28278 + Interview Questions in Maths in Class 12

1.	Find the set E of the vlaues of x for which the binomia expansions for the following are valid (i) (3-4x)^((3)/(4)) "" (ii) (2+5x)^((-1)/(2)) ""(iii) (7-4x)^(-5)
Answer» SOLUTION :N/A

Discussion

2.	If 4bar(a)+5bar(b)+9bar( c )=0 then (bar(a)xx bar(b))xx[(bar(b)xx bar( c ))xx(bar( c )xx bar(a))] = ………..
Answer» Perpendicular vector to the PLANE `BAR(a),bar(b)` and `bar( C )` Scalar QUANTITY `bar(0)` None of these Answer :C

Discussion

3.	P(x) is a polynomial satisfying P(x+3//20) = P(x), for all x. If P(5) =8 , then P(8) equals
Answer» 5 19/2 8 None of these Answer :C

Discussion

4.	Find the probability that a leap year contains (a) 52 mondays and 52 Sundays (b) 52 Mondays and 52 Wednesdays (c) 52 Sundays and 53 Mondays
Answer» Answer :(a) `(4)/(7)` (b) `(3)/(7)` (c) `(1)/(7)`

Discussion

5.	4/(n-3)=5/(n+2) Given the equation above, what is the value of n?
Answer» -7 -2 8 23 Answer :D

Discussion

6.	int_(3)^(4) (dx)/(root(3)(ln x))=
Answer» `LT (1)/(2)` `gt (1)/(2)` `=(1)/(2)` `lt 0` Answer :2

Discussion

7.	An urn contains 5 red and 2 black identical balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the values of X? Is X a random variable?
Answer» Solution :Sample space S={RR, RB, BR, BB} X is a REAL valued function DEFINED on S, which is taking the DISTINCT value 0,1,2. `therefore` X is a random variable.

Discussion

8.	The value of [vec(a)-vec(b) vec(b)-vec(c) vec(c)-vec(a)] is equal to
Answer» 0 1 `2[VEC(a)vec(b)vec(c)]` 2 Answer :A

Discussion

9.	The locus of z satisfying the inequality log _((1)/(3)) \|z + 1\| gt log_((1)/(3)) \| z- 1\| is
Answer» Re `(Z) GT 0` Re `(z) LT 0` IM `(z) gt 0` Im `(z) lt 0` ANSWER :B

Discussion

10.	Statement -I: The moon's distance from the earth is 36xx10^4 km and its diameter subtends an anlgeof 31' at the eye of the observer. The diameter of moon is 3247.62 km. Statement -II : Angle subtends at any point theta^c=("arc length ")/("radius")
Answer» ANSWER :A

Discussion

11.	int_(1)^(e^(3))(dx)/(x sqrt(1+ln x))=
Answer» 1 2 e 2e Answer :B

Discussion

12.	If P(n): "''" 2^(2n)-1 is divisible by k for all n in N"''"is true, then the value of 'K' is
Answer» 1)6 2)3 3)7 4)2 Answer :B

Discussion

13.	If E and F are events with P(E)leP(F) and P(EnnF)gt0, then
Answer» OCCURRENCE of E implies occurrence of F occurrence of F implies occurrence of E non-occurrence of E implies non-occurrence of F None of the above IMPLICATIONS HOLDS ANSWER :D

Discussion

14.	Evaluate P(Acup B) ,if 2 P (A)= P(B) = (5)/(13) and P (A//B) = (2)/(5)*
Answer» ANSWER :`(11)/(26)`

Discussion

15.	Ife^(x) = y + sqrt(1+y^2) then y =
Answer» `(E^(X) +e^(-x))/2` `(e^(x)-e^(-x))/2` `e^(x)+e^(-x)` `e^(x)-e^(-x)` ANSWER :B

Discussion

16.	If the sum of the coefficients in the expansion of (a^(2)x^(2) - 6ax + 11)^(10), where a is constant, is 1024, then the value of a is
Answer» 5 1 2 3 Answer :D

Discussion

17.	Focus of parabola y = ax^(2) + bx + c is
Answer» `((-b)/(2a).(b^(2)-4ac+1)/(4A))` `((-b)/(2a).(4ac-b^(2)+1)/(4a))` `((-b)/(2a).(b^(2)-4ac-1)/(4a))` `((b)/(2a).(b^(2)-4ac+1)/(4a))` Answer :B

