28278 + Interview Questions in Maths in Class 12 Page 90 InterviewSolution

4451.	Evaluate the following integrals. intsqrt(3+8x-3x^(2))dx
Answer» Answer :`(3x-4)/(6)sqrt(3+8x-3x^(2))+(25)/(6sqrt(3))sin^(-1)((3x-4)/(5))+C`

Discussion

4452.	Let the vectors a and b be such that \|a\|=3 and \|b\|=(sqrt(2))/(3), then axxb is a unit vector, if the angle between a and b is
Answer» `pi//6` `pi//4` `pi//3` `pi//2` ANSWER :B

Discussion

4453.	Assertion (A): The director circle of x^(2)+y^(20=4 is x^(2)+y^(2)= Reason(R): The angle between the tangents from any point on x^(2)+y^(2)=8 to x^(2)+y^(2)=4 is (pi)/2 The correct answer is
Answer» Both A and R are true and R si the correct EXPLANATION of A Both A and R are true andR is not the correct explanation of A A is true but R is FALSE A is false but R is true Answer :D

Discussion

4454.	Find the maximum possible number of real roots of the equation. x^(5)-6x^(2)-4x+5=0.
Answer» 5 4 3 2 Answer :B

Discussion

4455.	A is 3xx3 matrix and det(A) =7.IF B= adj A then det(AB)= …........
Answer» `7` `7^2` `7^5` `7^3` ANSWER :D

Discussion

4456.	Method of integration by parts : int (logx)/((x+1)^(2))dx=.....
Answer» `(-LOGX)/(x+1)+logx-log(x+1)` `(logx)/((x+1))+logx-log(x+1)` `(logx)/(x+1)-logx-log(x+1)` `(-logx)/(x+1)-logx-log(x+1)` ANSWER :A

Discussion

4457.	15 people are to travel by a bus which can carry 9 inside and 6 outside. The number of ways can the party be distributed between inside and outside, if 3 people refuse to go out side and 2 will refuse to go inside is
Answer» `""^(10)C_(6)` `""^(10)C_(9)` `""^(10)C_(5)` `""^(15)C_(9)` ANSWER :A

Discussion

4458.	The median from the following data
Answer» `83.17` ` 84.08` `82.17` `85.67` ANSWER :B

Discussion

4459.	Match the entries of column-I with those of column - II {:("Column-I", "Column-II"),(t in R " such that there is at least one z satisfying " \|Z\|=3"," \|z-{t-(1+i)-i}\|le 3 and \|z +2t - (t+1)i\|gt 3 , "(p) 6 "),("(B) Solve for x : " ((1+i)x-2i)/(3+i) + ((2-3i)y+i)/(3-i) = i , "(p) 0"),("(C) The integer n for which " ((1+i)/(1-i))^(n) " is real" , "(r) 3"),("(D) The greatest and least absolutte value of z + 1 , where " \|z+4\|le 3 "are" , "(s) 4"),(,"(t) 8"):}
Answer» <P> ANSWER :A(r,s),B(r ) , C(p,q,s,t) , D( p,q)

Discussion

4460.	If three numbers are chosen from 1 to 200. Find the probability for the three chosen numbers to be not consecutive.
Answer» ANSWER :`(19897)/(19900)`

Discussion

4461.	Let G denote the set of all n xx n non - singular matrices with rational numbers an entries. Then under matrix multiplication
Answer» G is a sub group G is a FINITE Ablian group G is an INFINITE, NON - ABELIAN group G is finite, Abelian Answer :C

Discussion

4462.	Solutions of the equation x\|x+1\|+1=0 are
Answer» `(1)/(2)(1+-SQRT5)` `(-1)/(2)(-1 +- sqrt5)` `(1)/(2)(-1+sqrt5)` `(1)/(2)(-1-sqrt5)` ANSWER :D

Discussion

4463.	The solution set of \|3x-2\| lt 1is
Answer» `[-1,1]` (1,3) `[1/3, 3]` `(1/3 , 1)` ANSWER :D

Discussion

4464.	A man is know to speak truth 4 out of 5 times. He tossed a coin and reports that it is head. Find the probability that it is actually head.
Answer» ANSWER :`(4)/(5)`

Discussion

4465.	Fromthe two systemsof linesx-h=0 , h=0,1,2,3,4,5 and y-k=0,1,2,3thenumberif squaresthat canbe formedis
Answer» 20 22 24 26 Answer :D

