28278 + Interview Questions in Maths in Class 12 Page 553 InterviewSolution

27601.	Let A,B and C be three sets such that P(A) cap P(B) = P(C ), then
Answer» `A CAP B sube C, A cap B ne C` `C sube A cap B, A cap B ne C` `A cap B = C` `A cap B cap C = phi` Answer :C

Discussion

27602.	The probability that A hits a target is 1/4 and the probability that B hits the target is 1/3. If each of them fired once, what is the probability that the target will be hit atleast once.
Answer» ANSWER :`(1)/(2)`

Discussion

27603.	If [x] denotes the greatest integer function then the extreme values of the function f(x)=[1+sinx]+[1+sin2x]+...+[1+sin nx], n in I^(+), x in (0,pi) are
Answer» (N-1) n (n+1) (n+2) ANSWER :B::C

Discussion

27604.	If f(x)=\|(0, x-a, x-b), (x+a, 0, x-c),(x+b, x+c, 0)\|, then
Answer» `F(a)=0` `f(B)=0` `f(0)=0` `f(1)=0` SOLUTION :N/A

Discussion

27605.	A variable plane moves so that the sum of the reciprocals of its intercepts on the coordinate axes is (1//2). Then, the plane passes through the point
Answer» `((1)/(2),(1)/(2),-(1)/(2))` `(-1,1,1)` (2,2,2) (0,0,0) ANSWER :C

Discussion

27606.	4 boys and 4 girls are arranged in a row at random. Find the probability that the boys and girls sit alternatively.
Answer» ANSWER :`(2 \|ul(4) XX \|ul(4))/(\|ul(8))`

Discussion

27607.	Let S={(x,y),x^(2)+y^(2)-6x-8y+21le0} then "max"{(12x)/7-(5y)/7,(x,y)inS}+"min" {1/2(x^(2)+y^(2)+1)+(x-y),(x-y)inS} -"min"{(sqrt(3)y+\|x-3\|)/(\|x-3\|),(x,y)inS}
Answer» SOLUTION :`[6]` `6+4-4`

Discussion

27608.	If f(x)=2sin^(-1)sqrt(1-x)+sin^(-1)(2sqrt(x(1-x))) where x in (0, (1)/(2)) then f'(x) has the value equal to
Answer» `(2)/(SQRT(x(1-x)))` Zero `-(2)/(sqrt(x(1-x)))` `PI` Solution :`F(x)` simplifies to `pi` `rArr""f'(x)=0` or `""`directly DIFFERENTIALE `f(x)` to GET zone

Discussion

27609.	If [overset(-)a xx overset(-)b xx overset(-)c overset(-)c xx overset(-)a]=lambda [overset(-)a overset(-)b overset(-)c]," then "lambda=
Answer» 0 1 2 3 Answer :B

Discussion

27610.	If the minimum value of f(x)=2x^(2)+alphax+8 is the same as the maximum value of g(x)=-3x^(2)-4x+alpha^(2) then alpha^(2)=
Answer» `(150)/(27)` `(160)/(27)` `(170)/(27)` `(181)/(27)` Answer :B

Discussion

27611.	Lothar has 6 stamps from utopia and 4 stamps from cornucopia in his collection. He will give two stamps of each type to his friend peggy sue. {:("Quantity A","Quantity B"),("The number of ways Lother",100),("can giv 4 stamps (two of each type) to Peddy Sue",):}
Answer» ANSWER :QUANTITY A is GREATER.

Discussion

27612.	Write the component statement "the school is closed if there is a holiday or a Sunday" compound statements and check whether the compound statement is true or false.
Answer» Solution :The component STATEMENTS are p: There is a holiday or a SUNDAY Q : The School is closed The truth VALUE of the COMPOUND statement is .True..

Discussion

27613.	Match the following
Answer» ANSWER :A::B::C::D

Discussion

27614.	The rate of increase in the number of bacteria in a certain becteria cultureis propotional to the number present at that time. If initiallly there are300 bacteria and after 2 hours, the bacteria polulation is increased by 20% then after 24 houre, the number of bacteria are (log 1.2=0.18232,e^(2.18784)=8.9166)
Answer» 2675 2674 3210 3209 Answer :A

Discussion

27615.	Let x=(a+2b)/(a+b) and y=(a)/(b), where a and b are positive integers. If y^(2) gt 2, then
Answer» `x^(2) le 2` `x^(2) LT 2` `x^(2) GT 2` `x^(2) ge 2` Answer :B

Discussion

27616.	int ( x cos x dx)/( sin^(3) x)
Answer» Answer :`-0.5 ((x)/( sin^(2) x) + COT x) + C`.

