28278 + Interview Questions in Maths in Class 12 Page 21 InterviewSolution

1001.	Sum of the series S=n^(2)((C_(0))/(C_(1)))+(n-1)^(2)((C_(1))/(C_(2)))+…+1^(2)((C_(n-1))/(C_(n))) equals
Answer» `1/6n(n+1)(2n+1)` `1/3n(n+1)(n+2)` `1/6n(n+1)(n+2)` `1/6n^(2)(n+1)(n+2)` ANSWER :C

Discussion

1002.	A rod of AB of length 3 rests on a wall as follows : P is a point on AB such thatAP : PB = 1 : 2If the rod slides along the wall, then the locus of P lies on
Answer» `2x + y + xy = 2 ` ` 4X^(2) + xy + xy + y^(2) = 4` ` 4x^(2) + y^(2) =4 ` ` x^(2) + y^(2) - x - 2Y =0` Answer :C

Discussion

1003.	A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, the probability that both are dead is ..........
Answer» `(33)/(56)` `(9)/(64)` `(1)/(64)` `(3)/(28)` Answer :D

Discussion

1004.	The vector equation of the line (3-x)/(3) = (2y - 3)/(5) = z/2 is ......
Answer» `BAR r = (3,5,2) + k (3,3,0)` `bar r = (3, (3)/(2),0) + k (3,5,2)` `bar r = (3,3,0) + k (3,5,2)` `bar r = (-6,5,4) + k (3, (3)/(2), 0)` Answer :B

Discussion

1005.	Find (dy)/(dx)," if "x-y =2pi.
Answer» ANSWER :`= 1`

Discussion

1006.	If the sum of the mean and variance of a binomial distribution for 6 trials is (10)/(3), find the binomial distribution.
Answer» ANSWER :`((2)/(3) + (1)/(3))^(6)`

Discussion

1007.	Total maximum number of degenerated orbitals in n=3 shell in H-atom ?
Answer» 5 9 3 0

Discussion

1008.	Which of the following set are finite and which are infinite ? The set of human beings
Answer» SOLUTION :"The SET of HUMAN BEINGS" is a FINITE set.

Discussion

1009.	Find the area of the portion of the parabola y^2=4x bounded by the double ordinate through(3,0).
Answer» Solution :Given parabole is `y^2=4x`. Area = `2int_0^3 ydx=2 int_0^3 sqrt4xdx` `=4[X^(3//2)/(3//2)]_0^3=8/3 3^(3//2)=8sqrt3`

Discussion

1010.	The quadratic equation 2x^(2)-(a^(3)+8a-1)x+a^(2)-4a=0 possesses roots of opposite sign. Then
Answer» `a le0` `0 LT a lt 4` `4 LE a lt 8` `a GE 8` ANSWER :b

Discussion

1011.	Write down negations of John is a friend of Thomas.
Answer» SOLUTION :JOHN is not a FRIEND of THOMAS.

Discussion

1012.	Find the equation of circle with centre (2, 3) and touching the line 3x - 4y + 1 = 0
Answer» Answer :` RARR X^ (2) + y ^(2) -4 x - 6y +12=0`

Discussion

1013.	If n(A) = 3, then number of reflexive relations that can be defined on A is
Answer» `2^(3)` `2^(6)` `2^(9)` `2^(27)` Answer :B

Discussion

1014.	Let f : R rarrR be defined as f(x)=x^4 . Choose the correct answer.
Answer» F is one - one ONTO f is many - one onto f is one - one but not onto f is neither one - one nor onto Solution :N/A

Discussion

1015.	A bag X contains 2 white and 3 black balls and another bag Y contains 4 white 2 black balls . One bag is selected at random and a ball is drawn from it . Then , the probability for the vall chosen to be white is ,
Answer» `(2)/(15)` `(7)/(15)` `(8)/(15)` `(14)/(15)` Answer :C

Discussion

1016.	Find the number of ways to arrange 10 students along a row by taking 4 at a time. In how many of these arrangements a specified student always occur.
Answer» ANSWER :`""^(10)P_4,4.""^9P_3`

Discussion

1017.	Findthe areaboundedbythelinesy= 4x + 5 , y=5 -xand4y = x +5.
Answer» ANSWER :`=15/2` SEQ. UNIT

Discussion

1018.	Find theprincipalvalueofsin ^(-1)(2 ), ifit exists .
Answer» ANSWER :sincethe domainof ` y= SIN^(-1)X ` is ` [-1,1]` and ` 2 in[-1,1]isn ^(-1)(2) ` doesnotexist

