28278 + Interview Questions in Maths in Class 12 Page 564 InterviewSolution

28151.	int (x^(5))/(x^(2) + 1)dx =
Answer» `(X^(4))/(4)+(x^(2))/(2)+Tan^(-1)x+c` `(x^(4))/(4)-(x^(2))/(2)+(1)/(2)log(x^(2)+1)+c` `(x^(4))/(4)+(x^(2))/(2)+Tan^(-1)x+c` `(x^(4))/(4)-(x^(3))/(3)-Tan^(-1)E` Answer :B

Discussion

28152.	For any two statements p and q , the negation of p v ( ~ p ^ q) is
Answer» <P>p `^^` Q ~p `^^` ~ q p `harr` q ~ p `VEE`~ q ANSWER :B

Discussion

28153.	If A=[{:(i,0),(0,i):}], n inNthen A^(4n)=...... (where I is imaginary complex number and i^(2)=-1)
Answer» `[{:(i,0),(0,i):}]` `[{:(0,0),(0,0):}]` `[{:(1,0),(0,1):}]` `[{:(0,-i),(i,0):}]` ANSWER :C

Discussion

28154.	Express in simplest form: cos^(-1)(3/5cosx+4/5sinx)
Answer» ANSWER :`x-tan^(-1)""4/3" or "x-cos^(-1)""3/5`

Discussion

28155.	Let C be the set of complex numbers . Prove that the mapping f : C rarr Rgiven by f(z) = \|z\| , AA z in C , is neither one - one nor onto .
Answer» SOLUTION :N/A

Discussion

28156.	Let A and B be two events such that P(A)= 0.4, P(A cup B)= 0.7 and P(B)= p. For what choice of p are A and B independent ?
Answer» `(1)/(2)` `(1)/(3)` `(3)/(4)` `(5)/(6)` Answer :A

Discussion

28157.	Determine the work which has to be done to bring an electric charge e_(2)=1 from infinity to a unit distance from a charge e_(1).
Answer» ANSWER :`e_(1)`

Discussion

28158.	A variable plane is at a constant distance h from the origin and meetsthe coordinateaxes in A,B,C . Locus of centroid of triangle ABC is
Answer» `x^(2)+y^(2)+Z^(2)=H^(-2)` `x^(2)+y^(2)+z^(2)=4h^(-2)` `x^(2)+y^(2)+z^(2)=16h^(2)` `1/(x^(2))+1/(y^(2))+1/(z^(2))=9/(h^(2))` Answer :D

Discussion

28159.	Find a value of A when cos 2A = sin 3A
Answer» SOLUTION :`cos 2A = sin 3A = cos (90^@-3A)`

Discussion

28160.	int (x tan^(-1)x)/(sqrt(1 + x^(2)))d x=
Answer» `sqrt(1 +X^(2)) TAN^(-1) " x- LOG "(x + sqrt(1 + x^(2))) + C` `sqrt(1 +x^(2)) tan^(-1) " x + log "(x + sqrt(1 + x^(2))) + c` ` (tan^(-1)x)/(sqrt(1 +x^(2))) "+ log "(x + sqrt(1 + x^(2))) + c` ` (tan^(-1)x)/(sqrt(1 +x^(2))) "- log "(x + sqrt(1 + x^(2))) + c` ANSWER :A

Discussion

28161.	If A= [(ab,b^(2)),(-a^(2),-ab)] then A^(2) is equal
Answer» O I `-I` NONE of these ANSWER :A

Discussion

28162.	If the velocity of a particle movingalong a straight line is directly proportional to the square of its distance from a fixedpoint on the line . Then its acceleration is proportional to ………………….
Answer» s `s^(2)` `s^(3)` `s^(4)` Answer :B::C

Discussion

28163.	Determine the maximum value of z = 11x + 7y subject to the constraints : 2x+y le 6, x le 2, x ge 0, y ge 0
Answer» Answer :The maximum value of objective function z is 42 at CORNER POINT (0, 6)

Discussion

28164.	Solve ( 1+e^(x).y) dx + xe^(x) dy = 0
Answer»

Discussion

28165.	If a random variable X can take all non- negative integral values and the probability that X takes the value r is proportional to alpha^(r)(0 lt alpha lt 1) then P(X = 0) is ………..
Answer» `1- ALPHA` `alpha` `(alpha)/(2)` `alpha^(2)` ANSWER :A

