28278 + Interview Questions in Maths in Class 12 Page 131 InterviewSolution

6501.	1/2t+4=3/4t-5 In the equation above . What is the value of t?
Answer» 4 9 18 36 Answer :D

Discussion

6502.	If theroot ofkx^3 - 18x^2- 36 x+8=0are inH.Pthenk=
Answer» 81 63 64 56 Answer :A

Discussion

6503.	If veca,vecb,vecc are such that veca.vecb = veca.vecc then show that veca = vec0 or vecb = vecc or veca is perpendicular to vecb.vecc.
Answer» Solution :GIVEN `veca.vecb` = `veca,VECC` `impliesveca.(vecb-vecc)` = 0 `IMPLIES veca` = 0 or `vecb-vecc` = 0 or `vecabot(vecb-vecc)` `implies veca` = 0 or `vecb-vecc` or `vecabot(vecb-vecc)

Discussion

6504.	Find the values of a, b, c and d from the following equation: [(2a+b,a-2b),(5c-d,4c+3d)]=[(4,-3),(11,24)]
Answer» ANSWER :a=1, b=2, c=3 and d=4

Discussion

6505.	Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector 3hati+5hatj-6hatk
Answer» Answer :The distance of the REQUIRED plane from the origin is p = 7. A vector normal to the plane = `3hati+5hatj-6hatk` `therefore` The unit vector normal to the plane `=(1)/abs(3hati+5hatj-6hatk) (3hati+5hatj-6hatk) = (1)/sqrt(9+25+36) (3hati+5hatj-6hatk) = (3hati+5hatj-6hatk)/sqrt70` Hence, the vector EQUATION of the plane is `VECR.((3hati+5hatj-6hatk)/sqrt70) = 7`

Discussion

6506.	If x=sin70^(0). sin50^(0)and y = cos60^(@). cos80^(0),then what is xy equal to ?
Answer» `1//16` `1//8` `1//4` `1//2` SOLUTION :`x=sin70^(@).sin50^(@)andy=cos60^(@).cos80^(@)` `rArrxy=cos60^(@).sin70^(@).sin50^(@).cos80^(@)` `xy=(1)/(2).sin(90-20)sin(90-40)cos80` `rArrxy=(1)/(2)cos20cos40cos80` `(becausesin(90-x)=cosx)` `rArrxy=(1)/(2)cos20^(@).cos(60-20)^(@).cos(60+20)^(@)` `rArrxy=(1)/(2)[(1)/(4)"cos"3(20^(@))]=(1)/(2)XX(1)/(4)xxcos60^(@)=(1)/(16)`. `[becausecosthetacos(60-theta)cos(60+theta)=(1)/(4)cos3theta]`

Discussion

6507.	Write the relations in tabular form and determine their type. R= {(x, y): y lt= x lt= 4} on A = {1,2,3,4,5)
Answer» Solution :R `{(x.u): y LE x le 4} "on" A ` ` ={1,2,3,4,5}` `{(1,1),(2,1),(2,2),(3,1),(3,2),(3,3),(4,1),(4,2),(4,3),(4,4)` R is NEITHER REFLEXIVE nor symmeyric but TRANSITIVE.

Discussion

6508.	If f(x)=x sin x, f'((pi)/(2))is equal to :
Answer» 0 1 `-1` `1/2`. ANSWER :B

Discussion

6509.	Evaluate:int_(0)^(1)x^(5)(1-x^(2))^(5)dx.
Answer» ANSWER :`(1)/(336)`

Discussion

6510.	A man is at the origin on the x-axis and takes a unit step either to the left or the right. He stops after 5 steps or if he reaches 3 or
Answer» REACHES -2 is 3 reaches 3 is 4 stops exactly after TAKING 5 steps is 12 can PERFORM the experiment is 20 Answer :A::B::D

Discussion

6511.	If x=cis alpha ,y=cis beta , then find x^4y^3+(1)/(x^4y^3)
Answer» ANSWER :`2COS(4alpha+3beta)`

Discussion

6512.	If A={(x,y)//x^(2)+y^(2)le 4,x, y in R} and B={(x,y)//x^(2)+y^(2)ge 9,x,y in R}, then
Answer» `A-B=PHI` `B-A=phi` `A NN B NE phi` `A nn B=phi` ANSWER :D

Discussion

6513.	(d)/(d theta) {sin h [log cot (pi//4+ theta )]}=
Answer» `- tan 2 THETA ` `-2 sec ^(2) 2 theta ` `2 sec ^(2) 2 theta ` NONE ANSWER :B

