28278 + Interview Questions in Maths in Class 12 Page 556 InterviewSolution

27751.	Statement-1: if A and B are two events, such that 0 lt P(A),P(B) lt 1, then P((A)/(overline(B)))+P((overline(A))/(overline(B)))=(3)/(2) Statement-2: If A and B are two events, such that 0 lt P(A), P(B) lt 1, then P(A//B)=(P(AcapB))/(P(B)) and P(overline(B))=P(A capoverline(B))+P(overline(A) cap overline(B))
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 :d

Discussion

27752.	A circle meets the rectangular hyperbola xy= 1 at A_(1)A_(2),A_(3) and A_(4)bethe distances from the y axis then minimumvalue of d_(1)+d_(2)+d_(3)+d_(4) is
Answer» ANSWER :4

Discussion

27753.	Solve (1-x)^(2))(dy)/(dx)+2xy=xsqrt(1-x^(2))
Answer» ANSWER :`(1)/SQRT(1-x^(2))+C`

Discussion

27754.	An urn contains 25 balls of which 10 balls bear a mark 'X' and the remaining 15 bear a mark 'Y'. A ball is drawn at random from the urn, its mark is noted down and it is replaced. If 6 balls are drawn in this way, find the probability that (i) all will bear 'X' mark. (ii) not more than 2 will bear 'Y' mark. (iii) at least one ball will bear 'Y' mark. (iv) the number of balls with 'X' mark and 'Y' mark will be equal.
Answer» ANSWER :(i) `((2)/(5))^(6)` (ii) `7((2)/(5))^(4)` (iii) `1-((2)/(5))^(6)` (iv) `(864)/(3125)`

Discussion

27755.	alpha,beta,gammaand delta are angles in I,II,II and IV quadrants, respectively and none of them is an integral multiple of pi//2. They form an increasing arithmetic progression.if alpha+beta+gamma+delta=thetaand alpha70^@, then
Answer» `400^@ltthetalt580^@` `470^@ltthetalt650^@` `680^@ltthetalt860^@` `540^@ltthetalt900^@` Solution :`0ltalphalt90^@,90^@ltbetalt180^@` `180^@ltgammalt270^@,270^@ltdeltalt360^@` `rArrgammalt270^@ltalpha+deltalt450^@` `rArr alpha+delta` lies in the I or IV quadrant and cosine in both is positive. If dis the common RATIO of theA.P., then `beta=alpha+d,gamma=alpha+2d,delta=alpha+3d` `rArr beta+gamma=alpha+delta,2(alpha-beta)=-2d=beta-delta` `and alpha+gamma=2beta`, Now, `beta-gamma=-d,alpha-delta=-3d` `270^@ltdeltalt360^@` `rArr 270^@ltalpha+3dlt360^@` `rArr 200^@lt3dlt290^@( :. alpha=70^@)` `rArr400^@lt+6d,580^@` `rArr 680^@lt4alpha+6dlt860^@` `680^@ lttheta lt 860^@`

Discussion

27756.	Probability of an event that newly purchase mobile and laptop will be in working condition after 8 years is(7)/(12) and (7)/(9) respectively. Then .... is the probability that both are not in working condition after 8 years.
Answer» `(5)/(54)` `(14)/(54)` `(49)/(108)` `(14)/(108)` ANSWER :A

Discussion

27757.	alpha,beta,gammaand delta are angles in I,II,II and IV quadrants, respectively and none of them is an integral multiple of pi//2. They form an increasing arithmetic progression.Which of the following does not hold?
Answer» `sin(beta+gamma)=sin(alpha+delta)` `sin(beta-gamma)=sin(alpha-delta)` `tan2(alpha+beta)=tan(beta+delta)` `cos(alpha+gamma)=cos2beta` SOLUTION :`0ltalphalt90^@,90^@ltbetalt180^@` `180^@ltgammalt270^@,270^@ltdeltalt360^@` `rArrgammalt270^@ltalpha+deltalt450^@` `rArr alpha+delta` LIES in the I or IV quadrant and cosine in both is positive. If DIS the common ratio of theA.P., then `beta=alpha+d,gamma=alpha+2d,delta=alpha+3d` `rArr beta+gamma=alpha+delta,2(alpha-beta)=-2d=beta-delta` `and alpha+gamma=2beta`, Now, `beta-gamma=-d,alpha-delta=-3d` `270^@ltdeltalt360^@` `rArr 270^@ltalpha+3dlt360^@` `rArr 200^@lt3dlt290^@( :. alpha=70^@)` `rArr400^@lt+6d,580^@` `rArr 680^@lt4alpha+6dlt860^@` `680^@ lttheta lt 860^@`