Discussion

1019.	Addition theorem on probaility : Statement : if (E_(1)),(E_(2)) an any two events of a random experiment and P is a probability function, then P(E_1cupE_2)=P(E_1)+P(E_2)-P(E_1capE_2)
Answer» <P> ANSWER :`P(E_1)+(E_2)-P(E_1capE_2)`

Discussion

1020.	Compute the ^12C_3
Answer» Solution :`""^12C_3 =((12)!)/(3!9!)=(121110)/(3*2)=220`

Discussion

1021.	For a positive integer n show that (1+i)^n+(1-i)^n=2^((n+2)/2) "cos((npi)/4)
Answer» Solution :`L.H.S.=(1+i)^n+(1-i)^n` `={sqrt2(1/sqrt2^1+i1/sqrt2)}^n+{sqrt2(1/sqrt2-i1/sqrt2)}^n` `=2^(n//2)[("cos"pi/4="isin"pi/4)^n="cos"pi/4 - "isin"pi/4)^n]` `=2^(n//2)xx2"cos"(NPI)/4=2^(n//2+1)"cos"(npi)/4` `=2^((n+2)/2) "cos"(npi)/4=R.H.S`

Discussion

1022.	If int (1)/(1 +cot x) dx = Ax + B log \| cos x+ sin x \| + c then ( A, B ) =
Answer» `((1)/(2) , (1)/(2))` (1, 1) (2,2) `((1)/(2), (-1)/(2))` ANSWER :D

Discussion

1023.	The subnormal at any point of a curve is of constant length '8'. Then the differential equation of the family of curves is
Answer» `(dy)/(DX) = 8` `y((dy)/(dx)) = 8` `ysqrt(1((dy)/(dx))^(2)) = 8` `ysqrt(1((dy)/(dx))^(2)) = 8dy//dx` Answer :B

Discussion

1024.	Let f(x)=(a-x)^(1//n)andg(x)=(f,f,f,......,f(x))/(2m" times"). Then int(dx)/((g(x))^(n)(1+(g(x))^(n))^(1//n)) equals
Answer» `(N)/(n-1)(1+(1)/(x^(n)))^((n-1)/(n))+C` `(n)/(1-n)(1+x^(-n))^((n-1)/(n))+C` `(n)/(1+n)(1+x^(n))^((n+1)/(n))+C` `(-1)/(n)(1-x^(n))^((n)/(n+1))+C` ANSWER :B

Discussion

1025.	Method of integration by parts : int[f(x)g''(x)-f''(x)g(x)]dx=....
Answer» `(F(X))/(G'(x))` `f'(x)g(x)-f(x)g'(x)` `f(x)g'(x)-f'(x)g(x)` `f(x)g'(x)+f'(x)g(x)` ANSWER :C

Discussion

1026.	Solve the following differential equations. (i) (dy)/(dx) =(1+y^(2))/(1+x^(2)) (ii) (dy)/(dx) = (sqrt(1-y^(2)))/(sqrt(1-x^(2))) (iii) (dy)/(dx) = 2y tan hx (iv) sqrt(1+x^(2))dx + sqrt(1+y^(2))dy = 0 (v) (dy)/(dy) = e^(x-y)+x^(2)e^(-y)
Answer» Answer :(i) `tan^(-1)x = tan^(-1) y+c` (II) `sin^(-1)y = sin^(-1)x + c` (III) `y = C COS H^(2)x` (iv) `xsqrt(1+x^(2))+ysqrt(1+y^(2)) + sin h^(-1) x + sn h^(-1) y = c` (v) `e^(y) = e^(x) + (x^(3))/(3) + c`

Discussion

1027.	P(2, 1), Q(4, -1), R(3, 2) are the vertices of a triangle and if through P and R lines parallel to opposites sides are drawn to intersect in S, then the area of PQRS is
Answer» 6 4 8 12 Answer :B

Discussion

1028.	If vec(a)=2hati+hatj+x hatk and vec(b)=hati+hatj-hatk then the minimum area of a parallelogram formed by the vectors vec(a) and vec(b) is ………….
Answer» `(sqrt(6))/(2)` `sqrt((3)/(2))` `(sqrt(3))/(2)` `(2)/(sqrt(3))` ANSWER :B

Discussion

1029.	Matchthefollowing
Answer» a,c,d,b d,c,b,a b,c,d,a c,d,a,c Answer :D

Discussion

1030.	If alpha is one root of the equation 4x^(2)+2x-1=0, then the other root is
Answer» `4alpha^(3)+3 ALPHA` `4alpha^(3)-3 alpha` `alpha^(3)+3 alpha` `alpha^(3)-3 alpha` ANSWER :B

Discussion

1031.	Can you say how many elements P(P(A)) If A has n elements?
Answer» <P> SOLUTION :If`\|A\| =N then\|P(A)\| =2^n "and" \|P(P(A))\|=2(2^n)`.