Discussion

6514.	A function f: X to Y is said to be onto, if for every yin Y there exists an element x in X such that
Answer» F(X)=y f(y)=0 f(x)+y=0 f(y)+x=0 Answer :A

Discussion

6515.	Prove that sum_(r=0)^(n) ""^(n)C_(r).(n-r)cos((2rpi)/(n)) = - n.2^(n-1).cos^(n)'(pi)/(n).
Answer» SOLUTION :`S = underset(r=0)overset(N)sum.^(n)C_(r) . (n-r) cos'((2rpi)/(n))"……"(1)` ` = underset(r=0)overset(n)sum.^(n)C_(n-r).(n-(n-r))cos((2(n-r)PI)/(n))` ` :. S =underset(r=0)overset(n)sum.^(n)C_(r).cos((2rpi)/(n)) "……."(2)` Adding (1) and (2), we get `2S = n underset(r=0)overset(n)sum.^(n)C_(r).cos((2rpi)/(n)) = n xx Re(underset(r=0)overset(n)sum.^(n )C_(r)e^(i(2rpi)/(n)))` `= n xx Re (1+e^((2pi)/(n)i))^(n)` ` = n xx Re (1+cos'(2pi)/(n)+isin'(2pi)/(n))^(n)` `= nxx Re(2cos^(2)'(pi)/(n)+2isin'(pi)/(n) cos'(pi)/(n))^(n)` `= n2^(n)cos^(n)'(pi)/(n) Re(cos'(pi)/(n) + isin'(pi)/(n))^(n)` `= n2^(n)cos^(n)'(pi)/(n)Re(cos'(NPI)/(n)+isin'(npi)/(n))` `:. S = - n2^(n-1)cos^(n)'(pi)/(n)`

Discussion

6516.	If X=[{:(3,1,-1),(5,-2,-3):}]andY=[{:(2,1,-1),(7,2,4):}], find (i) X+Y (ii) 2X-3Y (iii)A matrix Z such that X+Y +Z is a zero matrix.
Answer» ANSWER :(i)`=[{:(2,1,-2),(12,0,1):}]` (II) `=[{:(0,-1,1),(-11,-10,-18):}]` (iii) `=[{:(-5,-2,2),(-12,0,-1):}]`

Discussion

6517.	Find the number of proper divisors of 540
Answer» ANSWER :33

Discussion

6518.	Integrate thefunction in Exercise. x sqrt(x+2)
Answer» Answer :`(2(x+2)^((5)/(2)))/(5)-(4(x+2)^((3)/(2)))/(3)+C`

Discussion

6519.	Evaluate the following integrals. int(1)/(e^(x) - 1)
Answer» Answer :`LOG((E^(x)-1)/(e^(x)))+C`

Discussion

6520.	Find the second order derivative of the following functions logx
Answer» SOLUTION :`y=logx,dy/dx=1/x,(d^2y)/(dx^2)=-1/x^2`

Discussion

6521.	Which of the following is a fourth root of (1)/(2)+i(sqrt(3))/(2) ?
Answer» `CIS(pi)/(12)` `cis(pi)/(2)` `cis(pi)/(3)` `cis(pi)/(6)` ANSWER :A

Discussion

6522.	letf(x)=int_(0)^(x)(cost)/(t)(x gt 0) then for x=(2n+1)(pi)/(2), f(x)has :
Answer» MAXIMA when `N = 0, 2, 4, 6, ….. minima when n = 0, 2, 4, 6, …. neither maxima nor minima when n = -1, -3, -5, …. Information not SUFFICIENT Answer :1

Discussion

6523.	When a 10-question true -false quiz was given to 50 students , the number of correct answer ranged from 3 to 10 , as shown on the graph above . Each point on the graph shows the percent of students who earned scores less than or equal to x . For example , point P shows that 20 percent of the students received scores of 4 or less. According to the graph , how many students got scores of 6 ?
Answer» 5 10 15 20 Answer :A

Discussion

6524.	Find the values of the following integrals int(2x^(3)-3x+5)/(2x^(2))dx
Answer» ANSWER :`(X^(2))/(2) - (3)/(2) "log \| x\|" - (5)/(2x) + C `

Discussion

6525.	int sec^(2) " x cosec"^(4) x dx = - (1)/(3) cot^(3)x + k tan x - 2 cot x + c rArr k =
Answer» 4 3 2 1 Answer :D

Discussion

6526.	Constructiona composition table for binary operation ^^ defined asa ^^ b= minimum of {a,b} in the set {1,2,3,4,5} and (i) evaluate (2 ^^ 3) ^^4 and 2^^ (3^^ 4) (ii) is ^^ commutative ?
Answer» ANSWER :`(##NTN_MATH_XII_C01_E03_003_A01##)` (i) (23)4=2,2(34)=2 `""` (II) * is commutative

Discussion

6527.	The sum of the ordinates of two points on y(2)=4ax is equal to the sum of the ordinates of two other points on the same curve. Show that the chord joining the first two points is parallel to the chord joining the other two points.
Answer» ANSWER :`PQ and RS` are PARALLEL.