Discussion

27758.	Examine the continuity of the function f(x)= \|x\| + \|x-1\| at x=1
Answer» ANSWER :x=1

Discussion

27759.	alpha,beta,gammaand delta are angles in I,II,II and IV quadrants, respectively and none of them is an integral multiple of pi//2. They form an increasing arithmetic progression.Which of the following holds?
Answer» `COS(alpha-delta)GT0` `cos(alpha-delta)=0` `cos(alpha-delta)lt0` `cos(alpha-delta)gt0or cos(alpha-delta)lt0` Solution :`0ltalphalt90^@,90^@ltbetalt180^@` `180^@ltgammalt270^@,270^@ltdeltalt360^@` `rArrgammalt270^@ltalpha+deltalt450^@` `rArr alpha+delta` LIES in the I or IV QUADRANT and cosine in both is positive. If dis the common ratio of theA.P., then `beta=alpha+d,gamma=alpha+2d,delta=alpha+3d` `rArr beta+gamma=alpha+delta,2(alpha-beta)=-2d=beta-delta` `and alpha+gamma=2beta`, Now, `beta-gamma=-d,alpha-delta=-3d` `270^@ltdeltalt360^@` `rArr 270^@ltalpha+3dlt360^@` `rArr 200^@lt3dlt290^@( :. alpha=70^@)` `rArr400^@lt+6d,580^@` `rArr 680^@lt4alpha+6dlt860^@` `680^@ lttheta lt 860^@`

Discussion

27760.	If [x] denotes the greatest intger function then the velue of int_(0.5)^(4.5)[x]dx+int_(-1)^(1)\|x\|dx is
Answer» 9 8 7 6 Answer :A

Discussion

27761.	If 1,omega,omega^2 are the cube roots of unity then prove the followingi) (1-omega+omega^2) + (1+omega-omega^2)^5=32ii) (x+y+z)(x+yomega+zomega^2)(x+yomega^2+zomega)=x^3+y^3+z^3-3xyz
Answer» ANSWER :`i) =-32(-1)=32=R.H.S.` `II)=x^3+y^3+z^3-3xyz=R.H.S`

Discussion

27762.	Prove thaty (""^(4n)C_(2n))/(""^(2n)C_(n))=(1.3.5…..(4n-1))/({1.3.5…..(2n-1)}^(2))
Answer» ANSWER :`therefore (""^(4n)C_(2n))/(""^(2n)C_(N))=(1.3.5....(4n-1))/([1.3.5...(2n-1)]^(2))`

Discussion

27763.	Integrate the functions 1/((x^(2)+1)(x^(2)+4))
Answer» ANSWER :`1/3tan^(-1)x-1/6tan^(-1)x/2+C`

Discussion

27764.	Solve the equation for y as a function of x, satisfying x . int _(0) ^(x) y (t) dt = (x +1) int _(0) ^(x) t, y (t) dt where x gt 0 given y (1) =1.
Answer» ANSWER :125

Discussion

27765.	The minimum length of intercept on any tangent to the ellipse (x^(2))/(4)+(y^(2))/(9)=1 cut by the circlex^(2)+y^(2)=25 is :
Answer» 8 9 2 11 Answer :A

Discussion

27766.	cos 22^(@)+cos 78^(@)+cos80^(@)=
Answer» `4sin 11^(@)sin 39^(@)sin 40^(@)` `1+4cos 11^(@)cos 39^(@)cos 40^(@)` `1+4sin 11^(@)sin 39^(@)SIN40^(@)` `4 cos 11^(@)cos 39^(@)cos 40^(@)` ANSWER :C

Discussion

27767.	Let N be the number of quadratic equations with coefficients from {0, 1, 2, ……..,9} such that zero is a solution of each equation. Then the value of N is
Answer» INFINITE `2^(9)` 90 900 Answer :C