Discussion

1032.	The value of sum_(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C_(r ) is
Answer» `(1)/(n+1)` `(1)/(n)` `(1)/(n-1)` `0` Solution :`(a)` `(R )/(r+1)^(n)C_(r )=(1-(1)/(r+1))^(n)C_(r )` `=^(n)C_(r )-(1)/(r+1)(n!)/(r!(n-r)!)` `=^(n)C_(r )-(1)/(n+1)'^(n+1)C_(r+1)` `:.sum_(r=1)^(n)(-1)^(r-1)(r )/(r+1)^(n)C_(r )` `=^(n)C_(1)-^(n)C_(2)+C_(3)-.....-(1)/(n+1)['^(n+1)C_(2)-^(n+1)C_(3)+^(n+1)C_(4)-.....]` `=^(n)C_(0)-(1)/(n+1)[-^(n+1)C_(0)+^(n+1)C_(1)]` `=1-(1)/(n+1)[-1+(n+1)]` `=(1)/(n+1)`

Discussion

1033.	Assertion (A) : If 5 parallel lines intersect 4 parallel lines, then the number of parallelograms formed is 80 Reason (R) : The number of parallelograms formed when a set of m parallel lines are intersecting another set of n parallel lines is ""^(m)C_(2)xx""^(n)C_(2) The correct answer is
Answer» Both A and R are TRUE and R is the correct EXPLANATION of A Both A and R are true but R is not correct explanation of A A is true but R is FALSE A is false but R is true Answer :D

Discussion

1034.	Let from the point P(alpha, beta), tangents are drawn to the parabola y^(2)=4x, including the angle 45^(@) to each other. Then locus of P(alpha,beta) is(are)
Answer» <P>a circle with centre (-3,0) an ellipse with centre(-3,0) a RECTANGULAR hyperbola with centre(3,0) a rectangular hyperbola with centre (-3,0) Solution :Any tangent to `y^(2)=4X` is `y=mx+(1)/(m)rArr ` `-BETA m +1 = 0 " " ("As" , (P (alpha, beta) "lies on it " )` Here `(m_(1)+m_(2))=(beta)/(alpha)` and `m_(1).m_(2)=(1)/(alpha)`. Now, `tan 45^(@)=\|(m_(1)+m_(2))/(1+m_(1)m_(2))\|rArr (m_(1)+m_(2))^(2)-4m_(1)m_(2)=(1+m_(1)m_(2))^(2)rArr((beta)/(alpha))^(2)-(4)/(alpha)=(1+(1)/(alpha))^(2)` `rArr beta^(2)-4 alpha=(alpha+1)^(2)rArr(alpha+3)^(2)-beta^(2)=8` `(x+3^(2))-y^(2)=8`, which is a rectangular hyperbola with centre (-3,0).

Discussion

1035.	The random variable X has a probability distribution P(X) of the following form, where k is some number. Find P(X lt 2) P(x)={k, if x=0 ""2k, if x=1 ""3k if x=2 "" 0, otherwise}
Answer» <P> SOLUTION :`P(XLT2)`=P(X=0 or 1) =P(0)+P(1) =k+2k =3k=3/6=1/2

Discussion

1036.	Consider the equation of a pair of straight lines as lambdax^(2)-10xy+12y^(2)+5x-16y-3=0.The point of intersection of lines is (alpha, beta). Then the value of alpha beta is
Answer» 35 45 20 15 Solution :`2x^(2)=10xy+12y^(2)+5x-16y-3=0` Consider the HOMOGENEOUS PART `2x^(2)-10xy+12y^(2)=(x-2y)(2x-6)` `2x^(2)-10xy+12y^(2)+5x-16y-3` `-=(2x-6y+A)(x-2y+B)` Comparing coefficients , we get `A=-1,B=3` Hence , the lines are `2x-6y-1=0and x-2y+3=0`Solving , we get the intersection points as`(-10,-7//2)`. THEREFORE , Product `=35`

Discussion

1037.	The value of int_(0)^(0)(sqrt(a^(2)-x^(2)))^(3)dx is ……….
Answer» `(pia^(3))/(16)` `(3pia^(4))/(16)` `(3pia^(2))/(8)` `(3pia^(4))/(8)` ANSWER :B