Discussion

18.	The sequence {a_(n)} is defined by formula a _(0) =4 and a _(m +1)=a _(n)^(2) -2a_(n) + 2forn ge 0. Let the sequence { b _(n)} is defined by formula b _(0) =1/2 and b _(n) = (2 a_(0) a _(1) a _(2)……a _(n-1))/(AA n ge 1. The sequence {b _(n)}satisfies the recurrence formula :
Answer» `b _(N+1)=(2B _(n ))/(1- b _(n)^(2))` `b _(n+1)=(2b _(n ))/(1+ b _(n)^(2))` `(b _(n ))/(1+ b _(n)^(2))` `(b _(n ))/(1- b _(n)^(2))` Answer :B

Discussion

19.	The sequence {a_(n)} is defined by formula a _(0) =4 and a _(m +1)=a _(n)^(2) -2a_(n) + 2forn ge 0. Let the sequence { b _(n)} is defined by formula b _(0) =1/2 and b _(n) = (2 a_(0) a _(1) a _(2)……a _(n-1))/(AA n ge 1. The value of n which b _(n) =(3280)/(3281) is :
Answer» 2 3 4 5 Answer :B

Discussion

20.	A vector alongthe bisector of angle between the vectors vecb and vecc is,
Answer» `(2+sqrt(3))HATI + (1-sqrt(3))hatj+(2+sqrt(3))hatk` `(2+sqrt(3))hati+(1-sqrt(3))hatj-(2+sqrt(3))hatk` `(2+sqrt(3))hati-(1-sqrt(3))hatj-(2+sqrt(3))hatk` `(2+sqrt(3))hati-(1-sqrt(3))hatj+(2+sqrt(3))hatk` SOLUTION :Vector along the bisectors is `(hati-hatj+hatk)/sqrt(3) + (4hati+2hatj+4hatk)/6` `1/3(2+sqrt(3))hati+(1-sqrt(3))hatj+(2+sqrt(3))hatk` `THEREFORE` VECTORS is `(2+sqrt(3))hati+(1-sqrt(3))hatj+(2+sqrt(3))hatk`

Discussion

21.	One die and a coin tossed simultaneously find the probability of getting 5 on the top of the die and a tail on the coin.
Answer» ANSWER :`(1)/(12)`

Discussion

22.	int(1)/(x^(2)(x^(4)+1)^((3)/(4)))dx=..+c
Answer» `(1+(1)/(X^(4)))^((1)/(4))` `(x^(4)+1)^((1)/(4))` `(1-(1)/(x^(4)))^((1)/(4))` `-(1+(1)/(x^(4)))^((1)/(4))` ANSWER :D

Discussion

23.	If x+3y le 60, x+y ge 10, x le y , x ge 0, y ge 0 then the minimum value of f=2x+9y is
Answer» 60 90 120 180 Answer :D

Discussion

24.	Complex salt has two parts-one is ionisation sphere and another is coordination sphere. According to IUPAC nomenclature of complex, first we name positive ion then negative ion. According to VBT, metal ion should have vacent orbital equal to its coordination number. If ligand is strong field, pairing of electrons takes place. In the case of weak field ligand, pairing of electrons does not take place, generally. Crystal field splitting of d-orbitals of tetrahedral complex is just opposite to that octahedral complex.
Answer» `[Ni(CO)_(4)]` `[PD(NH_(3))_(4)]Cl_(2)` `[Fe(CO)_(5)]` `K_(2)[ZnCl_(4)]` Solution :`Pd^(+2)` in Coordination number 4 is square planar.

Discussion

25.	Complex salt has two parts-one is ionisation sphere and another is coordination sphere. According to IUPAC nomenclature of complex, first we name positive ion then negative ion. According to VBT, metal ion should have vacent orbital equal to its coordination number. If ligand is strong field, pairing of electrons takes place. In the case of weak field ligand, pairing of electrons does not take place, generally. Crystal field splitting of d-orbitals of tetrahedral complex is just opposite to that octahedral complex. If Delta_(0)=45000 unit, find out the value of Delta(t)
Answer» 2000 unit 20000 unit 45000 unit 11250 unit SOLUTION :`Delta_(t)=(4)/(9)Delta_(0)` `Delta_(t)=(4)/(9)xx45000=20,000" Unit"`