Discussion

6528.	If alpha, beta, gamma are the eccentric angles of three points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at which the normals are concurrent, then sin(alpha+beta)+sin(beta+gamma)+sin(gamma+alpha) is equal to______
Answer» Solution :SUPPOSE normals are `alpha, beta` and `GAMMA` are concurrent at `(h,k)` and LET `S` be the foot the fourth normals from `(h,k)` then we have `sum "TAN"(alpha)/2 "tan"(beta)/2=0` and `"tan"(alpha)/2 "tan" (beta)2"tan"(gamma)/2 "tan" (delta)/2=-1` Eliminating `"tan"(delt)/2` from above, we will get `SIN(alpha+beta)+sin(beta+gamma)+sin(gamma+alpha)=0`

Discussion

6529.	Integrate the following function : int(3x^(2))/(sqrt(9-x^(6)))dx
Answer» ANSWER :`sin^(-1)((X^(3))/(3))+c`

Discussion

6530.	The differential of e^(x^(3)) with respect to log x is
Answer» ANSWER :`3X^(2)E^(x^3)`

Discussion

6531.	Find int x cos xdx.
Answer» Answer :`(cosx)((X^(2))/(2))+INT (sinx*((x^(2))/(2)))DX`

Discussion

6532.	{:(I."The angle between the vectors" 2i. + j- kI - 4j - 2k, a. pi//6),(II. "The angle between the vectors" I + 2j - k2i + j + k, b. pi//4),(III. "The angle between a.b if a.b if a.b.a + b are unit vector",c. pi//3),(IV. "The angle between" vec(AC) vec(BD) if A = (1.1.0) B = (1. -1.0) C = (-1.1.0) D = (0.-1.1),d.pi//2):}
Answer» a,C,c,b d,c,c,b c,a,b,d d,c,c,a Answer :B

Discussion

6533.	If the normal at theta on the hyperbola x^(2)//a^(2)-y^(2)//b^(2)=1 meets the transverse axis at G, then AG. A'G=
Answer» `a^2(E^(4) SEC^(2) theta-1)` `a^(2)(e^(4) sec^(2) theta+1)` `b^(2)(e^(4) sec^(2) theta-1)` none Answer :A

Discussion

6534.	Let f (x) be a polynomial function of degree 3 where a lt b lt c and f (a) =f (b) = f(c ). If the graph of f (x) is as shown, which of the following statements are INCORRECT ? (Where c gt\|a\|)
Answer» `INT _(a) ^(C ) f (x ) DX = int _(b) ^(c ) f (x) dx + int _(c ) ^(b) f (x) dx ` `int _(a) ^(c ) f (x) dx LT a` ` int _(a) ^(b) f (x) dx lt int _( c)^(b) f (x) dx` `(1)/(b-a) int _(a ) ^(b) f(x) dx GT (1)/(c-b) int _(b) ^(c ) f (x) dx` Answer :B::C::D

Discussion

6535.	Consider the triangle whose vetices are (0,0) , (5,12) and (16,12).
Answer» Solution :(a). Centroid is `((0+5+16)/(3),(0+12+12)/(3))-=(7,8)` (b). Let the coordinates of CIRCUMCENTER be `O(x,y)` therefore, `OA=OB=OC` ` therefore x^2+y^2=(x-5)^2+(y-12)^2=(x-16)^2+(y-12)^2` ` therefore x^2+y^2=(x-5)^2+(y-12)^2` or `10x+24y=169` and `(x-5)^2+(y-12)^2=(x-16)^2+(y-12)^2` or `2x=21` Solving, we get `x=(21)/(2),y=(8)/(3)` (C). `I-=((0xx11+5xx20+16xx13)/(13+20+11),(0xx11+12xx20+13xx12)/(13+20+11))-=(7,9)` (d). `I_2-=((-5xx20+13xx16+11xx0)/(-20+13+11),(-12xx20+0xx11+13xx12)/(-20+13+11))-=(27,-21)`.

