28278 + Interview Questions in Maths in Class 12 Page 64 InterviewSolution

3151.	Match the following:
Answer» `{:("P","Q","R","S"),("2","1","4","3"):}` `{:("P","Q","R","S"),("4","2","3","1"):}` `{:("P","Q","R","S"),("4","1","2","3"):}` `{:("P","Q","R","S"),("2","4","1","3"):}` ANSWER :B

Discussion

3152.	Obtain the following integrals : int(1)/(sqrt(16-9x^(2)))dx
Answer» Answer :`:.I=(1)/(3)sin^(-1)((3X)/(4))+C`

Discussion

3153.	Common roots of the equations z^(3)+2z^(2)+2z+1=0 and z^(1985)+z^(100)+1=0 are
Answer» `OMEGA,omega^(2)` `1,omega,omega^(2)` `-1,omega,omega^(2)` `-omega,-omega^(2)` ANSWER :A

Discussion

3154.	If A is square matrix of order 2xx2 such that A^(2)=I,B=[{:(1,sqrt(2)),(0,1):}] and C=ABA then
Answer» `C^(2009)=A[{:(1,2009sqrt(2)),(0,1):}]` `C^(2009)=A[{:(1,2009+sqrt(2)),(0,1):}]` `\|C\|^(2009)=1` `C^(2009)=A[{:(1,2009sqrt(2)),(0,1):}]` Solution :`(ABA)^(2)=(ABA)(ABA)=AB(AA)BA=AB^(2)A` continuing in the MANNER `C^(2008)=AB^(2009)A` `B^(2)=[{:(1,2sqrt(2)),(0,1):}],B^(3)=[{:(1,3sqrt(2)),(0,1):}]` Continuing in this manner `B^(2009)=[{:(1,2009sqrt(2)),(0,1):}]`

Discussion

3155.	{:("Column A","", "Column B"),("The area of square with perimeter 12",,"The area of a parallelogram with perimeter 16"):}
Answer» If column A is larger If column B is larger If the COLUMNS are EQUAL If there is not enough INFORMATION to decide Answer :D

Discussion

3156.	I) The maximum value of c + 2bx -x^(2) is c+b^(2) II) The minimum value of x^(2) + 2bx + c is c-b^(2) Which of the above statements is true ?
Answer» ONLYI is true OnlyII ISTRUE BOTHI and IIare true nietherI nor IItrue ANSWER :A

Discussion

3157.	If int(cos^(3)xdz)/((sin^(4)+x+3sin^(2)x+1)tan^(-1)(sinx+cosec x))=-Alog \|tan^(-1)(sinx+cosecx)\|+C then A is equal to.
Answer» ANSWER :1

Discussion

3158.	If x+3y=16 is the perpendicular bisector of bar(AB)and A(5, 7), then B is
Answer» (2, 1) (3, 1) (9, 1) (-2, -3) ANSWER :B

Discussion

3159.	Form the differential equation of the family of circles having centre on y-axis and radius 5 units.
Answer» ANSWER :`(X^(2) - 9)(y')^(2) + x^(2) = 0`

Discussion

3160.	A cubic polynomial P is such that P(1) = 1, P(2) = 2, P(3) = 3 and P(4) = 5. Then P(6) is
Answer» ANSWER :16

Discussion

3161.	State which of the following matrices is symmetric,slew symmetric, both or not either: [[0,1,2],[-1,0,3],[-2,-3,0]]
Answer» SOLUTION :SKEW SYMMETRIC

Discussion

3162.	If (1+x+2x^(2)+4x^(3))^(10)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(30)x^(30). Find the value of a_(0)-a_(1)+a_(2)-a_(3)…+a_(30)
Answer» SOLUTION :N/A

Discussion

3163.	Differentiate sqrt(tanx
Answer» SOLUTION :LET `y=sqrt(TANX)=(tanx)^(1/2)` Then `dy/dx=1/2(tanx)^(1/2)xxd/dx(tanx)` `=1/(2sqrt(tanx))CDOT sec^2x`

Discussion

3164.	Two events A and B are such that P(B) = 0 . 55and P(AB') = 0 . 15 . Theprobability of occurenceof at least one of eventis
Answer» `0.70` `0.20` `0.35` `0.30` ANSWER :A

Discussion

3165.	IFalpha, betaare therootsof theequationax^2 + bx +c=0 andalphalt -1,beta gt 1 then1 +(c )/(a)+ \|(b)/(a)\| is
Answer» positive negative NONNEGATIVE NONPOSITIVE ANSWER :B