Discussion

26.	The coefficient ofx^(n) in the expansion of(1+x)(1-x)^(n) is
Answer» `N-1` `(-1)^(n)(1+n)` `(-1)^(n-1)(n-1)^(2)` `(-1)^(n-1)n`. ANSWER :B

Discussion

27.	Verify Mean value theorem, if f(x)= x^(2)-4x-3 in the interval [a,b] where a=1 and b=4
Answer» ANSWER :`C = 5//2 I (1" "4)` and CONCLUSION is must

Discussion

28.	Find an anti derivative (or integral) of the following functions . cos 3x
Answer» ANSWER :`1/3sin3x`

Discussion

29.	The value of (1.01)^(-2) correct to two decimal place is
Answer» 0.98 0.97 0.96 0.99 Answer :A

Discussion

30.	Express the following relationson A to B in each case in tabular form A = B = R f = {(x,y) : x^2 + y^2 = 1 and abs(x-y) = 1 }
Answer» SOLUTION :A = B = R F = `{(x,y) : x^2 + y^2 = 1` and `abs(x-y) = 1}` = {(0,1) (1,0), (-1,0), (0,-1)}

Discussion

31.	I : The equation of the circles cencentric with x^(2)+y^(2)-2x+8y-23=0 and passing through (2,3) is x^(2)+y^(2)-2x+8y-33=0 II. The equation of the circles passing through the points (1,1), (2,-1),(3,2) is x^(2)+y^(2)-5x+y+4=0
Answer» only I is true only II is true both I and II are true neither I nor II true Answer :C

Discussion

32.	Rate of increase in surface area of a sphere w.r.t radius is ……….
Answer» `8pi` (DIAMETER) `3PI` (diameter) `4PI` (diameter) `8pi` (RADIUS) ANSWER :D

Discussion

33.	IF a,b,cbe thenumberof positiveintegralintegraldivisorsof 2520, 1800 , 2880then theascendingorderof a,b,c is
Answer» a,B,C b, c ,a c, a, b a, c,b Answer :B

Discussion

34.	Find the angle between the planes whose vector equations are vecr.(2hati+2hatj-3hatk)=5 and vecr.(3hati-3hatj+5hatk)=3
Answer» ANSWER :`cos^(-1)((15)/(SQRT(731)))`

Discussion

35.	The probability distribution of a random variable X taking values 1, 2, 3, 4, 5 is given a. find the value of p . b. Find the mean of X c. Find the variance of X
Answer» ANSWER :`(367)/(256)`

Discussion

36.	STATEMENT-1 : If lines y = m_(1)x and y = m_(2)x are the conjugate diameter of the hyperbola xy = c^(2) then m_(1) + m_(2) =0. and STATEMENT-2 : Two lines are called conjugate diameter of hyperbola if they bisect the chords parallel to each other.
Answer» Statement-1 is TRUE, statement-2 is true, Statement -2 is a correct explanation for Statement -1 Statement -1 is true, Statement-2 is true , Statement-2 is NOT a correct explanation for statement-1 Statement-1 is true, Statement-2 is FALSE Statement-1 is False, Statement-2 is true Answer :A

Discussion

37.	Area lying between parabola y^(2)=4axand it's latuscrectum is
Answer» `(4)/(3)a^(2)` sq unit `(16)/(3)a^(2)` sq unit `(8)/(3)a^(2)` sp unit None of these Solution :Required AREA `=2int_(0)^(a)sqrt(4ax)dx` `=4sqrt(a)xx(2)/(3)[x^(3//2)]_(0)^(a)` `=(8)/(3)a^(2)` sq unit

Discussion

38.	If f(x)sinx cos xdx=(1)/(2(b^(2)-a^(2)))logf(x)+c, where c is constant of integration then f(x)=
Answer» `(2)/((B^(2)-a^(2))sin2x)` `(2)/(absin2x)` `(2)/((b^(2)-a^(2))COS2X)` `(2)/(abcos 2x)` ANSWER :C

Discussion

39.	Evalute the following integrals int ((" sin x - cos x"))/(("sin x + cos x")sqrt(" sin x cos x + " sin^(2) x cos^(2) x))dx
Answer» ANSWER :` - tan^(-1) ( SQRT((sin x + COS x )^(4) - 1)) + C `