Discussion

27617.	(i) Verify by method of contradicition p : There are infinitely many numbers (ii) Verify by method of contradicition p : If p and q are rational number q ne 0 and r is an irrational number, then p+qr is irrational
Answer» Solution :(i) Let us assume that there are only FINITELY many primes ,`p_1,p_2,……….p_n` Now contructing a number `p=p_1xxp_2xxp_3xx….xxp_(n+1)` CLEARLY , p is larger than all primes. So it is not divisble by any existing prime . So, according to defination of prime number p is true . So our ASSUMPTION is wrong So, given statement is true (ii) Let us assume that p+qr is irrational so, qr is irrational so, `(qr)/q=r` is RATIONAL , which contradicts so, p is true

Discussion

27618.	Find the distance between the lines overset(to)(r ) = hat(i) + 2 hat(j) - 4 hat(k) + lambda ( 2 hat(i) + 3 hat(j) + 6 hat(j) ) & overset(to)(r ) = 3 hat(i) + 3 hat(j) - 5 hat(k) + mu ( -2 hat(i) + 3 hat(j) + 8 hat(k) )
Answer» ANSWER :`d= ( SQRT( 293))/( 7) `

Discussion

27619.	If A=[{:(3,1),(-1,2):}] show that A^2-5A+7I=O. HencefindA^(-1)
Answer» ANSWER :`thereforeA^(-1)=1/7[{:(2,-1),(1,3):}]`

Discussion

27620.	Find all 7 digit numbers formed by using only the digits 5 and 7 and divisible by both 5 and 7.
Answer» ANSWER :`7775775, 7757575, 5577775, 7575575, 5777755, 7755755, 5755575, 5557755, 7555555`

Discussion

27621.	Examine the continuity of the following functions at indicated points.f(x)={((sin2x)/x if xne0 at x=0),(2 if x=0):}
Answer» Solution :`lim_(xto0)f(x)=lim_(xto0)(sin2x)/x` `lim_(xto0)2 cdot (sin2x)/(2X)=2 cdot lim_(2xto0)(sin2x)/(2x)=2 cdot 1` `=2(becauselim_(theta=0)(sintheta)/theta=1)` Again `f(0)=2implieslim_(xto0)f(x)=f(0)` `THEREFORE` The function f(x) is CONTINUOUS at x=0

Discussion

27622.	If a line has the direction ratios –18, 12, – 4, then what are its direction cosines ?
Answer» Answer :HENCE, the direction COSINES of a LINE are `(-9)/(11),(6)/(11),(-2)/(11)`.

Discussion

27623.	Lengths of common tangents of the circles x^(2)+y^(2)=6x,x^(2)+y^(2)+2x=0 are
Answer» `(SQRT(3))` `sqrt(3),3sqrt(3)` `2sqrt(3)` `2sqrt(3),3sqrt(3)` ANSWER :C

Discussion

27624.	What is the total number of ways of selecting atleast one item from each of the two sets containing 6 identical items each?
Answer» ANSWER :36

Discussion

27625.	If ((1+costheta+isintheta)/(sintheta+i+icostheta))^(4)=cosntheta+isinntheta then n=
Answer» 4 8 6 2 Answer :A

Discussion

27626.	Let a = sin^2 x hati + cos^2 x hatj + hatk ,( x in R). If the pairs of vectors a , hati , a , hatj and a , hatk are adjacent sides of 3 distinct parallelograms and A is the sum of the squares of areas these parallelograms ,then A lies in the interval
Answer» `(0 , 1)` `(3, 4)` `(0 , 2)` `(1, 2)` Answer :B

Discussion

27627.	Solve 5x-3 lt 7, when x is an integer.
Answer» ANSWER :The SOLUTION SET is {……….-3,-2,-1, 0,1}

Discussion

27628.	If A=[{:(alpha,beta),(gamma,-alpha):}] is such that A^(2)=I, then ……
Answer» `1+alpha^(2)+betagamma=0` `1-alpha^(2)+betagamma=0` `1-alpha^(2)-betagamma=0` `1+alpha^(2)-betagamma=0` ANSWER :C

Discussion

27629.	The solution of sec x(dy)/(dx) = y + sin x is
Answer» `y e^(-SIN X) = e^(-sin x)(-sinx-1)+C` `y e^(-sin x) = e^(sin x)(sinx+1)+c` `y e^(COS x) = e^(cosx)(sin x+1)+c` `y e^(-sin x) = e^(-sin x)(sinx+1)+c` Answer :A

