28278 + Interview Questions in Maths in Class 12 Page 91 InterviewSolution

4501.	Find the shortest distance between the linesvecr=(hati+2hatj+hatk)+lambda(hati-hatj+hatk) and vecr=2hati-hatj-hatk+mu(2hati+hatj+2hatk).
Answer» ANSWER :`=(3)/(SQRT2)`

Discussion

4502.	Differentiate the following w.r.t. x : logsin^(-1)(2xsqrt(1-x^(2)))
Answer» ANSWER :`1/(SQRT(1-x^(2))sin^(-1)x),XNE0,pm1`

Discussion

4503.	Solve the following equations : i) 9(x^(2)+(1)/(x^(2)))-27(x+(1)/(x))+8=0 ii) 9sqrt((x)/(x+3))-sqrt((x+3)/(x))=2 iii) sqrt((4x-1)/(4x+1))-sqrt((4x+1)/(4x-1))=(8)/(3) iv) sqrt(3x^(2)+1)+(4)/(sqrt(3x^(2)+1))=5 v) 2(x^(2)+(1)/(x^(2)))-3(x+(1)/(x))=1 vi) x(x+2)(x+3)(x+5)=72 vii) x(x-1)(x+2)(x-3)= -8 viii) (x-1)(x+1)(2x+3)(2x-1)=3
Answer» Answer :i) `{3, (1)/(3), (-1 +- isqrt(35))/(6 )}` ii) 1 iii) `(-5)/(16)` iv) `0, +- SQRT5` v) `{2, (1)/(2), (-1+- isqrt3)/(2)}` vi) `{-6, 1, (-5 +- I sqrt(23))/(2)}` vii) `{-1, 2, (1 +- sqrt(17))/(2)}` VIII) `{(-1)/(2), 0, (-1 +- sqrt(33))/(4)}`

Discussion

4504.	MATCH THE COLUMN {:(Column-I,Column-II),("(A) If "\|a_i\|lt1,lamda_1ge0 " fori=1,2,3,....n and " lamda_1+lamdaa_2+.....+lambda_n=1 and omega " is a complex cube root of unity , then "\|lamdaa_1a_1omega+lamdaa_2omega^2+.......+lamda_na_nomega^n\|" cannot exceed ",(P)\|z\|^n+1/(\|z\|)),((B)"IfRe" (z) gt0 ", then the value of " (Q)2(1+z+z^2+.....+z^n)"can not exceed",(Q)2),("(C) If"omega(ne1)" is a cube root of unity , (R)nthen " 1/sqrt(3)\|1+2omega+3omega^2+......+3nomega^(3n-1)(n inN)" cannot exceed",(R)n),(,(S)1),(,(T)\|a_1\|+\|a_2\|+...\|a_n\|):}
Answer» <P> ANSWER :`(A) -Q,S,T;(B)-P;(C)-R`

Discussion

4505.	If the line 3x+4y+lamda=0 divides the distance between the lines 3x+4y+5=0and3x+4y-5=0 in the ratio of 3:7 then a value of lamda is
Answer» `-2` 2 0 5 Answer :B

Discussion

4506.	If A is an invertible matrix of order 2, then det(A^(-1))=
Answer» DET (A) 1/det(A) 1 0 Answer :B

Discussion

4507.	In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -\|x ^(3)-1\|,, x ge 0):} then find the number of points where g (x)=f (\|x\|) is non-differentiable.
Answer» ANSWER :2

Discussion

4508.	If 8x-2y=10 and 3y-9x=12, then what is the value of y -x ?
Answer» `-8` 2 12 22 Solution :Rearrange the equations to be in the same form, with the y terms before the x terms, and then add: `-2Y + 8X =10` `9(+ (3y -9X =12))/(y-x=22)` The correct ANSWER is (D).

