28278 + Interview Questions in Maths in Class 12 Page 98 InterviewSolution

4851.	If f : RrarrR be the functions defined by f(x) = x^(3) + 5, thenf^(-1)(x)is ........
Answer» `(X+5)^(1/3)` `(x-5)^(1/3)` `(5-x)^(1/3)` `5 -x` SOLUTION :N/A

Discussion

4852.	If A(2,-1) and B(6,5) are two points. The ratio in which the foot of the perpendicular from (4,1) to AB divides it, is
Answer» `8:15` `5:8` `-5:8` `-8:5` ANSWER :B

Discussion

4853.	Four person entered the lift cabin on the ground floor of a 7 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first. The probability of all 4 persons leaving at differentfloors is
Answer» `5//18` `7//18` `6//18` none Answer :A

Discussion

4854.	Solve the following problems from (i) to (v) on functional equation. (i) The function f(x) defined on the real numbers has the property that f(f(x)) . (1 + f(x)) = –f(x) for all x in the domain of f. If the number 3 is the domain and range off, compute the value of f(3). (ii) Suppose f is a real function satisfying f(x + f(x)) = 4f(x) and f(1) = 4. Find the value of f(21). (iii) Let 'f' be a function defined from R^(+) to R^(+) . [f(xy)]^(2) = x (f(y))^(2) for all positive numbers x and y and f (2) = 6 , find the value of f (50) . (iv) Let f(x) be a function with two properties (a) for any two real number x and y, f(x + y)= x + f(y) and (b) f(0) = 2. Find the value of f(100). (v) Let f(x) be function such that f(3) = 1 and f(3x) = x + f(3x – 3) for all x. Then find the value of f(300).
Answer» Answer :(i) `(-3)/4`(ii) 64(III) 30(iv) 102(v)5050

Discussion

4855.	Find sum of the order and the degree of the differential equation :((d^(2)y)/( dx^(2))) +2((dx^(2))/(d^(2)y))= y^(2)
Answer» 2 3 4 6 Answer :C

Discussion

4856.	Statement - I : The differential equation of y = 5x - c is y_(1) = 5 Statement - II : The differential equaiton of y = Ae^(-2x) + Be^(5x) is y_(2) - 3y_(1) - 10y = 0 Statement - III : The solution of the differential equation y = Ae^(2x)(c_(1) + c_(2)x+c_(3)x^(2)) is y_(3)-6y_(2) - 12y_(1) - 8y = 0 Which of the above statement is correct.
Answer» I & III II & III I & II I, II & III Answer :C

Discussion

4857.	Find the number of ways in which 5 different books can be arranged on a shelf.
Answer» SOLUTION :The NUMBER of WAYS in which 5 different books can be arranged on a shelf is `5!=54321.=120`

Discussion

4858.	Sum of the coefficients of (1+ x/3 + (2y)/(3))^12
Answer» `2^6` `2^8` `2^12` `10^2` ANSWER :C

Discussion

4859.	Which of the following functions from Z into Z are bijections ?
Answer» `f(X) =x^3` `f(x) = x +2` `f(x) = 2x +1` `f(x) =x^(2)+1` Solution :N/A

Discussion

4860.	If the 6th term in the expansion of ((1)/(x^(8//3))+x^2 log_10 x)^8 is 5600, then the value of x=
Answer» ANSWER :10

Discussion

4861.	If alpha+beta+gamma=2 theta then cos theta+cos(theta-alpha)+cos (theta-beta)+cos(theta-gamma)=
Answer» `4"SIN"(alpha)/2."COS"(beta)/2."sin"(GAMMA)/2` `4"cos"(alpha)/2."cos"(beta)/2."cos"(gamma)/2` `4"sin"(alpha)/2."sin"(beta)/2"sin"(gamma)/2` `4SIN alpha.sin beta.singamma` Answer :B

Discussion

4862.	The slope of the tangent to the curve xy+ax+by=2 at a point (1, 1) then find the value of a and b.
Answer» ANSWER :`a=5, b=-4`

Discussion

4863.	If A,B, and C are three events, then P[Acap(BcupC)] =
Answer» <P>`P(A) + P(B) +P(C)-P(A NN B)-P(A nn C)` `P(A) +P(B) + P(C) - P(B)P(C)` `P(A nn B) + P(A nn C) - P(ANN BnnC)` `P(B nn C) + P(A nn B) - P(A uu B nn C)` ANSWER :C