Discussion

4466.	Triangle PQR above is equilateral with PQ = 44. The ratio ST to TU is 8:4. What is the length of bar(SQ)?
Answer» 6 16 `16sqrt3` 32 Answer :B

Discussion

4467.	If ab=a^b then (21)*2=
Answer» 8 2 4 16 Answer :B

Discussion

4468.	If {:(f(x),=(log)(sec^2x)^(cot^2x),",","for"x != 0),(,=k, ",","for"x = 0):} is continuous at x = 0 then k is
Answer» `E^(-1)` `1` e 0 Answer :B

Discussion

4469.	The sum of the series 1+(2)/(3)((1)/(8))+(2xx5)/(3xx6)((1)/(8))^2+(2xx5xx8)/(3xx6xx9)((1)/(8))^2+………. is
Answer» `(4)/(3sqrt(49))` `(3sqrt(49))/(4)` `(4)/(3sqrt(81))` `(3sqrt(81))/(4)` ANSWER :A

Discussion

4470.	Evaluate intsqrt((5-x)/(x-2)dx.
Answer» ANSWER :`sqrt((x-2)(5-x))+(3)/(2)SIN^(-1)((2x-7)/(3))+c`

Discussion

4471.	Find the position vector of R which divides the line segment joining the points A(1,-2,1)andB(1,4,-2) internally in the ratio 2:1
Answer» ANSWER :`HAT(i)+2HAT(J)-hat(K)`

Discussion

4472.	Evaluate the following determinants: [[14,3,28],[17,9,34],[25,9,50]]
Answer» SOLUTION :`[[14,3,28],[17,9,34],[25,9,50]]` =`2[[14,3,14],[17,9,17],[25,9,25]]=0` `(THEREFORE C_1=C_3)`

Discussion

4473.	Sum of the series (1)/(2)((1)/(2)+(1)/(3))-(1)/(4)((1)/(2^(2))+(1)/(3^(2)))+(1)/(6)((1)/(2^(3))+(1)/(3^(3)))-... is
Answer» `log_(E )3` `(1)/(2)log_(e )2` `(1)/(2)"LOG"_(e )(3)/(2)` `"log"_(e )(2)/(3)` Answer :B

Discussion

4474.	If the product of the slopes of the tangents drawn from an external point P to thehyperbola(x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is a constant k^(2), then thelocus of P is
Answer» `y^(2)+B^(2)=K^(2)(X^(2)-a^(2))` `y^(2)-b^(2)=k^(2)(x^(2)-a^(2))` `x^(2)+b^(2)=k^(2)(y^(2)-a^(2))` `x^(2)-b^(2)=k^(2)(y^(2)-a^(2))` ANSWER :A

Discussion

4475.	Two of the straight lines given by 3x^(3)+3x^(2)y-3xy^(2)+dy^(3)=0 are at right angles, if
Answer» `d=-1//3` `d=1//3` `d=-3` `d=3` ANSWER :D

Discussion

4476.	The set(A cup B cup C) cap (A cap B^(c ) cap C^(c ))^(c ) cap C^(c ) is equal to
Answer» `B CAP C^(c )` `A cap C` `B cap C^(c )` NONE of these Answer :C

Discussion

4477.	Let f(x)" then "g(x) be two functions having finite non-zero thirdorder derivatives. If : f(x)*g(x)=1 ," for all "x inR," then: "(f''')/(f)-(g'')/(g')=
Answer» `(F'')/(f)-(G'')/(g)` `((f'')/(f)-(g'')/(g))` `3((f'')/(f)-(g'')/(g))` NONE of theses Answer :C

Discussion

4478.	If a_(1) = 4 and a_(n + 1) = a_(n) + 4n for n gt= 1, then the value of a_(100) is
Answer» 19804 18904 18894 19904 Answer :A

Discussion

4479.	If x = -9 is a root of \|{:(x,3,7),(2,x,2),(7,6,x):}\|=0, then other two roots are "..........".
Answer» ANSWER :`thereforex=2,x=-9 and x=7`

Discussion

4480.	Let y = f(x) satisfies the differential equation (sin x)dy + (cos x)ydx = e^(x) dx with f(0) = 0. Then the value of lim_(x to 0)f(x) is
Answer» 0 1 `-1` Does not exist Solution :`(SIN x) dy + (cos x) ydx = E^(x) dx` `d[(sin x).y] = e^(x)dx` Intergrating `ysin x = e^(x) + C` Putting `f(0) = 0` `0 = 1 + c implies c = -1` `y = (e^(x) - 1)/(sin x)` `lim_(x to 0) (e^(x) - 1)/(x) (x)/(sin x) = 1`.