Discussion

4509.	let 0 lt a lt b lt c lt d lt e lt f lt gbe a geometric sequence of integers. Let* (k) denote the number of divisors of k. for example, (6)=4 because, 1,2,3,6 are divisors of 6. if (a)=7, *(g)=13 and d-c=432. then find the value of b:
Answer» ANSWER :972

Discussion

4510.	Let A=(a_(ij))_(3xx3),wherea_(ij) epsilon C the set of complex number.s If det (A)=2-3i, then det (A) equals:
Answer» `1/13(2-3i)` `1/13(2+3i)` `2-3i` `2+3i` ANSWER :B

Discussion

4511.	If f.g is continuous at x=a, then f and g are separately continuous at x= a.
Answer» ANSWER :FALSE

Discussion

4512.	Let lim_(xto0) ([x]^(2))/(x^(2))=m, where [.] denotes greatest integer. Then,
Answer» `-(1)/(SQRT(2))` `(1)/(sqrt(2))` `sqrt(2)` `-sqrt(2)` Solution :`([x]^(2))/(x^(2))=[{:(0", ""if "0LTXLT1),((1)/(x^(2))","" if "-1ltxlt0):}impliesl " does not exist"` `([x]^(2))/(x^(2))=[{:(0", ""if "0ltxlt1),(0","" if "-1ltxlt0):}impliesm" exists and is EQUAL to 0"`

Discussion

4513.	If I=int(cos^(3)xdx)/((sin^(4)x+3sin^(2)x+1)tan^(-1)(sinx+cosecx)) =Alog\|tan^(-1)(sinx+cosecx)\|+C then \|A\| is equal to
Answer» ANSWER :1

Discussion

4514.	Set A has 12 elements. The number of ways of selecting two subsets P and Q of A such that Statement-I : P and Q are disjoint is 3^(12). Statement -II : P and Q have equal number of elements is ""^(24)C_(12). Which of the above statements is true
Answer» only I is true only II is true both I and II are true either I nor II true Answer :C

Discussion

4515.	If A+B+C=pi, then prove the following. cos^2A+cos^2B+2cosA cdot cosB cdot cos C=sin^2 C
Answer» SOLUTION :`cos^2A+cos^2B+cos^2C` `=(1+cos2A)/2+(1+cos2B)/2+(1+cos2C)/2 `(3+cos2A+cos2B+cos2C)/2` `=(3-1-4cosAcosBcosC)/2` `=(2-4cosAcosBcosC)/2` `1-2cosAcosBcosC` or, `cos^2A+cos^2B+2cosAcosBcosC` `=1-cos^2C=sin^2C`

Discussion

4516.	Find the number of whole numbers formed on the screen of a calculator which can read upside done (i.e can be recognized as numbers with unique( correct) digits). It is given thatgreatest numbers that can be formed on the screen of the calculator is 99999999.
Answer» ANSWER :`6xx7^(7)+1`

Discussion

4517.	If A and B are non-empty sets such that AsupB, then
Answer» B'-A'=A-B B'-A'=B-A A'-B'=A-B A'`CAP`B'=B-A Answer :A

Discussion

4518.	Let g (x) = {{:( e ^(2x )"," , AA x lt 0), ( e ^(-2x) "," , AA x ge 0):}. Then g (x\|) does not satisfy the condition
Answer» continuous `AA X in R` not differentiable at `x =0` continuous `AA x in R` and non differentiable at `x =0` g (x) is continuous and differentiable everywhere Answer :D

Discussion

4519.	The number of ways to choose 3 distinct number in increasing GP from the set {1, 2, 3, ……100} is …. And corresponding probability is ………
Answer» ANSWER :`53,53/(.^100C_3)`

Discussion

4520.	Differentiate sin sqrt(x) with respect to x.
Answer» ANSWER :`(COS SQRT(X))/(2sqrt(x))`

Discussion

4521.	A man has 3 coins A, B, C. The coin A is unbiased. The probility that a head will show when B is tossed is 2/3. White it is 1/3 in case of the coin C. A coin is chosen at random and tossed 3 times giving 2 heads and one tall. Find the probability that the coin A was chosen.
Answer» ANSWER :`(9)/(25)`