Discussion

28166.	Find the area lying above x-axis and included between the circle x^(2) + y^(2) = 8x and inside the parabola y^(2) = 4x.
Answer» ANSWER :`4/3(8+3pi)`

Discussion

28167.	Evaluate the following determinates \|{:("2","-1","-2"),("0",2,"-1"),(3,"-5","0"):}\|
Answer» ANSWER :5

Discussion

28168.	Differentiate the functions x^(x)-2^(sin x)
Answer» ANSWER :`X^(x) (1 + LOG x)- 2^(sin x).cos x.log2`

Discussion

28169.	LetH:(x^(2))/(a^(2))-(y^(2))/(b^(2))=1, where a gt b gt 0, be a hperbola in the xy-plane whose conjugate axis LM subtends and angle of 60^(@) at one of its vertices N. Let the area of the triangle LMN be 4sqrt3. The correct option is :
Answer» `PrarrIV, QrarrII, R rarrI,SrarrIII` `PrarrIV,QrarrIII,R rarrI, SrarrII` `PrarrIV,QrarrI,R rarrIII, SrarrII` `PrarrIII, QrarrIV,R rarrII, S rarrI` Solution : `" Area of " DeltaLMN=4sqrt3` `(1)/(2)(2B)(sqrt3b)=4sqrt3` `rArr""b^(2)=4rArrb=2rArr2b=4` Here, `(a)/(b)=cot 30^(@)rArra=sqrt3b rArra=2sqrt3` Now, `b^(2)=a^(2)(E^(2)-1)` `therefore""4=12(e^(2)-1)` `rArr""e^(2)=1+(1)/(3)=(4)/(3)` `rArr""e=(2)/(SQRT3)` `"Distance between foci"=2ae=2xx2sqrt3xx(2)/(sqrt3)=8` `"LENGHT of latus rectum "=(2b^(2))/(a)=(2xx4)/(2sqrt3)=(4)/(sqrt3)`

Discussion

28170.	int (1)/(sin(x-a)sin (x-b))dx=
Answer» ANSWER :`(1)/(SIN(b-a))LOG\|(sin(x-a))/(sin(x-b))\|+C`

Discussion

28171.	The vlaues of k for which the circles x ^(2) + y ^(2) =1 and x ^(2) + y ^(2) - 4x +k=0 have two comon tangents is
Answer» `(- (9)/(4), (9)/(4))` `(-OO, - (9)/(4)) UU ((9)/(4) , oo)` `(-oo, - (9)/(4)] uu [ (9)/(4) , oo)` NONE of these Answer :B

Discussion

28172.	The two equal sides of an isosceles triangle with fixed base b are decreasing atthe rate of 3 cm per second. How fast is the area decreasing when the two equalsides are equal to the base ?
Answer» ANSWER :`bsqrt(3) CM^(3)//s`

Discussion

28173.	Whichof the statement(s)is / are incorrect ?
Answer» if f+G is continuousat X=a , thenf andg arecontinuousat x=a . `if lim_ (x to a)(fg) ` exists , THENBOTH` lim_( x to a ) f and lim_ (x to a)` g EXIST Discontinuityat `x= a implies ` non - existenceof limit. Allfunctiondefinfed on a closed intervalattainamaximumorminimum VALUEIN thatinterval. Answer :A::B::C::D

Discussion

28174.	Integrate the functions ((x-3)e^(x))/((x-1)^(3))
Answer» ANSWER :`(E^(X))/((x-1)^(2))+C`

Discussion

28175.	The value of alpha for which the shortest distance between the lines represented by y+z=0,z+x=0 and x+y=0,x+y+z=alpha is 1, is:
Answer» `SQRT((3)/(2))` `sqrt((3)/(5))` `sqrt((2)/(3))` `sqrt((5)/(3))` ANSWER :A

Discussion

28176.	The positive integer n for which 2 . 2^(2) + 3 . 2^(3) + 4 . 2^(4) + ...............n . 2^(n) = 2^(n+10)is
Answer» 510 511 512 513 Answer :D

Discussion

28177.	Find three positive integers x_i,i=1,1,3 "satisfying" 3x -= 2 "(mod 7)"
Answer» Solution :`3X -= 2 "MOD" 7` Least POSITIVE value of x=3 Each MEMBER of [3] is a solution `:. x=3, 10,17……….`