Discussion

27630.	What is (sintheta+1)/(costheta)equal to ?
Answer» `(sintheta+costheta-1)/(sintheta+costheta+1)` `(sintheta+costheta+1)/(sintheta+costheta-1)` `(sintheta-costheta-1)/(sintheta+costheta+1)` `(sintheta-costheta+1)/(sintheta+costheta-1)` Solution :CONSIDER`(1+sintheta)/(costheta)=(1+sintheta)/(costheta)=(1+(2"tan"(theta)/(2))/(1+"tan"^(2)(theta)/(2)))/((1-"tan"^(2)(theta)/(2))/(1+"tan"^(2)(theta)/(2)))` `(becausesin2theta=(2tantheta)/(1+tan^(2)theta)andcos2 theta=(1-tan^(2)theta)/(1+tan^(2)theta))` `=((1+"tan"(theta)/(2))^(2))/((1+"tan"(theta)/(2))(1+"tan"(theta)/(2)))` `=(1+"tan"(theta)/(2)"cos"(theta)/(2)+2"sin"^(2)(theta)/(2))/(2"sin"(theta)/(2) "cos "(theta)/(2)-2" sin"^(2)(theta)/(2))` `=(sintheta+1-costheta)/(sintheta-1+costheta)` `(becausesin2 theta=2sinthetacosthetaand COS2 theta=1-2sin^(2)theta)`

Discussion

27631.	The set of values of x for which the inequalitiesx^(2)-3x-10 lt 0, 10x-x^(2)-16 gt 0 hold simultaneously, is
Answer» (-2, 5) (2, 8) (-2, 8) (2, 5) ANSWER :D

Discussion

27632.	If the axes are rotated anticlockwise through an angle 90^@ then the equation x^2=4ay is changed to the equation
Answer» `y^2=4ax` `x^2=-4ay` `y^2=4ax` `x^2=4ay` ANSWER :A

Discussion

27633.	If x = tan^(-1) 1 -cos^(-1) ( - 1/2) + sin^(-1) 1/2 , y = cos (1/2 cos^(-1) (1/8)), then
Answer» ` X = PI y` ` y = pi x` ` TAN x = - (4//3) y` ` tan x = ( 4//3) y` ANSWER :C

Discussion

27634.	The mod-amplitude form of -sqrt3 - i
Answer» 2 cis `"" (-5PI)/(6)` 2 cis `"" (PI)/(6)` cis `"" (5pi)/(6)` cis `"" (pi)/(6)` ANSWER :A

Discussion

27635.	Find the number of integer solutions of [x/100[x/100]]=5 (Here [x] der Here [x] denotes the greatest integer less than or equal to x. (For example (3.4) = 3 and (-2.3) = -3).
Answer» ANSWER :50

Discussion

27636.	tan^-1(frac{1}{sqrt3}) - sin^-1(frac{1}{2}) is equal to :
Answer» `π/4` `π/3` `-π/4` `-π/3` ANSWER :C

Discussion

27637.	A plane meets the co-ordinate axes at A, B and C such that the centroid of the traingleABC is (3, 4, -6). Find the equation of the plane.
Answer» ANSWER :`4x+3y-2z=36`

Discussion

27638.	Out of 21 tickets numbered 10, 11, 12,…, 30, three tickets are drawn at random. Find the probability that the numbers on these tickets are in A.P.
Answer» ANSWER :`(10)/(133)`

Discussion

27639.	Find the area of the region enclosed by the parabola x^(2) = y, the line y = x + 2 and the x-axis.
Answer» ANSWER :`5/6`

Discussion

27640.	int (log x) ^(3) x ^(4) dx, where rho = log x
Answer» `(x ^(5))/(625) [125rho ^(3) -75p^(2) + 30 p -6]+c` ` (x ^(5))/(625) [125 p ^(3) - 25 p ^(2) + 30 rho -5]+c ` `(x ^(5))/(625) [125 p ^(3) - 60 p ^(2) -25P +5] +c` `(x ^(5))/(125) [625 p^(3) -75 p ^(2) + 30p+6] +c` Answer :A