Discussion

1038.	Find the mean deviation about the median for the data 13, 17,16,14,11,13,10,16,11,18,12,17.
Answer» ANSWER :`=2.33`

Discussion

1039.	A line tangentto the graph of the function y = f(x) at thepoint x = a formsan angle (pi)/(3)with the axis of abscissas and an angle (pi)/(4) at the point x = b
Answer» ANSWER :No

Discussion

1040.	If A is a matrix of order (2xx3) then A^(-1) will be :
Answer» `(3xx2)` MATRIX `(2XX2)` matrix `(3xx3)`matrix NONE of these ANSWER :D

Discussion

1041.	Differentiate the following with respect to x: (log x)/(1+ x log x)
Answer» ANSWER :`(1- X(LOG x)^(2))/(x(1 + x log x)^(2))`

Discussion

1042.	Consider all 3 element subsets of the set {1, 2, 3, ………. 300} then:
Answer» NUMBER of these subsets for which Sum of the three elements is multiple of 3 is`3xx""^(100)C_(3)+100^(3)` Number of these subsets for which sum of the three elements is not a multiple of 3 is `3xx""^(10)C_(3)+100^(3)` Number of these subsets for which sum of the three elements is even is `""^(151)C_(3)+149xx""^(150)C_(2)` of these subsets for which sum of the three elements is even is`""^(300)C_(2)-""^(150)C_(3)` ANSWER :A::C

Discussion

1043.	If A is a orthogonal matrix, then
Answer» DET(A) `det(A)=+-1` det(A)=2 None of these ANSWER :B

Discussion

1044.	If 1/x - 1/y=4, find the value of (2x+4xy-2y)/(x-y-2xy).
Answer» ANSWER :`2//3`

Discussion

1045.	Write down negations of If you read, you will pass.
Answer» SOLUTION :It is not TRUE that if you READ, you read, you will PASS.

Discussion

1046.	If PSis the median of the triangle with vertices P(2, 2), Q(6, –1) and R(7, 3), then equation of the line passing through (1, –1) and parallel to PS is:
Answer» `4x-7y-11=0` `2x+9y+7=0` `4x+7y+3=0` `2x-9y-11=0` ANSWER :B

Discussion

1047.	Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A sube X.
Answer» SOLUTION :F:`X RARR Y. "is INJECTIVE". Let x in A ` 1) (f(A))` `:. A =f^(-1) (f(A)) "for all A" sube X.`

Discussion

1048.	If A=[2" "1],B=[{:(5,3,4),(8,7,6):}]andC=[{:(-1,2,1),(1,0,2):}],verify A*(B+C)=AB+AC.
Answer» ANSWER :`=AB+BC`

Discussion

1049.	If F(x) = int((x^(2)+1)dx)/(3sqrt(x^(3)+3x+6))andF(1)=((25)/(2))^(1/3) then the value of F(-2) is
Answer» ANSWER :`2.00`

Discussion

1050.	Let A=[(0,1),(2,0)] and (A^(8)+A^(5)+A^(2)+I)V=[(32),(62)] where is the (2xx2 identity matrix). Then the product of all elements of matrix V is
Answer» 2 1 3 `-2` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

Sum of the series S=n^(2)((C_(0))/(C_(1)))+(n-1)^(2)((C_(1))/(C_(2)))+…+1^(2)((C_(n-1))/(C_(n))) equals

A rod of AB of length 3 rests on a wall as follows : P is a point on AB such thatAP : PB = 1 : 2If the rod slides along the wall, then the locus of P lies on

A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, the probability that both are dead is ..........

The vector equation of the line (3-x)/(3) = (2y - 3)/(5) = z/2 is ......

Find (dy)/(dx)," if "x-y =2pi.

If the sum of the mean and variance of a binomial distribution for 6 trials is (10)/(3), find the binomial distribution.

Total maximum number of degenerated orbitals in n=3 shell in H-atom ?

Which of the following set are finite and which are infinite ? The set of human beings

Find the area of the portion of the parabola y^2=4x bounded by the double ordinate through(3,0).

The quadratic equation 2x^(2)-(a^(3)+8a-1)x+a^(2)-4a=0 possesses roots of opposite sign. Then

Write down negations of John is a friend of Thomas.

Find the equation of circle with centre (2, 3) and touching the line 3x - 4y + 1 = 0

If n(A) = 3, then number of reflexive relations that can be defined on A is

Let f : R rarrR be defined as f(x)=x^4 . Choose the correct answer.