Discussion

40.	IF alpha , beta are the roots of x^2+bx+c=0, gamma,delta are the roots of x^2+b_1x+c_1=0 and gamma lt alpha lt delta lt beta, then (c-c_1)^2 lt
Answer» `(b_1-b)(bc_1-b_1c)` 1 `(b-b_1)^2` `(c-c_1)(b_1c-b_1c_1)` ANSWER :A

Discussion

41.	State whether the following statements are true or false, Justify. (i) For an arbitraty binary opertion on a set N, aa =a AA a in N. (ii) If is a commutative binary opertion on N, then a (b c) = (cb) *8a
Answer» ANSWER :(II) FALSE (ii) TRUE

Discussion

42.	If the unit vectors bar(a),bar(b) and bar( c )are coplanar then [2bar(a)-bar(b),2bar(b)-bar( c ),2bar( c )-bar(a)] = ……
Answer» 0 1 `-SQRT(3)` `sqrt(3)` ANSWER :A

Discussion

43.	Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, T_(A)//T_(B), is :
Answer» `(1)/(2)` 1 2 `sqrt((1)/(2))` Solution :NA

Discussion

44.	Evaluate the definite integrals int_(1)^(2)(5x^(2))/(x^(2)+4x+3)
Answer» ANSWER :`5-5/2(9log5/4-log3/2)`

Discussion

45.	m' men and 'n' women are to be seated in a row so that no two women sit next to each other. If mgen then the number of ways in which this can be done is
Answer» `((m+N)!)/(m!n!)` `(m!(m+1)!)/(n!(n+1)!)` `(m!(m+1)!)/((m-n+1)!)` m!n! ANSWER :C

Discussion

46.	Find the equation of chord of contact of A(2,3) w.r.t to parabola y^(2) = 4x. Find the points where chord of-contact meets the parabola using these find the equations of tangents passing through A to the given parabola
Answer» Answer :2x-3y + 4 = 0: (1 ,2), (4,4), X-y + 1= 0, x- 2Y + 4 = 0

Discussion

47.	Find the derivative of In_xa.
Answer» SOLUTION :`d/dxlog,a-d/dx(Ina)/(Inx)=Ina(-1)(Inx)^-2 1/X=(-Ina)/(x(Inx0^2))`

Discussion

48.	Prove that \|{:(1,,beta gamma+alpha delta,,beta^(2) gamma^(2)+alpha^(2),delta^(2)),(1,,gamma alpha+beta delta,,gamma^(2)alpha^(2)+beta^(2)delta^(2)),(1,,alpha beta + gamma delta ,,alpha^(2)beta^(2)+gamma^(2) delta^(2)):}\|
Answer» Solution :`\|{:(1,,beta gamma+alpha DELTA,,beta^(2) gamma^(2)+alpha^(2),delta^(2)),(1,,gamma alpha+beta delta,,gamma^(2)alpha^(2)+beta^(2)delta^(2)),(1,,alpha beta + gamma delta ,,alpha^(2)beta^(2)+gamma^(2) delta^(2)):}\|` APPLYING`R_(1) to R_(1) -R_(2) " and" R_(2) to R_(2) -R_(3)` `Delta = \|{:(0,,beta(gamma -delta)+alpha (delta -gamma),,beta^(2)(gamma^(2)-delta^(2))+alpha^(2)(delta^(2)-gamma^(2))),(0,,gamma(alpha-delta)++beta (delta-alpha),,gamma^(2)(alpha^(2)-delta^(2))+beta^(2)(delta^(2)-alpha^(2))),(1,,alpha beta +gamma delta ,,alpha^(2) beta^(2) +gamma^(2) delta^(2)):}\|` `=(gamma -delta )(alpha -delta)\|{:(0,,beta -alpha,,beta^(2)(gamma +delta)-alpha^(2)(gamma +delta)),(0,,gamma - beta ,,gamma^(2) (alpha+delta)),(1,,alpha beta + gamma delta ,,alpha^(2) beta ^(2) + gamma^(2) delta^(2)):}\|` ` \|{:(0,,beta-alpha,,(beta^(2)-alpha^(2))(gamma+delta)),(0,,gamma-beta,,gamma^(2)(alpha+delta)-beta^(2)(alpha+delta)),(1,,alphabeta+gammadelta,,alpha^(2)beta^(2)+gamma^(2)delta^(2)):}\|` `= (gamma -delta )(alpha-delta)(beta-alpha)(gamma-beta)\|{:(0,,1,,(beta+alpha)(gamma+delta)),(0,,1,,(gamma+beta)(alpha+delta)),(1,,alpha beta+gamma delta,,a^(2)beta^(2)+gamma^(2)delta^(2)):}\|` `\|{:(1,,(beta+alpha)(gamma+delta)),(1,,(gamma+beta)(alpha+delta)):}\|` `=(gamma - delta(alpha - delta)(beta-alpha)(gamma-beta)(gammadelta+alpha beta - beta gamma - alpha delta)` `=(gamma-delta) (alpha-delta)(beta-alpha)(gamma-beta)(beta-delta)(alpha-gamma)` `=-(alpha-delta)(beta-delta)(gamma-delta)(alpha-delta)(beta -gamma) (gamma - alpha)`