Discussion

4481.	Find the shortest distance between the linesvecr=(4hati-hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk).
Answer» ANSWER :`(6)/(SQRT5)`

Discussion

4482.	If the equation x^(2) + y^(2) - 2x -2y+ c=0 represents an empty set then find the value of c.
Answer» ANSWER :HENCE `C in R - {2}`

Discussion

4483.	Solve the following linear programming problem graphically: Minimise Z=200x+500y subject to the constraints: x+2yge10 3x+4yle24 xge0,yge0
Answer» ANSWER :(4,3)

Discussion

4484.	Mean and variance of binomial distribution of random variance X are 4 and 2 respectively then P(X = 1) =……….
Answer» `(1)/(16)` `(1)/(8)` `(1)/(4)` `(1)/(32)` ANSWER :D

Discussion

4485.	therestrictionon n, k andp so thatPY +Wywill bedefined are :
Answer» K=3,p=n K is ARBITRARY , p=2 PIS arobitray , k-3 `k=2,p=3` Solution :(A) Order of MATRIX p=p `xx`k Order of matrix `Y=3xxk` `therfore `PY willbe defined if K =3 ANDTHE order pf `Py=3xxk=pxx3` Orderof matrix`W=nxx3` Orderof matrix` Y=3xxK` here the matrix WY is defindedand itorder`=nxk=nxx3.` Now ,Py +Wy will be defindedifp=n `thereforep=n and l=3`

Discussion

4486.	If \|cosec x\|=(5pi)/(4)-\|(x)/(2)AA x in(-2pi,2pi), then the number of solutions are
Answer» 8 6 4 2 Solution :`\|cosec x\|=(5PI)/(4)-\|(x)/(2)\|` Draw the graphs of `y = \|cosec x\|` and `y = (5pi)/(4)-\|(x)/(2)\|` From the GRAPH, there are 8 SOLUTIONS.

Discussion

4487.	If ""^(n)P_(3)=1320, find n.
Answer» ANSWER :12

Discussion

4488.	Findproducts : [[1,0],[0,1]][[1,2],[3,4]]
Answer» SOLUTION :`[[1,0],[0,1]][[1,2],[3,4]]` `=[[1.1+0.3""1.2+0.4],[0.1+1.3" "0.2+1.4]]=[[1,2],[3,4]]`

Discussion

4489.	The logically equivalen proposition of p hArr q is
Answer» <P>`(p RARR Q) ^^ (q rarr p)` `(p rarr q) VV (q rarr p)` `(p ^^ q) rarr (p vv q)` `(p ^^ q) vv (p vv q)` ANSWER :A

Discussion

4490.	int_(0)^(oo) (45a)/((3+a+a t)^(4))dt=
Answer» `(15)/((3+a)^(2))` `(15)/((3+a)^(3))` `(15)/(3(3+a)^(3))` `(15)/(a(3+a)^(2))` ANSWER :B

Discussion

4491.	An analysis of monthly wages paid to the workers in two Firms. A and B belonging to the same industry gave thefollowing results : {:("Particulars","Firm A","Firm B",),("Number of wage-earners",586,648,),("Average monthly wages","Rs.52.5","Rs.47.5",),("Variance of distribution of wages",100,121,):} (i) Which firm, A or B, pay out layer amount as monthly wages ? (ii) In which firm A or B, is there greater variability in individual wages
Answer» Answer :(i) firm B pays a larger AMOUNT as monthly wages. (ii) there is GREATER variability in INDIVIDUAL wages in Firm B

Discussion

4492.	Let f(x) be a real function not identically zero in Z, such that for all x,y in R f(x+y^(2n+1))=f(x)={f(y)^(2n+1)}, n in Z If f'(0) ge 0, then f'(6) is equal to
Answer» 0 1 2 6 Solution :SEE Example. 36(page 4.33 of Mathematics for IIT-JEE by the same AUTHOR).