Discussion

4522.	Consider f(x) = int_(1)^(x)(t + 1t)dtand g(x) = f'(x) for x in [1/2, 3].If P is a point on the curve y = g(x)such that the tangent to curve at P is parallel to a chord joining the points (1/2, g(1/2))and (3,g(3))of the curve, then if ordinate of point P is lambda then sqrt(6) lambda is equal to:
Answer» SOLUTION :`f(x)=int_(1)^(x)(t+(1)/(t))DT` `G(x)=x+(1)/(x)" for "x in [(1)/(2),3]` `g((1)/(2))=(5)/(2),g(3)=(10)/(3)` `P(alpha, g(alpha)),alpha in [(1)/(2),3]` Let `"By L.M.V.T"` `g.(alpha)=(g(3)-g((1)/(2)))/(3-(1)/(2))` `1-(1)/(alpha^(2))=((10)/(3)-(5)/(2))/((5)/(2))=(4-3)/(3)=(+1)/(3)` `alpha^(2)=(3)/(2)rArr alpha=sqrt((3)/(2))` `g(alpha)=sqrt((3)/(2))+(1)/(sqrt(3//2))` `lambda=(5)/(sqrt6)` `lambdasqrt6=5`

Discussion

4523.	cos x+cos y=1/3,sinnx+siny=1/4 then sin(x+y)=
Answer» `7/25` `24/25` `25/24` `25/7` ANSWER :B

Discussion

4524.	If four people are chosen at random, then the probability that no two of them were born in the same day of the week
Answer» <P> ANSWER :`(.^(7)P_(4))/(7^(4))`

Discussion

4525.	If n in N, then lim_(nto oo)[sum_(k=0)^(n)1/(k+1)(""^(n)C_(k))(ksum_(l=1)^(k)(""^(i)C_(k)))+1/(n+l)]^(1//n) is equal to _______.
Answer» ANSWER :2

Discussion

4526.	int (1)/(x sqrt(x^(6) + 1))dx =
Answer» `(1)/(3) "sinh"^(-1) ((1)/(X^(3))) + C` `- (1)/(3) "sinh"^(-1) (x^(3)) + C ` `- (1)/(3)" sinh^(-1)((1)/(x^(3))) + C` `3 " sinh"^(-1) ((1)/(x^(3))) + C ` ANSWER :C

Discussion

4527.	int (1 - x^(7))/(x (1 + x^(7)))" dx = a l n" \|x\| + bln \|x^(7) + 1 \|+ crArr (a,b) =
Answer» `(1 , (2)/(7))` `(1, (-2)/(2))` `(1, (-2)/(7))` `(2 , (-2)/(7)) ` ANSWER :C

Discussion

4528.	Let N = 6 + 66+ 666+…+ 666…66, where there are hundred 6's in the last term in the sum. How many times does the digit 7 occur in the number N ?
Answer» ANSWER :33

Discussion

4529.	Which will elimination CO_(2) only on heating
Answer» `Me-underset(O)underset(\|\|)C-CH_(2)-COOH` `Ph-underset(O)underset(\|\|)C-CH_(2)-SO_(2)H` `CH_(2)=CH-CH_(2)-COOH` ANSWER :A::C::D

Discussion

4530.	Evaluate (i) int_(0)^(4)\|2-x\|dx(ii) int_(a)^(b) (\|x\|)/(x)dx
Answer» ANSWER :(i) 4, (II) `\|b\|-\|a\|`

Discussion

4531.	x + isqrt(x^(4) + x^(2) + 1)) =
Answer» `(SQRT(X^(2) + x + 1) + isqrt(x^(2) - x + 1))/(SQRT2)` `(sqrt(x^(2) + x + 1) - isqrt(x^(2) - x + 1))/(2)` `sqrt( x+1) + isqrt(x -1)` `sqrt(x - 1) +isqrt (x + 1)` Answer :A

Discussion

4532.	The points on the ellipse (x^(2))/(2)+(y^(2))/(10)=1 from which perpendicular tangents can be drawn to the hyperbola (x^(2))/(5)-(y^(2))/(1) =1 is/are
Answer» `(sqrt((3)/(2)),sqrt((5)/(2)))` `(sqrt((3)/(2)),-sqrt((5)/(2)))` `(-sqrt((3)/(2)),sqrt((5)/(2)))` `(sqrt((5)/(2)),sqrt((3)/(2)))` Solution :Required points will lie on the INTERSECTION of ellipse `(X^(2))/(2)+(y^(2))/(10)=1` with director circle of hyperbola `(x^(2))/(5)-(y^(2))/(1) =1` i.e. on `x^(2) + y^(2) =4` `rArr (sqrt(2)cos theta)^(2) + (sqrt(10)sin theta)^(2) =4` Solving, we GET `sin theta = +- (1)/(2), cos theta = +-(sqrt(3))/(2)` `:.` Points are `(+-sqrt((3)/(2)),+-sqrt((5)/(2)))`