Discussion

49.	If Integration using rigonometric identities : int(sec^(2)x)/((1+tanx)(2+tanx))dx we can take .... As substitution.
Answer» `1+tanx=t` `2+tanx=t` `tanx=t` NONE of these Answer :C

Discussion

50.	A bag A contains 1 white and 6 red balls. Another bag contains 4 white and 3 red balls. One of the bags is selected at random and a ball is drawn from it, Which is found to be white. Find the probability that the ball drawn is from the bag A.
Answer» ANSWER :`1/5`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Find the set E of the vlaues of x for which the binomia expansions for the following are valid (i) (3-4x)^((3)/(4)) "" (ii) (2+5x)^((-1)/(2)) ""(iii) (7-4x)^(-5)

If 4bar(a)+5bar(b)+9bar( c )=0 then (bar(a)xx bar(b))xx[(bar(b)xx bar( c ))xx(bar( c )xx bar(a))] = ………..

P(x) is a polynomial satisfying P(x+3//20) = P(x), for all x. If P(5) =8 , then P(8) equals

Find the probability that a leap year contains (a) 52 mondays and 52 Sundays (b) 52 Mondays and 52 Wednesdays (c) 52 Sundays and 53 Mondays

4/(n-3)=5/(n+2) Given the equation above, what is the value of n?

int_(3)^(4) (dx)/(root(3)(ln x))=

An urn contains 5 red and 2 black identical balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the values of X? Is X a random variable?

The value of [vec(a)-vec(b) vec(b)-vec(c) vec(c)-vec(a)] is equal to

The locus of z satisfying the inequality log _((1)/(3)) |z + 1| gt log_((1)/(3)) | z- 1| is

Statement -I: The moon's distance from the earth is 36xx10^4 km and its diameter subtends an anlgeof 31' at the eye of the observer. The diameter of moon is 3247.62 km. Statement -II : Angle subtends at any point theta^c=("arc length ")/("radius")

int_(1)^(e^(3))(dx)/(x sqrt(1+ln x))=

If P(n): "''" 2^(2n)-1 is divisible by k for all n in N"''"is true, then the value of 'K' is

If E and F are events with P(E)leP(F) and P(EnnF)gt0, then

Evaluate P(Acup B) ,if 2 P (A)= P(B) = (5)/(13) and P (A//B) = (2)/(5)*

Ife^(x) = y + sqrt(1+y^2) then y =

If the sum of the coefficients in the expansion of (a^(2)x^(2) - 6ax + 11)^(10), where a is constant, is 1024, then the value of a is

Focus of parabola y = ax^(2) + bx + c is

The sequence {a_(n)} is defined by formula a _(0) =4 and a _(m +1)=a _(n)^(2) -2a_(n) + 2forn ge 0. Let the sequence { b _(n)} is defined by formula b _(0) =1/2 and b _(n) = (2 a_(0) a _(1) a _(2)……a _(n-1))/(AA n ge 1. The sequence {b _(n)}satisfies the recurrence formula :

The sequence {a_(n)} is defined by formula a _(0) =4 and a _(m +1)=a _(n)^(2) -2a_(n) + 2forn ge 0. Let the sequence { b _(n)} is defined by formula b _(0) =1/2 and b _(n) = (2 a_(0) a _(1) a _(2)……a _(n-1))/(AA n ge 1. The value of n which b _(n) =(3280)/(3281) is :