Discussion

28178.	Find f'(x) if f(x)= (sin x)^(sin x) for all 0 lt x lt pi.
Answer» Answer :`(1 + LOG sin X) (sin x)^(sin x) cos x`

Discussion

28179.	Integrate the following functions : cos(logx)
Answer» Answer :`(x)/(2)[COS(LOGX)+SIN(logx)]+C`

Discussion

28180.	If overline(a), overline(b), overline(c) are non-coplanar and the vectors overline(p)=2overline(a)-4overline(b)+4overline(c), overline(q)=overline(a)+moverline(b)+4overline(c),overline(r)=-overline(a)+2overline(b)+4overline(c) are collinear then m=
Answer» `6` `-6` `2` `-2` ANSWER :C

Discussion

28181.	If {:A*[(7,6,-1),(4,2,3),(1,3,0)]:}={:[(4,2,3),(1,3,0),(7,6,-1)]:}, then A =
Answer» `{:[(1,0,0),(0,1,0),(0,0,1)]:}` `{:[(1,0,0),(0,0,1),(0,0,1)]:}` `{:[(0,1,0),(0,0,1),(1,0,0)]:}` `{:[(0,1,0),(0,0,1),(0,0,1)]:}` ANSWER :C

Discussion

28182.	Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ", " you will receive a promotion " Translate ~~(p vv q) rarr~~rstatements into English language .
Answer» SOLUTION :If you are NEITHER HONEST nor laborious then you will receive a PROMOTION.

Discussion

28183.	Out of 100 students, two sections of 40 are 60 an formed. If you and your friend are among the 100 students, find the probability that i) You both enter the same section. ii) You both enter the different sections.
Answer» ANSWER :`(i) (17)/(33)` `(II) (16)/(33)`

Discussion

28184.	Find the area of the smaller region bounded by the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 and the line (x)/(a) + (y)/(b) = 1.
Answer» ANSWER :`(AB)/(4) (pi-2)`

Discussion

28185.	If A is a square matrix of order 3 such that A^(2)= 2A then \|A\|^(2) is equal to
Answer» `2\|A\|` `8\|A\|` `16\|A\|` 0 Answer :B

Discussion

28186.	A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3. Then
Answer» <P>`0 LE P(B) le 0.3` `0 le P(B) le 0.6` `0.3 le P(B) le 0.9` `0.6 le P(B) le 0.9` ANSWER :B

Discussion

28187.	In a binomial distribution consistingof 5 independent trials, the probability of 1 and 2 successes are 0.4096 and 0.2048 respectively. Find the mean andvariance of the random variables.
Answer» ANSWER :MEAN = 1, VARIANCE = `4/5`

Discussion

28188.	A box contains 100 tickets, numbered 1,2,….100. Two tickets are chosen at random . It is given that the maximum number on the two chosen tickets is not more than 10. The minimum number of them is 5 with probability
Answer» `11//15` 13/17 `13//17` `13//19` ANSWER :B

Discussion

28189.	If f(x) is the primitive of (sin 3sqrt(x)log(1+3x))/((tan^(-1)sqrt(x))^(2)(e^(3sqrt(x))-1)) (xne0) then underset(xrarr0)lim f'(x) is
Answer» 0 `3/5` `5/3` NONE of these Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

int (x^(5))/(x^(2) + 1)dx =

For any two statements p and q , the negation of p v ( ~ p ^ q) is

If A=[{:(i,0),(0,i):}], n inNthen A^(4n)=...... (where I is imaginary complex number and i^(2)=-1)

Express in simplest form: cos^(-1)(3/5cosx+4/5sinx)

Let C be the set of complex numbers . Prove that the mapping f : C rarr Rgiven by f(z) = |z| , AA z in C , is neither one - one nor onto .

Let A and B be two events such that P(A)= 0.4, P(A cup B)= 0.7 and P(B)= p. For what choice of p are A and B independent ?

Determine the work which has to be done to bring an electric charge e_(2)=1 from infinity to a unit distance from a charge e_(1).

A variable plane is at a constant distance h from the origin and meetsthe coordinateaxes in A,B,C . Locus of centroid of triangle ABC is

Find a value of A when cos 2A = sin 3A

int (x tan^(-1)x)/(sqrt(1 + x^(2)))d x=

If A= [(ab,b^(2)),(-a^(2),-ab)] then A^(2) is equal

If the velocity of a particle movingalong a straight line is directly proportional to the square of its distance from a fixedpoint on the line . Then its acceleration is proportional to ………………….