Discussion

4533.	Find the equation of the circle for which the point given below are the end points of a diameter. (3,1) ,( 2,7)
Answer» ANSWER :` X^(2) + y^(2) -5X - 8Y + 13=0 `

Discussion

4534.	Let f(x)=([1//2+x ]-[1//2])/x , -1 lex le 2 and f(0) =0([x] is greatest integer less than or equal to x) then
Answer» F is not CONTINUOUS at x=0 f is a continuous FUNCTION on [-1/2,1/2] f is continuous on [-1,0] f is continuouson [0,2] ANSWER :B

Discussion

4535.	Two groups are competing for the positions on the board ofddirectors of acorporation. The probabilities that the first and the secon groups win are 0.6 and 0.4 respectively. Further, if the first group wmS, the probability of introducing a new product is 0.7 and when the second group wins, the correspondmg probability is 0.3. Find the probablity that the new product introduced was by the second group.
Answer» <P> Solution :Let `E_1`= event that the first group wins, `E_2` = event that the SECOND group wins, and E=event that a NEW product in INTRODUCED. Then, `P(E_1)=0.6,P(E_2)=0.4`, `P(E//E_1)=0.7,P(E//E_2)=0.3` Required probability `=P(E_2//E)` `=(P(E//E_2).P(E_2))/(P(E//E_1).P(E_1)+P(E//E_2).P(E_2))`

Discussion

4536.	Let A = {1,2,3,…,n} and B = {x,y}. Then the number of surjections from B into A is
Answer» <P>`""^(n)P_(2)` `2^(n) - 2` `2^(n)-1` NONE of these Answer :D

Discussion

4537.	Solution of the differential equation
Answer» `2y^(2)TAN^(-1)x-1=cy^(2)` `y^(2)tan^(-1)x-1=cy^(2)` `2y^(2)tan^(-1)x+1=cy^(2)` `y^(2)tan^(-1)x+1=cy^(2)` ANSWER :C

Discussion

4538.	Find (dy)/(dx) , ify= sin (x^2+5)
Answer» ANSWER :`= COS (x^2+5)(2X)`

Discussion

4539.	For any vector bara, show that \|bara xx barj\|^2 +\|bara xx bark\|^2 = 2\|bara\|^2.
Answer» ANSWER :`=2\|bara\|^2`

Discussion

4540.	int_(0)^(50)e^({x})dx where {x} denotes the fractional part of x
Answer» ANSWER :`0`

Discussion

4541.	Find the area under the given curves and given lines: (i) y = x^(2), x = 1, x = 2 and x -axis (ii) y = x^(4), x = 1, x = 5 and x -axis.
Answer» ANSWER :(i) `7/3` (II) 624.8

Discussion

4542.	Sketch the curve y=(x^(2)-3x)/((x-1))
Answer» ANSWER :`=-INFTY, x=1`

Discussion

4543.	Let a,b,c in Rbe such that2a +3b +6c =0 and g(x) be the anti derivative of f(x) =ax^2 +bx +c . If the slopes of the tangents drawn to the curve y= g(x) at (1,g(l)) and (2,g(2)) are equal, then
Answer» `a/3=b/(-8) =c/3` `a/6=b/(-18)=c/7` `a/3=b/(-6)=c/2` `a=b =c =-1` Answer :B

Discussion

4544.	If lx+my+n=0 is the perpendicular bisector of the segment of line joining (alpha, beta) and (gamma , beta) then which one of the following is correct ?
Answer» `(gamma-alpha)/(L) =(delta-BETA)/(m) =(-2(l alpha+ m beta+N))/(l ^(2) +m^(2))` `(gamma-alpha)/(l) =(delta-beta)/(m) =(2(l alpha+ m beta+n))/(l ^(2) +m^(2))` `(gamma-alpha)/(l) =(delta-beta)/(m) =(lalpha+ m beta +n)/(l^(2)+ m^(2))` `(gamma-alpha)/(m) =(delta-beta)/(l) =(lalpha+ m beta +n)/(l^(2)+ m^(2))` ANSWER :A