Discussion

27641.	The value of lambda, for which the four points 2hati+3hatj-hatk, hati+3hatk, 2hati+4hatj-2hatk, hati-6hatj+lambda hatk are coplanar, is
Answer» 2 4 6 8 Solution :Let `A=2hat(i)+3HAT(j)-hat(k), B =hat(i)-2hat(j)+3hat(k)`, `C=3hat(i)+4hat(j)-2hat(k)` and `D=hat(i)-6hat(j)+lambda hat(k)` Now, `AB=-hat(i)-5hat(j)+4hat(k), AC =hat(i)+hat(j)-hat(k)` and `AD=-hat(i)-9hat(j)+(lambda+1)hat(k)` These will be coplanar, if `[(AB,AC,AD)]=0` `:. \|(-1,-5,4),(1,1,-1),(-1,-9,(lambda+1))\|=0` `implies -1(lambda+1-9)+5(lambda+1-1)+4(-9+1)=0` `implies 4lambda -24 =0` `implies lambda =6`

Discussion

27642.	Evalute the following integrals int (x^(3))/( sqrt( x + 1)) dx
Answer» ANSWER :`2[((x+1)^(7//2))/(7)-(3(x+1)^(5//2))/(5)+(x+1)^(3//2)-SQRT(x+1)]+C`

Discussion

27643.	Find all the points of discontinuity of f defined by f(x)= \|x\|-\|x+1\|.
Answer» ANSWER :There is no POINT of DISCONTINUITY.

Discussion

27644.	The the area bounded by the curve \|x\| + \|y\| = c (c > 0) is 2c^(2), then the area bounded by \|ax + by\| + \|bx - ay\| = c where a^(2) + b^(2)= 1 is
Answer» `8C^(2)` `4c^(2)` `2c^(2)` `C^(2)` ANSWER :C

Discussion

27645.	Integrate the following : intx^5dx
Answer» SOLUTION :`intx^5dx`=`x^6/6+C`

Discussion

27646.	Let A=[[1,2,3,4,1], [4,5,6,1,2], [3,9,1,1,6]]Write down the entries a_31,a_25,a_23 ?
Answer» SOLUTION :`a_31=3,a_25=2,a_23=6`

Discussion

27647.	Integrate the functions (x^(2)+x+1)/((x+1)^(2)(x+2))
Answer» ANSWER :`-2logabs(x+1)-1/(x+1)+3logabs(x+2)+C`

Discussion

27648.	Find which of the operations given above has identity. a"*"b=(a-b)^2
Answer» SOLUTION :N/A

Discussion

27649.	Coordinates of the point O, P, Q and R are respectively (0,0,4),(4,6,2m),(2,0,2n) and (2,4,6). Let L,M,N and K be points on the sides OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjecent sides LM and side LK are each of length sqrt2. What are the values of m and n respectively ?
Answer» 6,2 1,3 3,1 None of the above SOLUTION :GO through the OPTION ( C)

Discussion

27650.	If four squares are chosen at random on a chess board, then the probability that they lie in a diagonal line is
Answer» `17//744` `31//744` `7//744` `1//744` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in .

Let A,B and C be three sets such that P(A) cap P(B) = P(C ), then

The probability that A hits a target is 1/4 and the probability that B hits the target is 1/3. If each of them fired once, what is the probability that the target will be hit atleast once.

If [x] denotes the greatest integer function then the extreme values of the function f(x)=[1+sinx]+[1+sin2x]+...+[1+sin nx], n in I^(+), x in (0,pi) are

If f(x)=|(0, x-a, x-b), (x+a, 0, x-c),(x+b, x+c, 0)|, then

A variable plane moves so that the sum of the reciprocals of its intercepts on the coordinate axes is (1//2). Then, the plane passes through the point

4 boys and 4 girls are arranged in a row at random. Find the probability that the boys and girls sit alternatively.

Let S={(x,y),x^(2)+y^(2)-6x-8y+21le0} then "max"{(12x)/7-(5y)/7,(x,y)inS}+"min" {1/2(x^(2)+y^(2)+1)+(x-y),(x-y)inS} -"min"{(sqrt(3)y+|x-3|)/(|x-3|),(x,y)inS}

If f(x)=2sin^(-1)sqrt(1-x)+sin^(-1)(2sqrt(x(1-x))) where x in (0, (1)/(2)) then f'(x) has the value equal to

If [overset(-)a xx overset(-)b xx overset(-)c overset(-)c xx overset(-)a]=lambda [overset(-)a overset(-)b overset(-)c]," then "lambda=

If the minimum value of f(x)=2x^(2)+alphax+8 is the same as the maximum value of g(x)=-3x^(2)-4x+alpha^(2) then alpha^(2)=

Lothar has 6 stamps from utopia and 4 stamps from cornucopia in his collection. He will give two stamps of each type to his friend peggy sue. {:("Quantity A","Quantity B"),("The number of ways Lother",100),("can giv 4 stamps (two of each type) to Peddy Sue",):}

Write the component statement "the school is closed if there is a holiday or a Sunday" compound statements and check whether the compound statement is true or false.