Determine the maximum value of z = 11x + 7y subject to the constraints : 2x+y le 6, x le 2, x ge 0, y ge 0

Solve ( 1+e^(x).y) dx + xe^(x) dy = 0

If a random variable X can take all non- negative integral values and the probability that X takes the value r is proportional to alpha^(r)(0 lt alpha lt 1) then P(X = 0) is ………..

Find the area lying above x-axis and included between the circle x^(2) + y^(2) = 8x and inside the parabola y^(2) = 4x.

Evaluate the following determinates |{:("2","-1","-2"),("0",2,"-1"),(3,"-5","0"):}|

Differentiate the functions x^(x)-2^(sin x)

LetH:(x^(2))/(a^(2))-(y^(2))/(b^(2))=1, where a gt b gt 0, be a hperbola in the xy-plane whose conjugate axis LM subtends and angle of 60^(@) at one of its vertices N. Let the area of the triangle LMN be 4sqrt3. The correct option is :

int (1)/(sin(x-a)sin (x-b))dx=

The vlaues of k for which the circles x ^(2) + y ^(2) =1 and x ^(2) + y ^(2) - 4x +k=0 have two comon tangents is

The two equal sides of an isosceles triangle with fixed base b are decreasing atthe rate of 3 cm per second. How fast is the area decreasing when the two equalsides are equal to the base ?

Whichof the statement(s)is / are incorrect ?

Integrate the functions ((x-3)e^(x))/((x-1)^(3))

The value of alpha for which the shortest distance between the lines represented by y+z=0,z+x=0 and x+y=0,x+y+z=alpha is 1, is:

The positive integer n for which 2 . 2^(2) + 3 . 2^(3) + 4 . 2^(4) + ...............n . 2^(n) = 2^(n+10)is

Find three positive integers x_i,i=1,1,3 "satisfying" 3x -= 2 "(mod 7)"

Find f'(x) if f(x)= (sin x)^(sin x) for all 0 lt x lt pi.

Integrate the following functions : cos(logx)

If overline(a), overline(b), overline(c) are non-coplanar and the vectors overline(p)=2overline(a)-4overline(b)+4overline(c), overline(q)=overline(a)+moverline(b)+4overline(c),overline(r)=-overline(a)+2overline(b)+4overline(c) are collinear then m=

If {:A*[(7,6,-1),(4,2,3),(1,3,0)]:}={:[(4,2,3),(1,3,0),(7,6,-1)]:}, then A =

Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ", " you will receive a promotion " Translate (p vv q) rarrrstatements into English language .

Out of 100 students, two sections of 40 are 60 an formed. If you and your friend are among the 100 students, find the probability that i) You both enter the same section. ii) You both enter the different sections.

Find the area of the smaller region bounded by the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 and the line (x)/(a) + (y)/(b) = 1.

If A is a square matrix of order 3 such that A^(2)= 2A then |A|^(2) is equal to

A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3. Then

In a binomial distribution consistingof 5 independent trials, the probability of 1 and 2 successes are 0.4096 and 0.2048 respectively. Find the mean andvariance of the random variables.

A box contains 100 tickets, numbered 1,2,….100. Two tickets are chosen at random . It is given that the maximum number on the two chosen tickets is not more than 10. The minimum number of them is 5 with probability

If f(x) is the primitive of (sin 3sqrt(x)log(1+3x))/((tan^(-1)sqrt(x))^(2)(e^(3sqrt(x))-1)) (xne0) then underset(xrarr0)lim f'(x) is

Explore topic-wise InterviewSolutions in .

int (x^(5))/(x^(2) + 1)dx =

For any two statements p and q , the negation of p v ( ~ p ^ q) is

If A=[{:(i,0),(0,i):}], n inNthen A^(4n)=...... (where I is imaginary complex number and i^(2)=-1)

Express in simplest form: cos^(-1)(3/5cosx+4/5sinx)

Let C be the set of complex numbers . Prove that the mapping f : C rarr Rgiven by f(z) = |z| , AA z in C , is neither one - one nor onto .

Let A and B be two events such that P(A)= 0.4, P(A cup B)= 0.7 and P(B)= p. For what choice of p are A and B independent ?