Discussion

4545.	Which of the following is true regarding the diagonals of a parallelogram?
Answer» If diagonals of a parallelogram are of EQUAL LENGTH, then the parallelogram is a square If diagonals of a parallelogram are of equal length, then the parallelogram is a rectangle If diagonals of a parallelogram are of equal length, then the parallelogram is a rhombus If diagonals of a parallelogram are of equal length, then the parallelogram is not a rectangle Answer :B

Discussion

4546.	The mean of marks obtained in an examination by a group of 100 students was found to be 49.96. The mean of the marks obtained in the same examination by another group of 200 students was 52.32, then the mean of the marks obtained by both the groups of students taken together is
Answer» 51.5 52 52.5 53 Answer :A

Discussion

4547.	Find the number of all 4-lettered words (not necessarily having meaning)that can be formed using the letters of the word BOOKLET.
Answer» Solution :We have to 4-LETTERED words USING the LETTERS of the word "BOOKLET". The word contains 7 letters out of which there are 2O's. So there are 6 letters.`:.` The number of 4 lettered words `""^7P_4-""^6P_4`=7654-6543=480.`

Discussion

4548.	Which of the following is trues?
Answer» The diagonal of a kite BISECT each other The diagonal of a kite are at RIGHT angle The diagonal of a kite are congruent The diagonal of a kite bisect eachat right angle Answer :B

Discussion

4549.	If equation x^(2)+ax+b=0, (a, b, in Q) and 2x^(3)+5x^(2)+2x-1=0 may have a common root, then sum of all possible values of (a-b) is :
Answer» Solution :`2x^(3)+5x^(2)+2x-1=(X+1)(2x^(2)+3x-1)` `rArr"either x "=-1 ` is ROOT of EQUATION or `x^(2)+ax+b=0 & 2x^(2)+3x-1=0` have both roots in common.

Discussion

4550.	LetP(n)=(n^5) /(5) +(n^3)/(3) +(7n)/(15)isnaturalnumber, istruestatement
Answer» Onlyfor ` N gt 1` onlyfor NISAN oddpositiveinteger Onlyfor nisan evenpositiveinteger `AAn in N` ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

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

Differentiate the following w.r.t. x : logsin^(-1)(2xsqrt(1-x^(2)))

If the line 3x+4y+lamda=0 divides the distance between the lines 3x+4y+5=0and3x+4y-5=0 in the ratio of 3:7 then a value of lamda is

If A is an invertible matrix of order 2, then det(A^(-1))=

In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0):} then find the number of points where g (x)=f (|x|) is non-differentiable.

If 8x-2y=10 and 3y-9x=12, then what is the value of y -x ?

let 0 lt a lt b lt c lt d lt e lt f lt gbe a geometric sequence of integers. Let* (k) denote the number of divisors of k. for example, *(6)=4 because, 1,2,3,6 are divisors of 6. if *(a)=7, *(g)=13 and d-c=432. then find the value of b:

Let A=(a_(ij))_(3xx3),wherea_(ij) epsilon C the set of complex number.s If det (A)=2-3i, then det (A) equals:

If f.g is continuous at x=a, then f and g are separately continuous at x= a.

Let lim_(xto0) ([x]^(2))/(x^(2))=m, where [.] denotes greatest integer. Then,

If I=int(cos^(3)xdx)/((sin^(4)x+3sin^(2)x+1)tan^(-1)(sinx+cosecx)) =Alog|tan^(-1)(sinx+cosecx)|+C then |A| is equal to

Set A has 12 elements. The number of ways of selecting two subsets P and Q of A such that Statement-I : P and Q are disjoint is 3^(12). Statement -II : P and Q have equal number of elements is ""^(24)C_(12). Which of the above statements is true

If A+B+C=pi, then prove the following. cos^2A+cos^2B+2cosA cdot cosB cdot cos C=sin^2 C

Find the number of whole numbers formed on the screen of a calculator which can read upside done (i.e can be recognized as numbers with unique( correct) digits). It is given thatgreatest numbers that can be formed on the screen of the calculator is 99999999.

If A and B are non-empty sets such that AsupB, then

Let g (x) = {{:( e ^(2x )"," , AA x lt 0), ( e ^(-2x) "," , AA x ge 0):}. Then g (x|) does not satisfy the condition

The number of ways to choose 3 distinct number in increasing GP from the set {1, 2, 3, ……100} is …. And corresponding probability is ………

Differentiate sin sqrt(x) with respect to x.