Discussion

3166.	Let f(x) = (x + x^(2) + ...+ x^(n)-n)/(x -1), x ne 1, the value of f (1)
Answer» N `(n+1)/(2)` `(n(n+1))/(2)` `(n(n-1))/(2)` ANSWER :C

Discussion

3167.	At a party, each man danced with exactly four women and each woman danced with exactly three men. Nine men attended the party. How many women attended the party?
Answer» ANSWER :12

Discussion

3168.	Which of following functions have the same graph?
Answer» `f(x)=log_(E)e^(x)` `G(x)=abs(x)sgnx` `h(x)=cot^(-1)(cotx)` `k(x)=lim_(n rarr INFTY)(2abs(x))/pi tan^(-1)(nx)` Answer :A::B::D

Discussion

3169.	Find the number of 4-digit number that can be formed using the digits 1,2,3,4,5,6 that are divisble by when repectiton is allowed
Answer» ANSWER :432

Discussion

3170.	If A and B are conjugate points w.r.t to circle x^(2)+y^(2)=r^(2) then OA^(2)+OB^(2)=
Answer» `AB^(2)-r^(2)` `AB^(2)+r^(2)` `AB^(2)+2r^(2)` `AB^(2)-2r^(2)` ANSWER :C

Discussion

3171.	Evaluate int_(0)^((1)/(sqrt(2)))(x^(3))/(sqrt(1-x^(2))) dx
Answer» ANSWER :`(8-5sqrt(2))/(12)`

Discussion

3172.	The tangent at any point P of a curve C meeta the x-axis at Q whose abscissa is positive and OP = OQ where O is origin, if C is a family of parabola having vertex (alpha, beta) and latus- rectum = 4a, then find value of (4(alpha+beta))/a ?
Answer» ANSWER :D

Discussion

3173.	If the system of linear equations ax+by+cz=0 cx+ay+bz=0 bx+cy+az=0 where a,b,c in R are non-zero and distinct , has a non-zero solution, then :
Answer» a+B+C=0 a,b,c are in A.P. `1/a,1/b,1/c` are inA.P. a,b,c are in G.P. SOLUTION :`\|(a,b,c),(c,a,b),(b,c,a)\|=0` `RARR (a^2-bc)-b(ac-b^2)+c(c^2-ab)=0 rArr a^3 -abc-abc+b^3+c^3-abc=0` `rArr a^3+b^3+c^3-3abc=0 rArr (a+b+c)(a^2+b^2+c^2-ab-b-ca)=0` `rArr` a+b+c=0

Discussion

3174.	Solve the following in equations : i) sqrt(x+2) gt sqrt(8-x^(2)) ii) sqrt((x-3)(2-x)) lt sqrt(4x^(2)+12x+11) iii) sqrt(x^(2)-3x-10) gt 8-x
Answer» Answer :i) `{x in R; 2 lt x LE 2SQRT2}` ii) `{x in R; 2 le x le 3}` iii) `((74)/(13), INFTY)`

Discussion

3175.	Let f(x)= x^(3)-x^(2) + x + 1 g(x) = max I {f(t), 0 le t le x}, 0 le x le 1= 3-x, 1 lt x le 2 Then in [0, 2] the points where g(x) is not differentiable is………
Answer» 0 1 2 None of these Answer :B

Discussion

3176.	If sqrt(9x^(2)+6x+1) lt 2-x, then
Answer» ` X in ((-3)/(2), 1/4)` `x in ((-3)/(2), 1/4]` `x in [(-3)/(2), 1/4)` `x LT 1/4` ANSWER :A

Discussion

3177.	If f(x)=x^2+1 , and g(x)=x-2 , find x such that f(g(x))=g(f(x))
Answer» 1 `3/2` `1.5` `2` ANSWER :B::C

Discussion

3178.	Find the number of possible common tangents that exist for the following pairs of circles. x^(2) + y^(2) = 4, x^(2) + y^(2) - 6 x - 8y + 16 = 0
Answer» ANSWER :`3`

Discussion

3179.	The value of Lim_(xto0) (5x^(2)+[x^(2)+1])^(((1)/(x^(2)+sin^(2)x))) is, [Note : [y] denotes greatest interger less than or equal to y.]
Answer» `(5)/(2)` `e^((5)/(2))` `(25)/(2)` `e^((25)/(2))` Solution :`underset(xto0)LIM(5x^(2)+[x^(2)+1])^(((1)/(x^(2)+SIN^(2)x)))=e^(L)` where `L=underset(xto0)Lim(1)/(x^(2)+sin^(2)x)(5x^(2)+[x^(2)+1]-1)=underset(xto0)Lim(5x^(2))/(x^(2)+sin^(2)x)=(5)/(2)` `:."Limit"=e^((5)/(2))`.