Discussion

27768.	Find the area of the region {(x , y): 0 le y le x^(2)+1, 0le y le x +1, 0lex le2}
Answer» ANSWER :`(23)/(6)`

Discussion

27769.	If \|veca\|=8,\|vecb\| = 3 and \|veca xxvecb\|=12, find veca.vecb
Answer» ANSWER :`12sqrt3`

Discussion

27770.	Evaluate the definite integrals int_(pi/2)^(pi)e^(x)((1-sinx)/(1-cosx))dx
Answer» ANSWER :`E^(pi/2)`

Discussion

27771.	Differentiate (x^(2)-5x + 8) (x^(3) + 7x + 9) in three ways mentioned below: By expanding the product to obtain a single polynomial Do they all give the same answer?
Answer» ANSWER :`5x^(4) -20x^(3) + 45X^(2)- 52x + 11`

Discussion

27772.	Show that the line 7x + 6y = 13 is a tangent to the parabola y^(2) - 7x- 8y + 14 = 0 and find the point of contact
Answer» ANSWER :(1,1)

Discussion

27773.	A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is (1)/(100) . What is the probability that he will win a prizea. atleast once b. exactly once c. atleast twice?
Answer» ANSWER :a. `1- ((99)/(100))^(50)` b. `(1)/(2)((99)/(100))^(49)`, C. `1- (149)/(100)((99)/(100))^(49)`

Discussion

27774.	lim_(x rarr 0) (1-ax)^(1/x) =
Answer» `E^(-a)` e `e^(a)` 1 Answer :A

Discussion

27775.	If vec(a), vec(b), vec(c) are the position vectors of corners A, B, C or a parallelogram ABCD, then what is the position vector of the corner D?
Answer» `VEC(a)+vec(B)+vec(C)` `vec(a)+vec(b)-vec(c)` `vec(a)-vec(b)+vec(c)` `-vec(a)+vec(b)+vec(c)` Solution :Let O be the ORIGIN and ABCD be the parallelogram. In `DeltaODC`, `vec(OD)=vec(OC)+vec(CD)` `vec(CD) = - vec(AB)` and, In `DeltaAOB, vec(AB)=vec(OB)-vec(OA)=vec(b)-vec(a)` Thus, `vec(CD)=-vec(AB)=vec(a)-vec(b)` So, `vec(OD)=vec(c)+vec(b)`[since, `vec(OC)=vec(C) and vec(CD)=vec(a)-vec(b)`]

Discussion

27776.	State with reason whether following functions have inverse : f : {1,2,3,4} rarr {10} with f: {(1,10),(2,10),(3,10),(4,10)}
Answer» SOLUTION :N/A

Discussion

27777.	For each operation * defined below, determine whether * is binary, commutative or associative. (i) On Z, define ab = a-b (ii) On Q, define ab = ab + 1 (iii) On Q, define ab =(ab)/(2) (iv) On Z^(+), define ab = (a)/(b+1) (v) On Z^(+), define ab=a^(b) (vi)On R- {-1}, defineab =(a)/(b+1)
Answer» SOLUTION :(i) `In Z , a b = a-b` Let `a,b in Z` `therefore a * b = a - b` `""b* a = b-a` `therefore a bne b a` Therefore, operation is not commutative. LETA, b, c`in`Z. `thereforea (bc) =a (b-c) =a -(b-c) = a- b +c` ` = a- b+c` ` and(ab) c = (a-b)c = a-b-c` `therefore a b(bc) ne (ab) c` Therefore, operation is not associative . (ii) In Q,ab = ab +1 Let a,b `in` Q `therefore a b= ab + 1=ab +1 = ba` Therefore,operation is commutative . Let a,b, `in` Q `therefore"" a(bC) = a * (bc +1)` `= a(bc + 1) c` `= (ab+1) c+1 = ABC + c+ 1` `ne a(bc)` Therefore, operation isnot associative. (III) In Q `""ab=(ab)/(2)` Let`a,b, in Q` `therefore""ab = (ab)/(2) =(ba)/(2) = ba` Therefore, operation is commutative. Let a,b, `in` Q ` therefore a (bc) = a((bc)/(2)) = (a((bc)/(2)))/(2) = (((ab)/(c))c)/(2)` `= ((ab)c)/(2) = (ab)c` Therefore, operation is commutative. Let `a,bc,in, Z^(+)` `because a(bc) = a(2^(bc)) = 2^(ba) = ba` and `(a b) c = (2^(ab)) c = 2^(ab_(c)) ne a (bc)` Therefore, operation is not associative. (v)In `Z^(+), ""ab = a^(b)` Let `a,b in Z^(+)` `therefore"" ab = a^(b) ne b^(a) ne ba` Therefore, operation is not commutative . Let`a, b,cin Z^(+)` `thereforea(bc)= a (b^(c)) (b^(c)) = a^((b^(c))` and`(ab) c = (a^(b)) c= (a^(b))^(c) = a^(bc)` `therefore""a(bc)ne(ab) c` Therefore , operationis not associative. (vi) InR-{-1} a, `b =(a)/(b+1)` Let a, b `in R - {-1}` `therefore ""ab = (a)/(b+1) ne (a)/(a+1) ne b a` Therefore, operation isnot commutative. Let a,b,c `in R - {-1}` `therefore a(bc) = a((b)/(c+1)) = (a)/(((b)/(c+1))) = (a(c+1))/(b+c+1)` and `(ab)c ((a)/(b+1)) c ((a)/(b+1))/(c+1) = (a)/((b+1)(c+1))` `thereforea* (bc) ne (ab) **c` Therefore, operation is not associative.