Discussion

4864.	f(x)= (1)/(2)- tan ((pi x)/(2)) -1 lt x lt 1 and g(x)= sqrt((3+4x-4x^(2))). Find domain of (f + g)
Answer» a.`(-1, 1)` B.`[-(1)/(2), (3)/(2)]` C.`[(-1)/(2), 1]` d.`[(-1)/(2), 1]` ANSWER :D

Discussion

4865.	If D,E and F are respectively the mid points of AB, AC and BC in triangleABC," then "overset(-)(BE)+overset(-)(AF) is
Answer» `OVERSET(-)(DC)` `1/2 overset(-)(BF)` `2 overset(-)(BF)` `3/2 overset(-)(BF)` ANSWER :A

Discussion

4866.	Find the coefficient of x^(8) in ((1+x)^(2))/((1-(2)/(3)x)^(3)).
Answer» ANSWER :`2048/243`

Discussion

4867.	Identify the statement(s) which is/are incorrect?
Answer» the function `f(x)=sinx+COSX` is neither odd nor even the fundamental PERIOD of `f(x)=cos(sinx)+cos(cosx)` is `pi` the RANGE of the function `f(x)=cos(3sinx)` is `[-1,1]` `f(x)=0` is a periodic function with period 2 Solution :NA

Discussion

4868.	A car manufacturing factory has two plants X and Y. Plant X manufactures 70% of tl1e cars and plant Y manufactures 30%. At plant X, 80% of the cars are rated of standard quality and at plant Y, 90% are rated of standard quality. A car is picked up at random and is found to be of standard quality. Find the probability that it has come from plantX.
Answer» <P> SOLUTION :LET `E_1 and E_2` be the EVENTS that the car is manugactured by PLANT X and Y respectively. Let E be the event that the car is of standard quality. Then, `P(E_1)=70/100=7/10,P(E_2)=30/100=3/10`, `P(E//E_1)=80/100=4/5,P(E//E_2)=90/100=9/10` `:. P(E_1//E)=(P(E_1)xxP(E//E_1))/(P(E_1)xxP(E//E_1)+P(E_2)xxP(E//E_2))` `=((7/10xx4/5))/((7/10xx4/5)+(3/10xx9/10))=56/83`.

Discussion

4869.	A mass M is attached to a spring oscillates with a period of 2 sec. If the mass is increased by 2 kg, the period increases by 1 sec. Assuming Hooker's law is obeyed the value of intital mass M is
Answer» `1.6 KG` `1.8 kg` `2.1 kg` `2 kg` ANSWER :A

Discussion

4870.	The solution of (dy)/(dx) = (y + x tan.(y)/(x))/(x) rArr sin.(y)/(x)=
Answer» `CX^(2)` cx `cx^(3)` `cx^(4)` ANSWER :A

Discussion

4871.	Sixfaces of an unbiased die are numbered with 2,3,5,7,11 and 13 . If two such dice are thrown , then the probability that the sum on the uppermost foces of the dice is an odd number , is
Answer» `(5)/(18)` `(5)/(36)` `(13)/(18)` `(25)/(36)` Answer :A

Discussion

4872.	The sum of 10 terms of the series 0.7+ 77+ 777+………is -
Answer» ANSWER :`(7)/(81) (89+ (1)/(10 ^(10)))`

Discussion

4873.	Greg is making a triangular sail for a boat , shaped like a right triangle and shown below . Sail material costs $8.99 for 150 square feet . If the material can be purchased in any quantity , which of the following is closest to the cost in dollars of the material needed to fill the area of the sail as shown ?
Answer» 360 280 200 180 Answer :D

Discussion

4874.	The solution (x+y+1)(dy)/(dx)=1 is
Answer» `y=(X+2)+CE^(x)` `y=-(x+2)+ce^(x)` `x=-(y+2)+ce^(y)` `x=(y+2)^(2)+ce^(y)` ANSWER :C

Discussion

4875.	Ifa, b gt 0 such thata^(2)+b^(2)=2^(5//3).3^(1//3) then find the maximum value of term independent of x in the expansion of (a/2) x^(1//6)+b/3 x^((-1//3))^(9).
Answer» ANSWER :7

Discussion

4876.	Find the number of 4-letter words that can be formed using the letters of the word "ARTICLE which contain the letter A
Answer» ANSWER :480

Discussion

4877.	Find the number of 4-letter words that can be formed using the letters of the word "ARTICLE which contain atleast one of A, E
Answer» ANSWER :720

Discussion

4878.	P, Q, R, S have position vectors bar(p), bar(q), bar(r), bar(s) respectively such that (bar(p)-bar(q))=2(bar(s)-bar(r)), then QS and PR
Answer» PQ and RS BISECT each other PQ and PR bisect each other PQ and RS TRISECT each other QS and PR trisect each other Answer :D