Discussion

4493.	Compute the area of the surface formed by revolving the lemniscate rho = a sqrt(cos 2 varphi) about the polar axis.
Answer» ANSWER :`2 PI a^(2) (2- SQRT2)`

Discussion

4494.	If (3x+2)/((x+1)(2^(2)+3))=(A)/(x+1)-(Bx+C)/(2x^(2)+3), then A+B-C=
Answer» 0 2 3 5 Answer :B

Discussion

4495.	Find the order and degree (if defined) of the differential equation ((d^(2)y)/(dx^(2)))+((dy)/(dx))^(2)+sin(dy/dx)+1=0
Answer» ANSWER :ORDER 2, DEGREE in not DEFINED.

Discussion

4496.	If (1 + 3 + 5 + …. +P ) + (1 + 3 + 5 + …. Q) = (1 + 3 + 5 + … r) where each set of parentheses contains the sum of consecutive odd integers as shown, the smallest possible value of p + q + r,is
Answer» 12 21 45 54 Answer :B

Discussion

4497.	If the letters of the word "ATTEMPT" are written down at random. The probability that all the T's come together is
Answer» `(1)/(21)` `(6)/(7)` `(1)/(7)` `(1)/(42)` ANSWER :C

Discussion

4498.	Let S be the set of circles x^(2)+y^(2)=r^(2)" for "r=1, 2 and 3 and T be the set of lines y= x+ksqrt(2)" for "k=0, ne 1 and pm 2. Find the number of distinct points of intersection of the graphs of set S and T.
Answer» ANSWER :22

Discussion

4499.	If(3x +2 ) /((x + 1 )(2x ^ 2+ 3 )) =(A)/(x + 1 )+ (Bx + C)/(2x ^ 2+3 ),then A + C - Bisequalto
Answer» 0 2 3 5 Solution : ` (3x + 2 ) /((x + 1 )(2x ^ 2+ 3 )) = ( A)/(( x +1 )) + (Bx+ C)/( 2x ^ 2+ 3 )` ` rArr(3x+ 2 )/((x + 1 )(2 x ^ 2+ 3 )) = (A(2x ^ 2+ 3 ) + (x + 1 )(Bx + C))/((x + 1 )(2x ^ 2 + 3 )) ` ` rArr3x + 2 = x ^ 2 (2A+ B)+ x (B+ C)+(3A + C) ` ` rArr 2A + B = 0 , B + C =3, 3A + C = 2` `rArrA = (-1)/(5) , B =(2)/(5) , C= (13)/(5) ` `therefore A + C + B =(-1)/(5)+(13)/(5)- (2)/(5) ` ` = 2 `

Discussion

4500.	I : The point on the line2x+3y=5 which is equidistant from (1, 2), (3, 4) is (4, 1). II : The point equidistant to the lines 4x+3y+10=0, 5x-12y+26=0, 7x+24y-50=0 is (0, 0).
Answer» only I is TRUE only II is true both I and II are true NEITHER I nor II are true ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in .

Evaluate the following integrals. intsqrt(3+8x-3x^(2))dx

Let the vectors a and b be such that |a|=3 and |b|=(sqrt(2))/(3), then axxb is a unit vector, if the angle between a and b is

Assertion (A): The director circle of x^(2)+y^(20=4 is x^(2)+y^(2)= Reason(R): The angle between the tangents from any point on x^(2)+y^(2)=8 to x^(2)+y^(2)=4 is (pi)/2 The correct answer is

Find the maximum possible number of real roots of the equation. x^(5)-6x^(2)-4x+5=0.

A is 3xx3 matrix and det(A) =7.IF B= adj A then det(AB)= …........

Method of integration by parts : int (logx)/((x+1)^(2))dx=.....

15 people are to travel by a bus which can carry 9 inside and 6 outside. The number of ways can the party be distributed between inside and outside, if 3 people refuse to go out side and 2 will refuse to go inside is

The median from the following data

If three numbers are chosen from 1 to 200. Find the probability for the three chosen numbers to be not consecutive.

Let G denote the set of all n xx n non - singular matrices with rational numbers an entries. Then under matrix multiplication

Solutions of the equation x|x+1|+1=0 are

The solution set of |3x-2| lt 1is

A man is know to speak truth 4 out of 5 times. He tossed a coin and reports that it is head. Find the probability that it is actually head.

Fromthe two systemsof linesx-h=0 , h=0,1,2,3,4,5 and y-k=0,1,2,3thenumberif squaresthat canbe formedis

Triangle PQR above is equilateral with PQ = 44. The ratio ST to TU is 8:4. What is the length of bar(SQ)?