Discussion

27778.	An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the possible values of X? Is X a random variable ?
Answer» ANSWER :X is RANDOM VARIABLE.

Discussion

27779.	The maximum value oflog_(20)(3 sin x-4 cos x+15) is equal to :
Answer» 1 2 3 4 Answer :A

Discussion

27780.	Evaluate the following integrals int(dx)/(sinx+sin2x)
Answer» ANSWER :`(1)/(6)log\|1-cosx\|+(1)/(2)log\|1+cosx\|-(2)/(3)log\|1+2cosx\|+c`

Discussion

27781.	int x^(2)tan^(-1)xdx
Answer» ANSWER :`1/6 LOG (1+x^2)+C`

Discussion

27782.	A vertical tower, OP stands at the center O of a square ABCD. Let h and b denotethe length OP and AB respectively. If /_APB=60^(@), what is therelationship beween h and b?
Answer» `2B^(2)=h^(2)` `2H^(2)=b^(2)` `3B^(2)=2h^(2)` `3h^(2)=2b^(2)` ANSWER :B

Discussion

27783.	Solve the differential equation y e^(x)/(y) dx = (x e^(x)/(y) + y^(2))dy ( y ne 0).
Answer» ANSWER :`E^((X)/(y)) = y + C`

Discussion

27784.	int_(0)^(pi//2) x^(2)sin x dx=
Answer» `pi-2` `pi+2` `pi+4` `pi-4` ANSWER :A

Discussion

27785.	The locus of the midpoints of the focal chords of the parabola y^(2)=4ax is
Answer» x+a=0 x+2a=0 x+3a=0 x+4a=0 Answer :D

Discussion

27786.	Every gram of wheat provides 0.1 g of proteins and 0.25g of carbohydrates the correspondin values of rice are 0.05 g and 0.5 , respectively. Wheat costs Rs. 4 per kg and rice Rs. 6. the minimum daily requirements of proteins and carbohydrtes for an average child are 50g annd 200g respectively. then, in what quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirements of proteins and carbohydrates at minimum cost ?
Answer» 400, 200 300, 400 200, 400 400, 300 Answer :A

Discussion

27787.	Find the slope of the tangent to the curve y=x^3-3x+2 at the point whose x-coordinate is 3.
Answer» SOLUTION :`y=x^3-3x+2(DY)/DX=3x^2-3` SLOPE of the TANGENT `=(dy)/dx]_(x=3)=3xx3^2-3=24`

Discussion

27788.	Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.
Answer» ANSWER :`(25)/(102)`

Discussion

27789.	Verify: The value of the determinant remains unchanged if its rows and columns are interchanged. Delta=\|{:(2,-3,5),(6,0,4),(1,5,-7):}\|
Answer» Answer :`M_(11)=-20,M_(12)=46,A_(13)=30,M_(21)=4,M_(22)=-19,M_(23)=-13,M_(31)=-12,M_(32)=22,M_(33)=18` `A_(11)=-20,A_(12)=-46,A_(13)=30,A_(21)=-4,A_(22)=-19,A_(23)=13,A_(31)=-12,A_(32)=-22,A_(33)=18`

Discussion

27790.	d/dx(1/3x^)
Answer» `1 /3x^3` `-2 /3x^3` `1 /6X` `x^2` ANSWER :D

Discussion

27791.	The point which lies in the plane given by the equation 5x + y - z = 7 is
Answer» `(0, - 7, 0)` `(- 7, 0, 0)` `(0, 0, - 7)` `(0, 0, 0)` ANSWER :C

Discussion

27792.	(i)Show that [ vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a vec b vec c]. (ii)If vec a, vec b, vec c are coplanar, prove that vec a + vec b, vec b + vec c, vec c + vec a are also coplanar.
Answer» ANSWER :(i) `(because[VEC a, vec b, vec c] = [vec b, vec c, vec a])` (II)`vec a + vec b , vec b + vec c, vec c + vec a`are coplanar.