A bag X contains 2 white and 3 black balls and another bag Y contains 4 white 2 black balls . One bag is selected at random and a ball is drawn from it . Then , the probability for the vall chosen to be white is ,

Find the number of ways to arrange 10 students along a row by taking 4 at a time. In how many of these arrangements a specified student always occur.

Findthe areaboundedbythelinesy= 4x + 5 , y=5 -xand4y = x +5.

Find theprincipalvalueofsin ^(-1)(2 ), ifit exists .

Addition theorem on probaility : Statement : if (E_(1)),(E_(2)) an any two events of a random experiment and P is a probability function, then P(E_1cupE_2)=P(E_1)+P(E_2)-P(E_1capE_2)

Compute the ^12C_3

For a positive integer n show that (1+i)^n+(1-i)^n=2^((n+2)/2) "cos((npi)/4)

If int (1)/(1 +cot x) dx = Ax + B log | cos x+ sin x | + c then ( A, B ) =

The subnormal at any point of a curve is of constant length '8'. Then the differential equation of the family of curves is

Let f(x)=(a-x)^(1//n)andg(x)=(f,f,f,......,f(x))/(2m" times"). Then int(dx)/((g(x))^(n)(1+(g(x))^(n))^(1//n)) equals

Method of integration by parts : int[f(x)g''(x)-f''(x)g(x)]dx=....

Solve the following differential equations. (i) (dy)/(dx) =(1+y^(2))/(1+x^(2)) (ii) (dy)/(dx) = (sqrt(1-y^(2)))/(sqrt(1-x^(2))) (iii) (dy)/(dx) = 2y tan hx (iv) sqrt(1+x^(2))dx + sqrt(1+y^(2))dy = 0 (v) (dy)/(dy) = e^(x-y)+x^(2)e^(-y)

P(2, 1), Q(4, -1), R(3, 2) are the vertices of a triangle and if through P and R lines parallel to opposites sides are drawn to intersect in S, then the area of PQRS is

If vec(a)=2hati+hatj+x hatk and vec(b)=hati+hatj-hatk then the minimum area of a parallelogram formed by the vectors vec(a) and vec(b) is ………….

Matchthefollowing

If alpha is one root of the equation 4x^(2)+2x-1=0, then the other root is

Can you say how many elements P(P(A)) If A has n elements?

The value of sum_(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C_(r ) is

Assertion (A) : If 5 parallel lines intersect 4 parallel lines, then the number of parallelograms formed is 80 Reason (R) : The number of parallelograms formed when a set of m parallel lines are intersecting another set of n parallel lines is ""^(m)C_(2)xx""^(n)C_(2) The correct answer is

Let from the point P(alpha, beta), tangents are drawn to the parabola y^(2)=4x, including the angle 45^(@) to each other. Then locus of P(alpha,beta) is(are)

The random variable X has a probability distribution P(X) of the following form, where k is some number. Find P(X lt 2) P(x)={k, if x=0 ""2k, if x=1 ""3k if x=2 "" 0, otherwise}

Consider the equation of a pair of straight lines as lambdax^(2)-10xy+12y^(2)+5x-16y-3=0.The point of intersection of lines is (alpha, beta). Then the value of alpha beta is

The value of int_(0)^(0)(sqrt(a^(2)-x^(2)))^(3)dx is ……….

Find the mean deviation about the median for the data 13, 17,16,14,11,13,10,16,11,18,12,17.

A line tangentto the graph of the function y = f(x) at thepoint x = a formsan angle (pi)/(3)with the axis of abscissas and an angle (pi)/(4) at the point x = b

If A is a matrix of order (2xx3) then A^(-1) will be :

Differentiate the following with respect to x: (log x)/(1+ x log x)

Consider all 3 element subsets of the set {1, 2, 3, ………. 300} then:

If A is a orthogonal matrix, then

If 1/x - 1/y=4, find the value of (2x+4xy-2y)/(x-y-2xy).

Write down negations of If you read, you will pass.

If PSis the median of the triangle with vertices P(2, 2), Q(6, –1) and R(7, 3), then equation of the line passing through (1, –1) and parallel to PS is:

Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A sube X.

If A=[2" "1],B=[{:(5,3,4),(8,7,6):}]andC=[{:(-1,2,1),(1,0,2):}],verify A*(B+C)=AB+AC.

If F(x) = int((x^(2)+1)dx)/(3sqrt(x^(3)+3x+6))andF(1)=((25)/(2))^(1/3) then the value of F(-2) is

Let A=[(0,1),(2,0)] and (A^(8)+A^(5)+A^(2)+I)V=[(32),(62)] where is the (2xx2 identity matrix). Then the product of all elements of matrix V is