A vector alongthe bisector of angle between the vectors vecb and vecc is,

One die and a coin tossed simultaneously find the probability of getting 5 on the top of the die and a tail on the coin.

int(1)/(x^(2)(x^(4)+1)^((3)/(4)))dx=..+c

If x+3y le 60, x+y ge 10, x le y , x ge 0, y ge 0 then the minimum value of f=2x+9y is

The coefficient ofx^(n) in the expansion of(1+x)(1-x)^(n) is

Verify Mean value theorem, if f(x)= x^(2)-4x-3 in the interval [a,b] where a=1 and b=4

Find an anti derivative (or integral) of the following functions . cos 3x

The value of (1.01)^(-2) correct to two decimal place is

Express the following relationson A to B in each case in tabular form A = B = R f = {(x,y) : x^2 + y^2 = 1 and abs(x-y) = 1 }

I : The equation of the circles cencentric with x^(2)+y^(2)-2x+8y-23=0 and passing through (2,3) is x^(2)+y^(2)-2x+8y-33=0 II. The equation of the circles passing through the points (1,1), (2,-1),(3,2) is x^(2)+y^(2)-5x+y+4=0

Rate of increase in surface area of a sphere w.r.t radius is ……….

IF a,b,cbe thenumberof positiveintegralintegraldivisorsof 2520, 1800 , 2880then theascendingorderof a,b,c is

Find the angle between the planes whose vector equations are vecr.(2hati+2hatj-3hatk)=5 and vecr.(3hati-3hatj+5hatk)=3

The probability distribution of a random variable X taking values 1, 2, 3, 4, 5 is given a. find the value of p . b. Find the mean of X c. Find the variance of X

STATEMENT-1 : If lines y = m_(1)x and y = m_(2)x are the conjugate diameter of the hyperbola xy = c^(2) then m_(1) + m_(2) =0. and STATEMENT-2 : Two lines are called conjugate diameter of hyperbola if they bisect the chords parallel to each other.

Area lying between parabola y^(2)=4axand it's latuscrectum is

If f(x)sinx cos xdx=(1)/(2(b^(2)-a^(2)))logf(x)+c, where c is constant of integration then f(x)=

Evalute the following integrals int ((" sin x - cos x"))/(("sin x + cos x")sqrt(" sin x cos x + " sin^(2) x cos^(2) x))dx

IF alpha , beta are the roots of x^2+bx+c=0, gamma,delta are the roots of x^2+b_1x+c_1=0 and gamma lt alpha lt delta lt beta, then (c-c_1)^2 lt

State whether the following statements are true or false, Justify. (i) For an arbitraty binary opertion **on a set N, a**a =a AA a in N. (ii) If ** is a commutative binary opertion on N, then a ** (b **c) = (c**b) *8a

If the unit vectors bar(a),bar(b) and bar( c )are coplanar then [2bar(a)-bar(b),2bar(b)-bar( c ),2bar( c )-bar(a)] = ……

Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular orbit of radius 2R around the earth. The ratio of their kinetic energies, T_(A)//T_(B), is :

Evaluate the definite integrals int_(1)^(2)(5x^(2))/(x^(2)+4x+3)

m' men and 'n' women are to be seated in a row so that no two women sit next to each other. If mgen then the number of ways in which this can be done is

Find the equation of chord of contact of A(2,3) w.r.t to parabola y^(2) = 4x. Find the points where chord of-contact meets the parabola using these find the equations of tangents passing through A to the given parabola

Find the derivative of In_xa.

Prove that |{:(1,,beta gamma+alpha delta,,beta^(2) gamma^(2)+alpha^(2),delta^(2)),(1,,gamma alpha+beta delta,,gamma^(2)alpha^(2)+beta^(2)delta^(2)),(1,,alpha beta + gamma delta ,,alpha^(2)beta^(2)+gamma^(2) delta^(2)):}|

If Integration using rigonometric identities : int(sec^(2)x)/((1+tanx)(2+tanx))dx we can take .... As substitution.

A bag A contains 1 white and 6 red balls. Another bag contains 4 white and 3 red balls. One of the bags is selected at random and a ball is drawn from it, Which is found to be white. Find the probability that the ball drawn is from the bag A.

State whether the following statements are true or false, Justify. (i) For an arbitraty binary opertion on a set N, aa =a AA a in N. (ii) If is a commutative binary opertion on N, then a (b c) = (cb) *8a