Discussion

3180.	Three poles whose feet lie on a circle subtend angle alpha, beta, gamma respectively at the centre of the circle. If the height of the poles are in A.P. then cot alpha, cot beta, cot gamma are in
Answer» A.P. G.P. H.P. None of these ANSWER :C

Discussion

3181.	If p is any statement, then (^^~p) is a
Answer» contingency contradiction tautology theorem Answer :B

Discussion

3182.	If p is any statement, then (p^^~) is a
Answer» contingency contradiction tautology paradox Answer :C

Discussion

3183.	If y = mx + c is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 if C=
Answer» `(a^(2)-B^(2))/(a^(2)m^(2)+b^(2))` `(a^(2)-b^(2))/(a^(2)m^(2))` `(a^(2)-b^(2)m^(2))/(a^(2)+b^(2)m^(2))` `(a^(2)-b^(2)m^(2))/(a^(2)m^(2)+b^(2))` ANSWER :C

Discussion

3184.	A = {1,2,3,4} , B = {1,5,9,11,15,16} f = {(1,5),(2,9),(3,1),(4,5),(2,11)} Is f a relation from A to B ? Give reason for your answer.
Answer» SOLUTION :N/A

Discussion

3185.	An electric bulb will last 190 days or more with a probability 0.7 and it will last for atmost 200 days with a probability of 0.8. The probability that the bulb will last between 190 and 200 days is
Answer» `0.5` `0.56` `0.2` `0.3` ANSWER :A

Discussion

3186.	Consider the circlex^(2)+y^(2)_4x-2y+c=0 whose centre is A(2,1). If the point P(10,7) is such that the line segment PA meets the circle in Q with PQ=5 then c=
Answer» `-15` 20 30 20 Answer :D

Discussion

3187.	The set of allpointswhere f(x) = root(3)(x^(2)\|x\|)-\|x\|-1 is notdifferentiableis
Answer» {0} (-1,0,1} {0,1} NONEOF these Answer :D

Discussion

3188.	int (dx)/((x+2)(x^(2)+1))=a log\|1+x^(2)\|+btan^(-1)x+(1)/(5)log\|x+2\|+C then ... Of the following is true. a) a=-(1)/(10), b=-(2)/(5)b) a=(1)/(10), b=-(2)/(5)c) a=-(1)/(10), b=(2)/(5)d) a=(1)/(10), b=(2)/(5)
Answer» `a=-(1)/(10), b=-(2)/(5)` `a=(1)/(10), b=-(2)/(5)` `a=-(1)/(10), b=(2)/(5)` `a=(1)/(10), b=(2)/(5)` ANSWER :C

Discussion

3189.	Consider the parabola whose focus is at (0,0) and tangent at vertex is x-y+1=0 Tangents drawn to the parabola at the extremities of the chord 3x+2y=0 intersect at angle
Answer» `pi//6` `pi//3` `pi//2` none of these Solution :(3) The distance between the focus and tangent at the vertex is `(\|0-0+1\|)/(sqrt(1^(2)+1^(2)))=(1)/(sqrt(2))` The directrix is the line parallel to the tangent vertex ant at a distance `2xx1sqrt(2)` from the focus. Let the EQUATION of the directrix be `x-y+lamda=0` where `(lamda)/(sqrt(1^(2)+1^(2)))=(2)/(sqrt(2))` `:." "lamda=2` Let P (x,y) be any moving point on the parabola. Then, OP=PM `orx^(2)+y^(2)=((x-y+2)/(sqrt(1^(2)+1)))^(2)` `or2x^(2)+=2y^(2)=(x-y+2)^(2)` `orx^(2)+y^(2)+2xy-4x+4y-4=0` Latus rectum length `=2xx` (Distance of focus from directrix) `2\|(0-0+2)/(sqrt(1^(2)+1^(2)))\|=2sqrt(2)` Solving the parabola with the x-axis, we get `x^(2)-4x-4=0` `orx=(4pmsqrt(32))/(2)=2pm2sqrt(2)` THEREFORE, the length of chord on the x-axis is `4sqrt(2)`. Since the chord 3x+2y=0 PASSES through the focus, it is focus chord. Hence, tangents at the EXTREMITIES of chord are perpendicular.