A man has 3 coins A, B, C. The coin A is unbiased. The probility that a head will show when B is tossed is 2/3. White it is 1/3 in case of the coin C. A coin is chosen at random and tossed 3 times giving 2 heads and one tall. Find the probability that the coin A was chosen.

Consider f(x) = int_(1)^(x)(t + 1t)dtand g(x) = f'(x) for x in [1/2, 3].If P is a point on the curve y = g(x)such that the tangent to curve at P is parallel to a chord joining the points (1/2, g(1/2))and (3,g(3))of the curve, then if ordinate of point P is lambda then sqrt(6) lambda is equal to:

cos x+cos y=1/3,sinnx+siny=1/4 then sin(x+y)=

If four people are chosen at random, then the probability that no two of them were born in the same day of the week

If n in N, then lim_(nto oo)[sum_(k=0)^(n)1/(k+1)(""^(n)C_(k))(ksum_(l=1)^(k)(""^(i)C_(k)))+1/(n+l)]^(1//n) is equal to _______.

int (1)/(x sqrt(x^(6) + 1))dx =

int (1 - x^(7))/(x (1 + x^(7)))" dx = a l n" |x| + bln |x^(7) + 1 |+ crArr (a,b) =

Let N = 6 + 66+ 666+…+ 666…66, where there are hundred 6's in the last term in the sum. How many times does the digit 7 occur in the number N ?

Which will elimination CO_(2) only on heating

Evaluate (i) int_(0)^(4)|2-x|dx(ii) int_(a)^(b) (|x|)/(x)dx

x + isqrt(x^(4) + x^(2) + 1)) =

The points on the ellipse (x^(2))/(2)+(y^(2))/(10)=1 from which perpendicular tangents can be drawn to the hyperbola (x^(2))/(5)-(y^(2))/(1) =1 is/are

Find the equation of the circle for which the point given below are the end points of a diameter. (3,1) ,( 2,7)

Let f(x)=([1//2+x ]-[1//2])/x , -1 lex le 2 and f(0) =0([x] is greatest integer less than or equal to x) then

Let A = {1,2,3,…,n} and B = {x,y}. Then the number of surjections from B into A is

Solution of the differential equation

Find (dy)/(dx) , ify= sin (x^2+5)

For any vector bara, show that |bara xx barj|^2 +|bara xx bark|^2 = 2|bara|^2.

int_(0)^(50)e^({x})dx where {x} denotes the fractional part of x

Find the area under the given curves and given lines: (i) y = x^(2), x = 1, x = 2 and x -axis (ii) y = x^(4), x = 1, x = 5 and x -axis.

Sketch the curve y=(x^(2)-3x)/((x-1))

Let a,b,c in Rbe such that2a +3b +6c =0 and g(x) be the anti derivative of f(x) =ax^2 +bx +c . If the slopes of the tangents drawn to the curve y= g(x) at (1,g(l)) and (2,g(2)) are equal, then

If lx+my+n=0 is the perpendicular bisector of the segment of line joining (alpha, beta) and (gamma , beta) then which one of the following is correct ?

Which of the following is true regarding the diagonals of a parallelogram?

The mean of marks obtained in an examination by a group of 100 students was found to be 49.96. The mean of the marks obtained in the same examination by another group of 200 students was 52.32, then the mean of the marks obtained by both the groups of students taken together is

Find the number of all 4-lettered words (not necessarily having meaning)that can be formed using the letters of the word BOOKLET.

Which of the following is trues?

If equation x^(2)+ax+b=0, (a, b, in Q) and 2x^(3)+5x^(2)+2x-1=0 may have a common root, then sum of all possible values of (a-b) is :

LetP(n)=(n^5) /(5) +(n^3)/(3) +(7n)/(15)isnaturalnumber, istruestatement

let 0 lt a lt b lt c lt d lt e lt f lt gbe a geometric sequence of integers. Let* (k) denote the number of divisors of k. for example, (6)=4 because, 1,2,3,6 are divisors of 6. if (a)=7, *(g)=13 and d-c=432. then find the value of b: