/(1-(6)/(7))=7`

Discussion

9230.	The vector equation of the line passing through hati-hatj+3hatk and parallel to 3hati+2hatj-5hatk is
Answer» `barr=hati-hatj+3hatk+lambda(3hati+2hatj-5hatk)` `barr=3hati+2hatj-5hatk+lambda(hati-hatj+3hatk)` `barr=-hati+hatj-3hatk+lambda(-3hati-2hatj+5hatk)` `barr=-3hati-2hatj+5hatk+lambda(-hati+hatj-3hatk)` ANSWER :A

Discussion

9231.	Integrate the function (x+1)/(sqrt(x^(2)+2x+3))
Answer»

Discussion

9232.	Solution of the differential equation(2+ 2x ^(2)sqrty) ydx+(x ^(2) sqrty+2) x dy =0 is/are:
Answer» `XY ( X ^(2) sqrty +5 )=C` `xy (x ^(2) sqrty +3)=c` `xy (y ^(2) sqrtx+3)=c` `xy (y ^(2) sqrtx +5)=c` ANSWER :B

Discussion

9233.	If the line ax+by+c=0 touches both the parabolas y^(2)=-32y then the ascending order of a,b,c is
Answer» a,B,c b,c,a c,a,b b,a,c Answer :D

Discussion

9234.	If A and B are two events such that P(A\|B) =0.6 , P(B\|A)=0.3, P(A) = 0.1, then P(overlineA cup overlineB)=
Answer» 0.88 0.12 0.6 0.4 Answer :A

Discussion

9235.	IF 4hati+7hatj+8hatk,2hati+3hatj+4hatk,2hati+5hatj+7hatkare respectively the positions vectors of the vertices A,B,C of Delta ABC then the position vector of the point where the bisector of angle A meet BC is
Answer» `2hati+13/3hatj+2hatk` `2hati-13/3hatj+6hatk` `2hati+13hatj+6hatk` `2hati+13/3hatj+6hatk` ANSWER :D

Discussion

9236.	If the normals at P, Q, R on the rectangular hyperbola xy = c2 intersect at a point S on the hyperbola, then centroid of the triangle PQR is at
Answer» it MEETS the conjugate hyperbola in IMAGINARY points the conjugate diameter meets the GIVEN hyperbola in real points the conjugate diameter meets the conjugate hyperbolain imaginary points none of these Answer :B

Discussion

9237.	Find x, y and z if vectors xhati-2hatj+zhatk=2hati-yhatj+hatk
Answer» `2, 1, 2` `1, 2, 2` `1, 1, 2` `2, 2, 1` ANSWER :D

Discussion

9238.	Find the slope of the polar of (1, 3) with respect to the circle x^(2) + y^(2) - 4x - 4y = 0 Also find the distance fromthe centre to it.
Answer» ANSWER :` 1,6 SQRT2`

Discussion

9239.	If e and e' are the ecentricities of the ellipse 5x^(2)+9y^(2)=45 and the hyperboala 5x^(2)-4y^(2)=45 respectively, then ee' is equal to
Answer» 1 4 5 9 Answer :A

Discussion

9240.	There are n white and n black balls marked 1,2,3,………..n. The number of ways in which we can arrange theseballs in a row so that neighbouring balls are of different colours are:
Answer» `N!` `(2N)!` `2(n!)^(2)` `((2n)!)/((n!)^(2))` Solution :CASE I: `(W_(1))/1(B_(1))/2 (W_(2))/3 (B_(2))/4 (W_(3))/5 (B_(3))/6…………W_(n)(B_(n))/(2n^(th)"place")=n!xx!` CaseII `(B_(1))/1 (W_(1))/2(B_(2))/3(W_(2))/4(B_(3))/5 (W_(3))/6……….B_(n)(W_(n))/(2n^(th)"place")=n!xxn!` Son number of ways `=2(n!)^(2)`

Discussion

9241.	There are three units circles each of which is tangential to the other two.A triangle is drawn such that each side of the triangle is tangential to exactly two of the circles, then the perimeter of this triangle is
Answer» ANSWER :`16.39`

Discussion

9242.	Two students A and B are having 8 different books and 5 different books respectvely. In how many ways they can exchange the books.
Answer» ANSWER :`""^(m+c)C_m`

Discussion

9243.	Show that the function f : R todefined by f (x) = x^(3) + 3 is invertible. Find f^(-1). Hence find f^(-1)(30)
Answer» ANSWER :`F^(-1) : R to R` such that `f^(-1) (y) = (y - 1)^((1)/(3)) ; f^(-1) (30) = 3 `