Determine the work which has to be done to bring an electric charge e_(2)=1 from infinity to a unit distance from a charge e_(1).

A variable plane is at a constant distance h from the origin and meetsthe coordinateaxes in A,B,C . Locus of centroid of triangle ABC is

Find a value of A when cos 2A = sin 3A

int (x tan^(-1)x)/(sqrt(1 + x^(2)))d x=

If A= [(ab,b^(2)),(-a^(2),-ab)] then A^(2) is equal

If the velocity of a particle movingalong a straight line is directly proportional to the square of its distance from a fixedpoint on the line . Then its acceleration is proportional to ………………….

Determine the maximum value of z = 11x + 7y subject to the constraints : 2x+y le 6, x le 2, x ge 0, y ge 0

Solve ( 1+e^(x).y) dx + xe^(x) dy = 0

If a random variable X can take all non- negative integral values and the probability that X takes the value r is proportional to alpha^(r)(0 lt alpha lt 1) then P(X = 0) is ………..

Find the area lying above x-axis and included between the circle x^(2) + y^(2) = 8x and inside the parabola y^(2) = 4x.

Evaluate the following determinates |{:("2","-1","-2"),("0",2,"-1"),(3,"-5","0"):}|

Differentiate the functions x^(x)-2^(sin x)

LetH:(x^(2))/(a^(2))-(y^(2))/(b^(2))=1, where a gt b gt 0, be a hperbola in the xy-plane whose conjugate axis LM subtends and angle of 60^(@) at one of its vertices N. Let the area of the triangle LMN be 4sqrt3. The correct option is :

int (1)/(sin(x-a)sin (x-b))dx=

The vlaues of k for which the circles x ^(2) + y ^(2) =1 and x ^(2) + y ^(2) - 4x +k=0 have two comon tangents is

The two equal sides of an isosceles triangle with fixed base b are decreasing atthe rate of 3 cm per second. How fast is the area decreasing when the two equalsides are equal to the base ?

Whichof the statement(s)is / are incorrect ?

Integrate the functions ((x-3)e^(x))/((x-1)^(3))

The value of alpha for which the shortest distance between the lines represented by y+z=0,z+x=0 and x+y=0,x+y+z=alpha is 1, is:

The positive integer n for which 2 . 2^(2) + 3 . 2^(3) + 4 . 2^(4) + ...............n . 2^(n) = 2^(n+10)is

Find three positive integers x_i,i=1,1,3 "satisfying" 3x -= 2 "(mod 7)"

Find f'(x) if f(x)= (sin x)^(sin x) for all 0 lt x lt pi.

Integrate the following functions : cos(logx)

If overline(a), overline(b), overline(c) are non-coplanar and the vectors overline(p)=2overline(a)-4overline(b)+4overline(c), overline(q)=overline(a)+moverline(b)+4overline(c),overline(r)=-overline(a)+2overline(b)+4overline(c) are collinear then m=

If {:A*[(7,6,-1),(4,2,3),(1,3,0)]:}={:[(4,2,3),(1,3,0),(7,6,-1)]:}, then A =

Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ", " you will receive a promotion " Translate ~~(p vv q) rarr~~rstatements into English language .

Out of 100 students, two sections of 40 are 60 an formed. If you and your friend are among the 100 students, find the probability that i) You both enter the same section. ii) You both enter the different sections.

Find the area of the smaller region bounded by the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 and the line (x)/(a) + (y)/(b) = 1.

If A is a square matrix of order 3 such that A^(2)= 2A then |A|^(2) is equal to

A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3. Then

In a binomial distribution consistingof 5 independent trials, the probability of 1 and 2 successes are 0.4096 and 0.2048 respectively. Find the mean andvariance of the random variables.

A box contains 100 tickets, numbered 1,2,….100. Two tickets are chosen at random . It is given that the maximum number on the two chosen tickets is not more than 10. The minimum number of them is 5 with probability

If f(x) is the primitive of (sin 3sqrt(x)log(1+3x))/((tan^(-1)sqrt(x))^(2)(e^(3sqrt(x))-1)) (xne0) then underset(xrarr0)lim f'(x) is

Let p,q, r denote respectively the statements :" you are honest ", "you are laborious ", " you will receive a promotion " Translate (p vv q) rarrrstatements into English language .