Discussion

27793.	Let A be any non zero set more than one elements * is a binary operation on A defined as a* b=a AA a,b in A. Check the commutativity and associativity.
Answer» ANSWER :is ASSOCIATIVE but not COMMUTATIVE

Discussion

27794.	If y =1 (1)/(1!) + (x ^(2))/(2!)+.. then (dy)/(dx)=
Answer» `E ^(X)` `1//1+x` `COS x ` NONE ANSWER :A

Discussion

27795.	Prove that [vecaxxvecbvecbxxveccveccxxveca] = [vecavecbvecc]^2
Answer» Solution :`[vecaxxvecbvecbxxveccveccxxveca] = (VECAXXVECB).[vecbxxvec)xx(veccxxveca)]` [using VECTOR triple product. =`(vecaxxvecb).{(vecbxxvecc)xxveca)vecc-(vecbxxvecc).vecc)veca}` = `(vecaxxvecb).{((vecbxxvecc).veca)vecc}[because (vecbxxvecc).vecc = 0]` =`{vecaxxvecb).vecc} {vecbxxvecc).veca}` =`{veca.(vecbxxvecc} {veca.(vecbxxvecc)}` [therefore In scalar triple product dot and cross can be interchanged and dot product is COMMUTATIVE.] =`{vecavecbvec][vecavecbvecc] = [vecavecbvecc]^2`(Proved).

Discussion

27796.	Digestion of food complete in :-
Answer» Duodenum Jejunum IIeum Colon Answer :A

Discussion

27797.	int_(0)^(pi) (1-x^(2))/((1+x^(2))^(2))dx
Answer» ANSWER :`(1)/(2)`

Discussion

27798.	If A(x)=\|(x+1,2x+1,3x+1),(2x+1,3x+1,x+1),(3x+1,x+1,2x+1)\| then int_(0)^(1) A (x) dx=
Answer» `15` `(-15)/(2)` `-30` `-5` ANSWER :B

Discussion

27799.	For which values of p does the pair of equations given below has unique solution ? 4x+py+8=0 2x+2y+2=0
Answer» SOLUTION :N/A

Discussion

27800.	int((x-1)^(2))/((x^(2)+1)^(2))dx=tan^(-1)x+f(x)+c then f(x)=....
Answer» `TAN^(-1)X+(1)/(x^(2)+1)` `(1)/((x^(2)+1)^(2))` `(1)/(x^(2)+1)` None of these Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

A circle meets the rectangular hyperbola xy= 1 at A_(1)A_(2),A_(3) and A_(4)bethe distances from the y axis then minimumvalue of d_(1)+d_(2)+d_(3)+d_(4) is

Solve (1-x)^(2))(dy)/(dx)+2xy=xsqrt(1-x^(2))

alpha,beta,gammaand delta are angles in I,II,II and IV quadrants, respectively and none of them is an integral multiple of pi//2. They form an increasing arithmetic progression.if alpha+beta+gamma+delta=thetaand alpha70^@, then

Probability of an event that newly purchase mobile and laptop will be in working condition after 8 years is(7)/(12) and (7)/(9) respectively. Then .... is the probability that both are not in working condition after 8 years.

alpha,beta,gammaand delta are angles in I,II,II and IV quadrants, respectively and none of them is an integral multiple of pi//2. They form an increasing arithmetic progression.Which of the following does not hold?

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If [x] denotes the greatest intger function then the velue of int_(0.5)^(4.5)[x]dx+int_(-1)^(1)|x|dx is

If 1,omega,omega^2 are the cube roots of unity then prove the followingi) (1-omega+omega^2) + (1+omega-omega^2)^5=32ii) (x+y+z)(x+yomega+zomega^2)(x+yomega^2+zomega)=x^3+y^3+z^3-3xyz

Prove thaty (""^(4n)C_(2n))/(""^(2n)C_(n))=(1.3.5…..(4n-1))/({1.3.5…..(2n-1)}^(2))

Integrate the functions 1/((x^(2)+1)(x^(2)+4))

Solve the equation for y as a function of x, satisfying x . int _(0) ^(x) y (t) dt = (x +1) int _(0) ^(x) t, y (t) dt where x gt 0 given y (1) =1.