Discussion

4879.	If the primitive of (sinx)/(sqrt(1+sinx))dx is -1sqrtf(x) + sqrt(2)log \|tang(x)\|+C then.
Answer» f(x) = 1 + sin x `g(x) = (3pi//8) - (x//4)` f(x) = 2 (1 - sin x) NONE of these Answer :B

Discussion

4880.	If (pi)/(5) and (pi)/(3) are respectively the arguments of barz_(1) and z_(2) , then the value of Arg (z_(1)- z_(2)) is
Answer» `(pi)/(15)` `(3PI)/(15)` -`(8pi)/(15)` `(4PI)/(15)` ANSWER :C

Discussion

4881.	If a is positive and if A and G are the arithmetic mean and the geometric mean of the roots x^(2)-2ax+a^(2)=0 respectively, then
Answer» A = G A= 2G 2A= G `A^(2)= G` ANSWER :A

Discussion

4882.	Differentiate log(cose^x) with respect to x
Answer» Answer :`-e^(X)tan e^(x), e^(x) ne (2n+1)(PI)/(2), n in N`.

Discussion

4883.	f : R to R : f (x) = cos xis
Answer» ONE-one and into one-one and onto many- one and into many-one and onto Answer :C

Discussion

4884.	A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not take the same three children to the zoo more than once. She finds that the number of times she goes to the zoo is 84 more than a particular child goes to the zoo. Number of children in her class is
Answer» 12 10 60 40 Answer :B

Discussion

4885.	Out of the following,……..is not a unit vector.
Answer» `(COS ALPHA, SIN alpha)` `(-cos alpha,-sin alpha)` `(-COS2ALPHA,sin2alpha)` `(cos2alpha,sin alpha)` ANSWER :D

Discussion

4886.	Let x_(1) and x_(2) be two solutions of the equalition log_(x)(3x^(log_(5)x)+4) = 2log_(5)x , then the product x_(1)x_(2) is equal to
Answer» 2 4 3 1 Solution :LET `x_(1)` and `x_(2)` be two ………….. we have `3X^(log_(5)x)+4=X^(2log_(5)x)` `implies 3t+4=t^(2), where t = X^(log_(5)x)` `implies t = -1 or t = 4` `implies X^(log_(5)x)= -1`(rejected) or `X^(log_(5)x)=4` `implies log_(5) (X^(log_(5)x)) = log_(5)4implies (log_(5)X)^(2) = log_(5)4` `implies log_(5)x= += sqrt(log_(5)4) implies x = 5+- sqrt(log_(5)4)` `:. x_(1)x_(2)= 5sqrt(log_(5)^(4)) x 5^(-sqrt(log_(5)^(4)) = 5^(@) = 1`

Discussion

4887.	int(e^x+2)dx
Answer» SOLUTION :`INT(e^x+2)dx=inte^xdx+2intdx` =`e^x+2x+C`

Discussion

4888.	Let x and y are optimal solution of a LPP, then …
Answer» `Z = LAMBDAX+(1-lambda)y, lambda in R` is ALSO an optimal SOLUTION `Z=lambdax+(1-lambda)y, 0 le lambda le 1` gives an optimal solution `Z=lambdax+(1+lambda)y, 0 le lambda le 1` gives an optimal solution `Z=lambdax+(1+lambda)y, lambda in R` gives an optimal solution Answer :B

Discussion

4889.	Assertion (A): If alpha, beta are the roots of x^(2)-x+1=0, then alpha^(5)+beta^(5)=1 Reason (R) : The roots of x^(2)-x+1=0 are omega,omega^(2).
Answer» Both A, R are true and R EXPLAIN Assertion Both A, R are true but R does't explain A A is true R is FALSE A is false R is true Answer :C

Discussion

4890.	Four slip of papers with the number 1,2,3,4 written on them are put in a box. They are drawn one by one (without replacement) at random. In how many ways it can happen that the ordinal number of atleast one slip coincide with its own number?
Answer» ANSWER :15

Discussion

4891.	If A=[{:(1,0,1),(0,1,2),(0,0,4):}] then show that [3A]=27[A]
Answer» ANSWER :108

Discussion

4892.	If A is an invertible matrix of order 2, then det (A^(-1)) is equal to …….
Answer» DET(A) `1/(det(A))` 1 0 Answer :B