Discussion

9244.	The mean and standard deviation of 20 items is found to be 10 and 2 respectively. At the time of checking it was found that one item 8 was incorrect. If it is replaced by 12, then find the mean and variance
Answer» 10.2, 4.01 10.1, 3.69 10.2, 3.96 10.2, 3.76 Answer :C

Discussion

9245.	Find the constant k so that the planes x - 2y + kz = 0, 2x + 5y-z = 0 are at right angles.
Answer»

Discussion

9246.	Ifveca xx vec b xx vec c ne 0 ,prove thatvec a +vec cis parallel tovec b.Hence express vec a + vec cin terms ofvec b.
Answer» ANSWER :` VEC a +vec C = LAMBDA vec B `

Discussion

9247.	The mean of the 'Sixes' in two tosses of an unbiased die is
Answer» `(1)/(3)` `(1)/(6)` `(2)/(3)` `(5)/(18)` Answer :A

Discussion

9248.	A circle passes through (-2,4) and touches the y-axis at (0,2). Which one of the following equations can represent a diameter of this circle
Answer» `2x-3y+10=0` `3x+4y-3=0` `4x+5y-6=0` `5x+2y+4=0` ANSWER :A

Discussion

9249.	How many numbers between 5000 and 10000 can be formed using the digits 1,2,3,4,5,6,7,8,9 each digit appearing not more than once in each number?
Answer» `5xx""^(8P_(3))` `5xx""^(8)C_(8)` `5!XX""^(8)P_(3)` `5xx""^(8)C_(3)xx3!` Answer :A::D

Discussion

9250.	Find the differential equation governing all the straight lines (x)/(a)+(y)/(b)=1, a ne 0, b ne 0.
Answer» SOLUTION :N/A

Discussion

Explore topic-wise InterviewSolutions in .

Which of the following reagents or process are suitable to distinguish MeOH & EtOH ?

Integrate the following intx(sqrt(x^2+3)dx (x^2+3=v)

If x_1,x_2,x_3 are three non-zero real numbers such that(x_1^(2) +x_2^(2)) (x_2^(2) +x_3^(2)) le (x_1x_2+x_2x_3)^(2)then the G.M.Of x_1 ,x_2 ,x_3 is

underset(x to 0+)"Lt" [x] sin"" 1/x=

Integration by partial fraction : int(3sinx+2 cosx)/(3 cosx+ 2 sinx)dx=...

Let alpha, beta , gamma be the roots of x^(3)+x+10=0. Write alpha_(1)=(alpha+beta)/(alpha^(2)),beta_(1)=(beta+gamma)/(alpha^(2)), gamma_(1)=(gamma+alpha)/(beta^(2)). Then the value of (alpha_(1)^(3)+beta_(1)^(3)+gamma_(1)^(3))-(1)/(10)(alpha_(1)^(2)+beta_(1)^(2)+gamma_(1)^(2)) is

5 Indian and 5 Russian couples meet at a party and shake hands. The probability that no wife shakes hands with her husband and no Indian wife shakes hands with a male is

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

Let A and B be sets. Show that f: A xxB rarr B xxA such that f(a,b) = (b,a) is bijecive function.

The locus of the point of intersection of two perpendicular tangents to the circle x^(2)+y^(2)=a^(2)is

lim_(x rarr 0) ((1 + tan x)/(1 - tan x))^(1//x) is :

Evaluation of definite integrals by subsitiution and properties of its : g(x)=int_(0)^(x)f(t)dt where (1)/(2)lef(t)le1,tin[0,1] and 0lef(t)le(1)/(2),tin(1,2] then ………..

Which of the following options is the only correct combination ?

Which of the following options is the only correct combination ?

Which of the following options is the only correct combination ?

A: In a Delta ABC, Delta =a^2-(b-c)^2 then tan""A/2=1/2 R: In a Delta ABC, tan""A/2= Delta/((s-b)(s-c))

The sum of the series ""^20C_0 - ""^20C_1 + ""^20C_2 - ""^20C_3 +…….""^20C_10 is

Let a, b, c in R and alpha, beta are the real roots of the equation ax​2 + bx + c = 0 and if a + b + c < 0, a – b + c < 0 and c > 0 then [alpha] + [beta] is equal to (where [.] denotes the greatest integer function.)

Derive the equation of a line space passing through two given points both in vector and cartesian form.