If a*b=a^b then (2*1)*2=

If {:(f(x),=(log)(sec^2x)^(cot^2x),",","for"x != 0),(,=k, ",","for"x = 0):} is continuous at x = 0 then k is

The sum of the series 1+(2)/(3)((1)/(8))+(2xx5)/(3xx6)((1)/(8))^2+(2xx5xx8)/(3xx6xx9)((1)/(8))^2+………. is

Evaluate intsqrt((5-x)/(x-2)dx.

Find the position vector of R which divides the line segment joining the points A(1,-2,1)andB(1,4,-2) internally in the ratio 2:1

Evaluate the following determinants: [[14,3,28],[17,9,34],[25,9,50]]

Sum of the series (1)/(2)((1)/(2)+(1)/(3))-(1)/(4)((1)/(2^(2))+(1)/(3^(2)))+(1)/(6)((1)/(2^(3))+(1)/(3^(3)))-... is

If the product of the slopes of the tangents drawn from an external point P to thehyperbola(x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is a constant k^(2), then thelocus of P is

Two of the straight lines given by 3x^(3)+3x^(2)y-3xy^(2)+dy^(3)=0 are at right angles, if

The set(A cup B cup C) cap (A cap B^(c ) cap C^(c ))^(c ) cap C^(c ) is equal to

Let f(x)" then "g(x) be two functions having finite non-zero thirdorder derivatives. If : f(x)*g(x)=1 ," for all "x inR," then: "(f''')/(f)-(g'')/(g')=

If a_(1) = 4 and a_(n + 1) = a_(n) + 4n for n gt= 1, then the value of a_(100) is

If x = -9 is a root of |{:(x,3,7),(2,x,2),(7,6,x):}|=0, then other two roots are "..........".

Let y = f(x) satisfies the differential equation (sin x)dy + (cos x)ydx = e^(x) dx with f(0) = 0. Then the value of lim_(x to 0)f(x) is

Find the shortest distance between the linesvecr=(4hati-hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk).

If the equation x^(2) + y^(2) - 2x -2y+ c=0 represents an empty set then find the value of c.

Solve the following linear programming problem graphically: Minimise Z=200x+500y subject to the constraints: x+2yge10 3x+4yle24 xge0,yge0

Mean and variance of binomial distribution of random variance X are 4 and 2 respectively then P(X = 1) =……….

therestrictionon n, k andp so thatPY +Wywill bedefined are :

If |cosec x|=(5pi)/(4)-|(x)/(2)AA x in(-2pi,2pi), then the number of solutions are

If ""^(n)P_(3)=1320, find n.

Findproducts : [[1,0],[0,1]][[1,2],[3,4]]

The logically equivalen proposition of p hArr q is

int_(0)^(oo) (45a)/((3+a+a t)^(4))dt=

Let f(x) be a real function not identically zero in Z, such that for all x,y in R f(x+y^(2n+1))=f(x)={f(y)^(2n+1)}, n in Z If f'(0) ge 0, then f'(6) is equal to

Compute the area of the surface formed by revolving the lemniscate rho = a sqrt(cos 2 varphi) about the polar axis.

If (3x+2)/((x+1)(2^(2)+3))=(A)/(x+1)-(Bx+C)/(2x^(2)+3), then A+B-C=

Find the order and degree (if defined) of the differential equation ((d^(2)y)/(dx^(2)))+((dy)/(dx))^(2)+sin(dy/dx)+1=0

If (1 + 3 + 5 + …. +P ) + (1 + 3 + 5 + …. Q) = (1 + 3 + 5 + … r) where each set of parentheses contains the sum of consecutive odd integers as shown, the smallest possible value of p + q + r,is

If the letters of the word "ATTEMPT" are written down at random. The probability that all the T's come together is

Let S be the set of circles x^(2)+y^(2)=r^(2)" for "r=1, 2 and 3 and T be the set of lines y= x+ksqrt(2)" for "k=0, ne 1 and pm 2. Find the number of distinct points of intersection of the graphs of set S and T.

If(3x +2 ) /((x + 1 )(2x ^ 2+ 3 )) =(A)/(x + 1 )+ (Bx + C)/(2x ^ 2+3 ),then A + C - Bisequalto

I : The point on the line2x+3y=5 which is equidistant from (1, 2), (3, 4) is (4, 1). II : The point equidistant to the lines 4x+3y+10=0, 5x-12y+26=0, 7x+24y-50=0 is (0, 0).

If ab=a^b then (21)*2=