Discussion

4893.	White solving logarithmic equations or logarithmic inequalities care must be taken to ensure that the value of the variable obtained do indeed satisfy the given equation . Often the solution consists in transforming the original equation to form which can be solved with ease . But in bargain the process the transformations carried out are hot always equivalent .In what follows one must verify that the values of veriablesobtained indeed satisfy original equation or inequation. The solution of the inequality The solution of the inequality x log_(1)/(10) (x^(2) + x = 1) gt 0 is given by
Answer» `-oo LT X lt 2` `-oo lt x lt - 1` `- 3 lt x lt 1` `1 lt x lt 3 ` ANSWER :2

Discussion

4894.	Find the maximum or minimum values of the following expressions i) 2x -7 – 5x^(2) ii) 3x^(2)+2x+11 iii) ax^(2)+bx+a, a,b in R, a != 0 iv) x^(2)-x+7
Answer» Answer :i) maximum value = `-(34)/(5)` ii) minimum value = `(32)/(3)` III) If `a gt 0`, minimum value = `(4a^(2)-b^(2))/(4a)` If `a lt 0`, maximum value = `(4a^(2)-b^(2))/(4a)` IV) `a=1 gt 0`, minimum value = `(27)/(4)`

Discussion

4895.	A) Area bounded by sqrt(x)+sqrt(y)=2 and coordinate axes B) Area bounded by y^(2)=4x and x^(2)=4y C) Area bounded by y=4x+x^(2) between x = 0, x = 1, X-axis D) Area bounded by y^(2)=4x and y=2x Arrange the above statements in the ascending order of areas.
Answer» 1) C, B, D, A 2) D, C, A, B 3) A, D, B, C 4) B, A, C, D Answer :B

Discussion

4896.	If (1-p)hati+2(1+p)hatj+(3+p)hatk and 3hati+hatj are at right angle to each other then value of p is :
Answer» -5 3 5 3 Solution :N/A

Discussion

4897.	Match the following from List-I to List-II {:(list-I,list-II),("major axis of"3(x-1^(2))+4(y+2^(2))=12,y-sqrt(2)=0),("minor axis of" 2(x+1^(2))+3(y-1^(2))=6,x-2sqrt(2)=0),("directirx of" x^(2)+2y^(2)=4,y+2=0),("latus rectum of" 2x^(2)+y^(2)=4,x+1=0):}
Answer» 3124 3214 4132 3421 Answer :D

Discussion

4898.	White solving logarithmic equations or logarithmic inequalities care must be taken to ensure that the value of the variable obtained do indeed satisfy the given equation . Often the solution consists in transforming the original equation to form which can be solved with ease . But in bargain the process the transformations carried out are hot always equivalent .In what follows one must verify that the values of veriablesobtained indeed satisfy original equation or inequation. Let S be the set of all solutions x in real numbers of the equation(log_(5) x)^(2) + log_(5x) (5)/(x) = 1 . Thensum _( x in S) x
Answer» 126 `(151)/(25)` `(131)/(25)` 131 Answer :2

Discussion

4899.	Find the number of ways of giving away 20 biscuits (like) to three children so that each gets atleast one and no two gets the same number of biscuits.
Answer» ANSWER :144

Discussion

4900.	Find the area of the triangle formed by the normal at (3,-4) to the circle x^(2) +y^(2) -22x - 4y + 25 = 0 with the co-ordinate axes.
Answer» ANSWER : ` ( 625)/( 24) ` SQ UNITS

Discussion

Explore topic-wise InterviewSolutions in .

If f : RrarrR be the functions defined by f(x) = x^(3) + 5, thenf^(-1)(x)is ........

If A(2,-1) and B(6,5) are two points. The ratio in which the foot of the perpendicular from (4,1) to AB divides it, is

Four person entered the lift cabin on the ground floor of a 7 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first. The probability of all 4 persons leaving at differentfloors is

Find sum of the order and the degree of the differential equation :((d^(2)y)/( dx^(2))) +2((dx^(2))/(d^(2)y))= y^(2)

Find the number of ways in which 5 different books can be arranged on a shelf.

Sum of the coefficients of (1+ x/3 + (2y)/(3))^12

Which of the following functions from Z into Z are bijections ?

If the 6th term in the expansion of ((1)/(x^(8//3))+x^2 log_10 x)^8 is 5600, then the value of x=

If alpha+beta+gamma=2 theta then cos theta+cos(theta-alpha)+cos (theta-beta)+cos(theta-gamma)=

The slope of the tangent to the curve xy+ax+by=2 at a point (1, 1) then find the value of a and b.