Discussion

6536.	Let A and B be independent events with P(A)= 0.3 and P( B)= 0.4. Find P (B \| A)
Answer» ANSWER :0.4

Discussion

6537.	Find the equations of the tangent to the curve y=cos(x+y) which is parallel to the line x+2y=0.
Answer» ANSWER :`2x+4y+3pi=0, 2x+4y-pi=0`

Discussion

6538.	Using the properties of determinants, prove the following \|{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}\|=2abc(a+b+c)^3
Answer» ANSWER :`2ABC(a+b+c)^3`

Discussion

6539.	Solvex^3 -7x^2 + 36 =0givenone rootbeingtwicethe other.
Answer» ANSWER :`3,6,-2`

Discussion

6540.	Let \|X\| dentoe the number of elements in a set X. Let S={1,2,3,4,5,6} be a sample space, where each element is equally likely to occur. If A and B are independent events associated with S, then the number of ordered paris , (A,B) such that 1le\|B\|lt\|A\|, equals............
Answer» Solution :GIVEN sample space S `={1,2,3,4,5,6}` andlet there are `i` elements in set A an j elements in set B, Now, according to information `1 le j lt I le 6`. So, total number of ways of choosing sets A and `B=sum_(1lejltile6)(sum""sum) .^(6)C_(i)" ".^(6)C_(j)` `=((UNDERSET(r=1)overset(6)(sum).^(6)C_(r))^(2)-underset(r=1)overset(6)(sum)(.^(6)C_(r))^(2))/(2)=((2^(6)-1)^(2)-(.^(12)C_(6)-1))/(2)` `=((63)^(2)-(12!)/(6!6!)+1)/(2)` `=(3969-924+1)/(2)=(3046)/(2)=1523`

Discussion

6541.	Integrate the functions 1/((x+a)(x-b))
Answer»

Discussion

6542.	The area bounded by the curve y = x\|x\|, x-axis and the ordinates x = -1 and x = 1 is given by
Answer» -9 `-15/4` `15/4` `17/4` ANSWER :D

Discussion

6543.	Determine order and degree (if defined) of differential equations ((d^(2)y)/(dx^(2)))^(2) + 2cos ((dy)/(dx)) = 0
Answer» ANSWER :ORDER 2; DEGREE not DEFINED

Discussion

6544.	Lisa spends (3)/(8) or her monthly paycheck on rent and (5)/(12) on food. Her roommate, Carrie, who earns twice as much as Lisa, spends (1)/(4) for her monthly paycheck on rent and (1)/(2) on food. If the two women decide to donate the remainder of their money to charity each month, what fraction of their combined monthly income will they donate (Assume all income in question is after taxes.)
Answer» ANSWER :`(17)/(72)`

Discussion

6545.	Consider the non exmpty set consisting of children in a house, consider a relation R , xRy iff x is brother of y then R is
Answer» symmetric but not TRANSITIVE transitive but not symmetric and REFLEXIVE NEITHER symmetric nor transitive both symmetric and transitive Answer :B

Discussion

6546.	Evaluate the following integrals. int(dx)/(a^(2)+(b+cx)^(2))
Answer» ANSWER :`(1)/(C)SIN^(-1)((b+cx)/(a))+K`

Discussion

6547.	f:[-(pi)/2,pi/2]rarr[-1,1] is a bijection , if ......
Answer» `F(X) = \|x\|` `f(x) = SINX ` `f(x) =x^2` `f(x) = COS x ` SOLUTION :N/A

Discussion

6548.	Using the first Guldin theorem, find the centre of gravity of a semicircle of radius a.
Answer» ANSWER :`2(a)/(PI)`

Discussion

6549.	If a line makes angles. 90^@, 60^@, 30^@ with the x, y and z axes respectively, find its direction cosines
Answer» Answer :`cos90^@, cos 60^@, cos 30^@` i.e., 0, (1)/2, (sqrt3)/2`

Discussion

6550.	Using elementary transformation, find the inverse of the matrix ({:(2, -1, 1), (-1, 2, -1), (1, -1, 2):})
Answer» ANSWER :`A^(-1)=1/4[{:(3,1,-1), (1,3,1),(-1,1,3):}]`

Discussion

Explore topic-wise InterviewSolutions in .

1/2t+4=3/4t-5 In the equation above . What is the value of t?

If theroot ofkx^3 - 18x^2- 36 x+8=0are inH.Pthenk=

If veca,vecb,vecc are such that veca.vecb = veca.vecc then show that veca = vec0 or vecb = vecc or veca is perpendicular to vecb.vecc.

Find the values of a, b, c and d from the following equation: [(2a+b,a-2b),(5c-d,4c+3d)]=[(4,-3),(11,24)]

Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector 3hati+5hatj-6hatk

If x=sin70^(0). sin50^(0)and y = cos60^(@). cos80^(0),then what is xy equal to ?