Prove that [hati""hatj""hatk]=1, Hence give geometric interpretation.

Define negative of a vector.

((C_0 + C_1)(C_1 + C_2)(C_2 + C_3)………(C_(n-1) + C_n) )/(C_0C_1C_2…C_n)

Let barA, barB and barC be vectors of length 3, 4 and 5 respectively. Let barAbot(barB+barC).barb bot(barC+barA) and barCbot(barA+barB). Then (barA.barBxxbarC)/(barCxxbarA.barB)+(barB.barAxxbarC)/(barC.barAxxbarB)=…

If f(x)=int(x^(2)dx)/((1+x^(2))(1+sqrt(1+x^(2)))) and f(0) = 0 then f(1) =

If A=[(1,5),(6,7)], the find A+A'

If X follows binomial distribution with parameters n= 5, p and P(X=2)= 9 P(X=3) then p = ……….

(i) int(x^(2) - 1/(x^(2)))^(3) dx , (ii) int(sqrt(x) -1/(sqrt(x))) dx (iii) int(sqrt(x) + 1/(sqrt(x)))^(2) dx , (iv) int((1+2x)^(3))/(x^(4)) (v) int((1+x)^(3))/(sqrt(x)) dx , (vi) int(2x^(2)+x-2)/((x-2)) dx

Let f:R rarr R defined by f(x)=cos^(-1)(-{-x}), where{x} denotes fractional part of x. Then, which of the following is/are correct?

The vector equation of the line passing through hati-hatj+3hatk and parallel to 3hati+2hatj-5hatk is

Integrate the function (x+1)/(sqrt(x^(2)+2x+3))

Solution of the differential equation(2+ 2x ^(2)sqrty) ydx+(x ^(2) sqrty+2) x dy =0 is/are:

If the line ax+by+c=0 touches both the parabolas y^(2)=-32y then the ascending order of a,b,c is

If A and B are two events such that P(A|B) =0.6 , P(B|A)=0.3, P(A) = 0.1, then P(overlineA cup overlineB)=

IF 4hati+7hatj+8hatk,2hati+3hatj+4hatk,2hati+5hatj+7hatkare respectively the positions vectors of the vertices A,B,C of Delta ABC then the position vector of the point where the bisector of angle A meet BC is

If the normals at P, Q, R on the rectangular hyperbola xy = c2 intersect at a point S on the hyperbola, then centroid of the triangle PQR is at

Find x, y and z if vectors xhati-2hatj+zhatk=2hati-yhatj+hatk

Find the slope of the polar of (1, 3) with respect to the circle x^(2) + y^(2) - 4x - 4y = 0 Also find the distance fromthe centre to it.

If e and e' are the ecentricities of the ellipse 5x^(2)+9y^(2)=45 and the hyperboala 5x^(2)-4y^(2)=45 respectively, then ee' is equal to

There are n white and n black balls marked 1,2,3,………..n. The number of ways in which we can arrange theseballs in a row so that neighbouring balls are of different colours are:

There are three units circles each of which is tangential to the other two.A triangle is drawn such that each side of the triangle is tangential to exactly two of the circles, then the perimeter of this triangle is

Two students A and B are having 8 different books and 5 different books respectvely. In how many ways they can exchange the books.

Show that the function f : R todefined by f (x) = x^(3) + 3 is invertible. Find f^(-1). Hence find f^(-1)(30)

The mean and standard deviation of 20 items is found to be 10 and 2 respectively. At the time of checking it was found that one item 8 was incorrect. If it is replaced by 12, then find the mean and variance

Find the constant k so that the planes x - 2y + kz = 0, 2x + 5y-z = 0 are at right angles.

Ifveca xx vec b xx vec c ne 0 ,prove thatvec a +vec cis parallel tovec b.Hence express vec a + vec cin terms ofvec b.

The mean of the 'Sixes' in two tosses of an unbiased die is

A circle passes through (-2,4) and touches the y-axis at (0,2). Which one of the following equations can represent a diameter of this circle

How many numbers between 5000 and 10000 can be formed using the digits 1,2,3,4,5,6,7,8,9 each digit appearing not more than once in each number?

Find the differential equation governing all the straight lines (x)/(a)+(y)/(b)=1, a ne 0, b ne 0.

Let a, b, c in R and alpha, beta are the real roots of the equation ax2 + bx + c = 0 and if a + b + c < 0, a – b + c < 0 and c > 0 then [alpha] + [beta] is equal to (where [.] denotes the greatest integer function.)