The minimum length of intercept on any tangent to the ellipse (x^(2))/(4)+(y^(2))/(9)=1 cut by the circlex^(2)+y^(2)=25 is :

cos 22^(@)+cos 78^(@)+cos80^(@)=

Let N be the number of quadratic equations with coefficients from {0, 1, 2, ……..,9} such that zero is a solution of each equation. Then the value of N is

Find the area of the region {(x , y): 0 le y le x^(2)+1, 0le y le x +1, 0lex le2}

If |veca|=8,|vecb| = 3 and |veca xxvecb|=12, find veca.vecb

Evaluate the definite integrals int_(pi/2)^(pi)e^(x)((1-sinx)/(1-cosx))dx

Differentiate (x^(2)-5x + 8) (x^(3) + 7x + 9) in three ways mentioned below: By expanding the product to obtain a single polynomial Do they all give the same answer?

Show that the line 7x + 6y = 13 is a tangent to the parabola y^(2) - 7x- 8y + 14 = 0 and find the point of contact

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is (1)/(100) . What is the probability that he will win a prizea. atleast once b. exactly once c. atleast twice?

lim_(x rarr 0) (1-ax)^(1/x) =

If vec(a), vec(b), vec(c) are the position vectors of corners A, B, C or a parallelogram ABCD, then what is the position vector of the corner D?

State with reason whether following functions have inverse : f : {1,2,3,4} rarr {10} with f: {(1,10),(2,10),(3,10),(4,10)}

For each operation * defined below, determine whether * is binary, commutative or associative. (i) On Z, define a*b = a-b (ii) On Q, define a*b = ab + 1 (iii) On Q, define a*b =(ab)/(2) (iv) On Z^(+), define a*b = (a)/(b+1) (v) On Z^(+), define a*b=a^(b) (vi)On R- {-1}, definea*b =(a)/(b+1)

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

The maximum value oflog_(20)(3 sin x-4 cos x+15) is equal to :

Evaluate the following integrals int(dx)/(sinx+sin2x)

int x^(2)tan^(-1)xdx

A vertical tower, OP stands at the center O of a square ABCD. Let h and b denotethe length OP and AB respectively. If /_APB=60^(@), what is therelationship beween h and b?

Solve the differential equation y e^(x)/(y) dx = (x e^(x)/(y) + y^(2))dy ( y ne 0).

int_(0)^(pi//2) x^(2)sin x dx=

The locus of the midpoints of the focal chords of the parabola y^(2)=4ax is

Find the slope of the tangent to the curve y=x^3-3x+2 at the point whose x-coordinate is 3.

Two cards are drawn at random and without replacement from a pack of 52﻿ playing cards. Find the probability that both the cards are black.

Verify: The value of the determinant remains unchanged if its rows and columns are interchanged. Delta=|{:(2,-3,5),(6,0,4),(1,5,-7):}|

d/dx(1/3x^)

The point which lies in the plane given by the equation 5x + y - z = 7 is

(i)Show that [ vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a vec b vec c]. (ii)If vec a, vec b, vec c are coplanar, prove that vec a + vec b, vec b + vec c, vec c + vec a are also coplanar.

Let A be any non zero set more than one elements * is a binary operation on A defined as a* b=a AA a,b in A. Check the commutativity and associativity.

If y =1 (1)/(1!) + (x ^(2))/(2!)+.. then (dy)/(dx)=

Prove that [vecaxxvecbvecbxxveccveccxxveca] = [vecavecbvecc]^2

Digestion of food complete in :-

int_(0)^(pi) (1-x^(2))/((1+x^(2))^(2))dx

If A(x)=|(x+1,2x+1,3x+1),(2x+1,3x+1,x+1),(3x+1,x+1,2x+1)| then int_(0)^(1) A (x) dx=

For which values of p does the pair of equations given below has unique solution ? 4x+py+8=0 2x+2y+2=0

int((x-1)^(2))/((x^(2)+1)^(2))dx=tan^(-1)x+f(x)+c then f(x)=....

For each operation * defined below, determine whether * is binary, commutative or associative. (i) On Z, define ab = a-b (ii) On Q, define ab = ab + 1 (iii) On Q, define ab =(ab)/(2) (iv) On Z^(+), define ab = (a)/(b+1) (v) On Z^(+), define ab=a^(b) (vi)On R- {-1}, defineab =(a)/(b+1)

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

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.