Match the following

Let x=(a+2b)/(a+b) and y=(a)/(b), where a and b are positive integers. If y^(2) gt 2, then

int ( x cos x dx)/( sin^(3) x)

(i) Verify by method of contradicition p : There are infinitely many numbers (ii) Verify by method of contradicition p : If p and q are rational number q ne 0 and r is an irrational number, then p+qr is irrational

Find the distance between the lines overset(to)(r ) = hat(i) + 2 hat(j) - 4 hat(k) + lambda ( 2 hat(i) + 3 hat(j) + 6 hat(j) ) & overset(to)(r ) = 3 hat(i) + 3 hat(j) - 5 hat(k) + mu ( -2 hat(i) + 3 hat(j) + 8 hat(k) )

If A=[{:(3,1),(-1,2):}] show that A^2-5A+7I=O. HencefindA^(-1)

Find all 7 digit numbers formed by using only the digits 5 and 7 and divisible by both 5 and 7.

Examine the continuity of the following functions at indicated points.f(x)={((sin2x)/x if xne0 at x=0),(2 if x=0):}

If a line has the direction ratios –18, 12, – 4, then what are its direction cosines ?

Lengths of common tangents of the circles x^(2)+y^(2)=6x,x^(2)+y^(2)+2x=0 are

What is the total number of ways of selecting atleast one item from each of the two sets containing 6 identical items each?

If ((1+costheta+isintheta)/(sintheta+i+icostheta))^(4)=cosntheta+isinntheta then n=

Let a = sin^2 x hati + cos^2 x hatj + hatk ,( x in R). If the pairs of vectors a , hati , a , hatj and a , hatk are adjacent sides of 3 distinct parallelograms and A is the sum of the squares of areas these parallelograms ,then A lies in the interval

Solve 5x-3 lt 7, when x is an integer.

If A=[{:(alpha,beta),(gamma,-alpha):}] is such that A^(2)=I, then ……

The solution of sec x(dy)/(dx) = y + sin x is

What is (sintheta+1)/(costheta)equal to ?

The set of values of x for which the inequalitiesx^(2)-3x-10 lt 0, 10x-x^(2)-16 gt 0 hold simultaneously, is

If the axes are rotated anticlockwise through an angle 90^@ then the equation x^2=4ay is changed to the equation

If x = tan^(-1) 1 -cos^(-1) ( - 1/2) + sin^(-1) 1/2 , y = cos (1/2 cos^(-1) (1/8)), then

The mod-amplitude form of -sqrt3 - i

Find the number of integer solutions of [x/100[x/100]]=5 (Here [x] der Here [x] denotes the greatest integer less than or equal to x. (For example (3.4) = 3 and (-2.3) = -3).

tan^-1(frac{1}{sqrt3}) - sin^-1(frac{1}{2}) is equal to :

A plane meets the co-ordinate axes at A, B and C such that the centroid of the traingleABC is (3, 4, -6). Find the equation of the plane.

Out of 21 tickets numbered 10, 11, 12,…, 30, three tickets are drawn at random. Find the probability that the numbers on these tickets are in A.P.

Find the area of the region enclosed by the parabola x^(2) = y, the line y = x + 2 and the x-axis.

int (log x) ^(3) x ^(4) dx, where rho = log x

The value of lambda, for which the four points 2hati+3hatj-hatk, hati+3hatk, 2hati+4hatj-2hatk, hati-6hatj+lambda hatk are coplanar, is

Evalute the following integrals int (x^(3))/( sqrt( x + 1)) dx

Find all the points of discontinuity of f defined by f(x)= |x|-|x+1|.

The the area bounded by the curve |x| + |y| = c (c > 0) is 2c^(2), then the area bounded by |ax + by| + |bx - ay| = c where a^(2) + b^(2)= 1 is

Integrate the following : intx^5dx

Let A=[[1,2,3,4,1], [4,5,6,1,2], [3,9,1,1,6]]Write down the entries a_31,a_25,a_23 ?

Integrate the functions (x^(2)+x+1)/((x+1)^(2)(x+2))

Find which of the operations given above has identity. a"*"b=(a-b)^2

If four squares are chosen at random on a chess board, then the probability that they lie in a diagonal line is