Write the relations in tabular form and determine their type. R= {(x, y): y lt= x lt= 4} on A = {1,2,3,4,5)

If f(x)=x sin x, f'((pi)/(2))is equal to :

Evaluate:int_(0)^(1)x^(5)(1-x^(2))^(5)dx.

A man is at the origin on the x-axis and takes a unit step either to the left or the right. He stops after 5 steps or if he reaches 3 or

If x=cis alpha ,y=cis beta , then find x^4y^3+(1)/(x^4y^3)

If A={(x,y)//x^(2)+y^(2)le 4,x, y in R} and B={(x,y)//x^(2)+y^(2)ge 9,x,y in R}, then

(d)/(d theta) {sin h [log cot (pi//4+ theta )]}=

A function f: X to Y is said to be onto, if for every yin Y there exists an element x in X such that

Prove that sum_(r=0)^(n) ""^(n)C_(r).(n-r)cos((2rpi)/(n)) = - n.2^(n-1).cos^(n)'(pi)/(n).

If X=[{:(3,1,-1),(5,-2,-3):}]andY=[{:(2,1,-1),(7,2,4):}], find (i) X+Y (ii) 2X-3Y (iii)A matrix Z such that X+Y +Z is a zero matrix.

Find the number of proper divisors of 540

Integrate thefunction in Exercise. x sqrt(x+2)

Evaluate the following integrals. int(1)/(e^(x) - 1)

Find the second order derivative of the following functions logx

Which of the following is a fourth root of (1)/(2)+i(sqrt(3))/(2) ?

letf(x)=int_(0)^(x)(cost)/(t)(x gt 0) then for x=(2n+1)(pi)/(2), f(x)has :

Find the values of the following integrals int(2x^(3)-3x+5)/(2x^(2))dx

int sec^(2) " x cosec"^(4) x dx = - (1)/(3) cot^(3)x + k tan x - 2 cot x + c rArr k =

Constructiona composition table for binary operation ^^ defined asa ^^ b= minimum of {a,b} in the set {1,2,3,4,5} and (i) evaluate (2 ^^ 3) ^^4 and 2^^ (3^^ 4) (ii) is ^^ commutative ?

The sum of the ordinates of two points on y(2)=4ax is equal to the sum of the ordinates of two other points on the same curve. Show that the chord joining the first two points is parallel to the chord joining the other two points.

If alpha, beta, gamma are the eccentric angles of three points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at which the normals are concurrent, then sin(alpha+beta)+sin(beta+gamma)+sin(gamma+alpha) is equal to______

Integrate the following function : int(3x^(2))/(sqrt(9-x^(6)))dx

The differential of e^(x^(3)) with respect to log x is

Find int x cos xdx.

If the normal at theta on the hyperbola x^(2)//a^(2)-y^(2)//b^(2)=1 meets the transverse axis at G, then AG. A'G=

Let f (x) be a polynomial function of degree 3 where a lt b lt c and f (a) =f (b) = f(c ). If the graph of f (x) is as shown, which of the following statements are INCORRECT ? (Where c gt|a|)

Consider the triangle whose vetices are (0,0) , (5,12) and (16,12).

Let A and B be independent events with P(A)= 0.3 and P( B)= 0.4. Find P (B | A)

Find the equations of the tangent to the curve y=cos(x+y) which is parallel to the line x+2y=0.

Using the properties of determinants, prove the following |{:((b+c)^2,a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2):}|=2abc(a+b+c)^3

Solvex^3 -7x^2 + 36 =0givenone rootbeingtwicethe other.

Let |X| dentoe the number of elements in a set X. Let S={1,2,3,4,5,6} be a sample space, where each element is equally likely to occur. If A and B are independent events associated with S, then the number of ordered paris , (A,B) such that 1le|B|lt|A|, equals............

Integrate the functions 1/((x+a)(x-b))

The area bounded by the curve y = x|x|, x-axis and the ordinates x = -1 and x = 1 is given by

Determine order and degree (if defined) of differential equations ((d^(2)y)/(dx^(2)))^(2) + 2cos ((dy)/(dx)) = 0

Consider the non exmpty set consisting of children in a house, consider a relation R , xRy iff x is brother of y then R is

Evaluate the following integrals. int(dx)/(a^(2)+(b+cx)^(2))

f:[-(pi)/2,pi/2]rarr[-1,1] is a bijection , if ......

Using the first Guldin theorem, find the centre of gravity of a semicircle of radius a.

If a line makes angles. 90^@, 60^@, 30^@ with the x, y and z axes respectively, find its direction cosines

Using elementary transformation, find the inverse of the matrix ({:(2, -1, 1), (-1, 2, -1), (1, -1, 2):})