If A,B, and C are three events, then P[Acap(BcupC)] =

f(x)= (1)/(2)- tan ((pi x)/(2)) -1 lt x lt 1 and g(x)= sqrt((3+4x-4x^(2))). Find domain of (f + g)

If D,E and F are respectively the mid points of AB, AC and BC in triangleABC," then "overset(-)(BE)+overset(-)(AF) is

Find the coefficient of x^(8) in ((1+x)^(2))/((1-(2)/(3)x)^(3)).

Identify the statement(s) which is/are incorrect?

A mass M is attached to a spring oscillates with a period of 2 sec. If the mass is increased by 2 kg, the period increases by 1 sec. Assuming Hooker's law is obeyed the value of intital mass M is

The solution of (dy)/(dx) = (y + x tan.(y)/(x))/(x) rArr sin.(y)/(x)=

Sixfaces of an unbiased die are numbered with 2,3,5,7,11 and 13 . If two such dice are thrown , then the probability that the sum on the uppermost foces of the dice is an odd number , is

The sum of 10 terms of the series 0.7+ 77+ 777+………is -

The solution (x+y+1)(dy)/(dx)=1 is

Ifa, b gt 0 such thata^(2)+b^(2)=2^(5//3).3^(1//3) then find the maximum value of term independent of x in the expansion of (a/2) x^(1//6)+b/3 x^((-1//3))^(9).

Find the number of 4-letter words that can be formed using the letters of the word "ARTICLE which contain the letter A

Find the number of 4-letter words that can be formed using the letters of the word "ARTICLE which contain atleast one of A, E

P, Q, R, S have position vectors bar(p), bar(q), bar(r), bar(s) respectively such that (bar(p)-bar(q))=2(bar(s)-bar(r)), then QS and PR

If the primitive of (sinx)/(sqrt(1+sinx))dx is -1sqrtf(x) + sqrt(2)log |tang(x)|+C then.

If (pi)/(5) and (pi)/(3) are respectively the arguments of barz_(1) and z_(2) , then the value of Arg (z_(1)- z_(2)) is

If a is positive and if A and G are the arithmetic mean and the geometric mean of the roots x^(2)-2ax+a^(2)=0 respectively, then

Differentiate log(cose^x) with respect to x

f : R to R : f (x) = cos xis

A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not take the same three children to the zoo more than once. She finds that the number of times she goes to the zoo is 84 more than a particular child goes to the zoo. Number of children in her class is

Out of the following,……..is not a unit vector.

Let x_(1) and x_(2) be two solutions of the equalition log_(x)(3x^(log_(5)x)+4) = 2log_(5)x , then the product x_(1)x_(2) is equal to

int(e^x+2)dx

Let x and y are optimal solution of a LPP, then …

Assertion (A): If alpha, beta are the roots of x^(2)-x+1=0, then alpha^(5)+beta^(5)=1 Reason (R) : The roots of x^(2)-x+1=0 are omega,omega^(2).

Four slip of papers with the number 1,2,3,4 written on them are put in a box. They are drawn one by one (without replacement) at random. In how many ways it can happen that the ordinal number of atleast one slip coincide with its own number?

If A=[{:(1,0,1),(0,1,2),(0,0,4):}] then show that [3A]=27[A]

If A is an invertible matrix of order 2, then det (A^(-1)) is equal to …….

Find the maximum or minimum values of the following expressions i) 2x -7 – 5x^(2) ii) 3x^(2)+2x+11 iii) ax^(2)+bx+a, a,b in R, a != 0 iv) x^(2)-x+7

A) Area bounded by sqrt(x)+sqrt(y)=2 and coordinate axes B) Area bounded by y^(2)=4x and x^(2)=4y C) Area bounded by y=4x+x^(2) between x = 0, x = 1, X-axis D) Area bounded by y^(2)=4x and y=2x Arrange the above statements in the ascending order of areas.

If (1-p)hati+2(1+p)hatj+(3+p)hatk and 3hati+hatj are at right angle to each other then value of p is :

Match the following from List-I to List-II {:(list-I,list-II),("major axis of"3(x-1^(2))+4(y+2^(2))=12,y-sqrt(2)=0),("minor axis of" 2(x+1^(2))+3(y-1^(2))=6,x-2sqrt(2)=0),("directirx of" x^(2)+2y^(2)=4,y+2=0),("latus rectum of" 2x^(2)+y^(2)=4,x+1=0):}

Find the number of ways of giving away 20 biscuits (like) to three children so that each gets atleast one and no two gets the same number of biscuits.

Find the area of the triangle formed by the normal at (3,-4) to the circle x^(2) +y^(2) -22x - 4y + 25 = 0 with the co-ordinate axes.