Discussion

3190.	The polars of any two points A and B wrt a circle, centre O meet at P. Then AP^(2)-BP^(2)=
Answer» `AO^(2)+BO^(2)` `OA^(2)-OB^(2)` OA.OB none Answer :B

Discussion

3191.	Statement-1 :The weighted mean of first n natural numbers whose weights are equal is given by ((n+1)/2) . Statement-2 : If omega_1,omega_2,omega_3, … omega_n be the weights assigned to be n values x_1,x_2,… x_n respectively of a variable x, then weighted A.M. is equal to (Sigma_(i=1)^(n) omega_ix_i)/(Sigma_(i=1)^(n) omega_i)
Answer» ANSWER :1

Discussion

3192.	A manufacture produces two models of bike model X and model Y. Model X takes a 6 man hours to make per unit, while model Y takes 10 man hours per unit. There is a total of 450 man hour availbale per week. Handling and marketing costs are 2000 and 1000 per unit of model X and Y, respectively. The tota funds available for these purposes are 8000 per week. Profits per unit for models X and Y are 1000 and manufacturer produce, so, as to yeild a maximum profit? Find the maximum profit.
Answer» Solution :Let the manufacturer produces x number of models X and y number of model Y BIKES. Model X takes a 6 man hours to make per UNIT and model Y takes 10 man hours to make per unit. There isa total of 450man hour available per week `therefore 6x+10y le 450` `Rightarrow3x+5y le 225....(i) ` For models X and Y, handling and marketing costs are 2000 and 1000 respectively, total FUNDS available for these purposes are 80000 per week. `therefore 2000x+1000y ge 80000` `Rightarrow 2x+y ge 80` Also, `x ge 0, y ge....(ii)` Hence the profits per unit fo r models X and Y are 1000 and 500 respectively`therefore "Required LPP i"` Maximise Z=1000x+500y Subject to `3x+5y le 225, 2x+y le 80, x ge 0, y ge 0` From the shaded feasible region, it is clear that COORDINATES of corner points are (0,) (40,0),(25,30) and (0,45) On solving 3x+5y=225 and 2x+y=80, we get x=25, y=30 So, the manufacturer should poroduce 25 bikes of model X and 30 bikes of model Y to get a maximum PROFIT of 40000. Since in question it is asked that each model bikes should be produced.

Discussion

3193.	Where line XY is parallel to line QU. If b=4x, e=x+2y and d=3y+8, find h.
Answer» ANSWER :`68^(@)`

Discussion

3194.	Find the direction cosines of perpendicular from the origin to the plane vecr.(6hati-3hatj-2hatk)+1=0.
Answer» ANSWER :`6/7,(-3)/(7),(-2)/(7)`

Discussion

3195.	Distance between parallel lines r=2i+lambda(i+j+k) and r=-3j+mu(i+j+k) is
Answer» `SQRT((14)/(3))` `sqrt((3)/(14))` `sqrt(3)` `2sqrt(3)` ANSWER :A

Discussion

3196.	Let f be a function defined on R by f(x)=lim_(n to oo) (log (3+x)-x^(2n) sinx)/(1+x^(2n)) then
Answer» F is CONTINUOUS on R f is continuous on R ~ {-1,1} f is continuous on R ~{0} NONE of these ANSWER :B

Discussion

3197.	Assertion (A) : If alpha is a root of x^5=1 then the value of(1-alpha)(1-alpha^2)(1-alpha^3)(1-alpha^4)=5Reason (R) : If omega is n^(th) roots od unity then the values of (1-omega)(1-omega^2)(1-omega^3)…...(1-omega^(n-1))=n
Answer» Both A and R are TRUE R is CORRECT explanation to A Both A and R are true but R is not correct explanation to A A is true R is FALSE A is false R is true ANSWER :A

Discussion

3198.	Let a_(n)=i^((n+1)^2), where i=sqrt(-1)" and "n=1, 2, 3,"………..". Then the value of a_(1)+a_(3)+a_(5)+"……….."+a_(25) is
Answer» `13` `13+i` `13-i` `12` ANSWER :A

Discussion

3199.	Show that the function f(x)=x^(3)+1/(x^(3)) is decreasing function in the interval [-1,1]-{0}.
Answer»

Discussion

3200.	"The maximum or the minimum of the objective function occurs only at the corner points of the feasible region". This theorem is know as fundamental theorem of
Answer» Agebra ARITHMETIC CALCULUS EXTREME POINTS ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in .

Match the following:

Obtain the following integrals : int(1)/(sqrt(16-9x^(2)))dx

Common roots of the equations z^(3)+2z^(2)+2z+1=0 and z^(1985)+z^(100)+1=0 are

If A is square matrix of order 2xx2 such that A^(2)=I,B=[{:(1,sqrt(2)),(0,1):}] and C=ABA then

{:("Column A","", "Column B"),("The area of square with perimeter 12",,"The area of a parallelogram with perimeter 16"):}

I) The maximum value of c + 2bx -x^(2) is c+b^(2) II) The minimum value of x^(2) + 2bx + c is c-b^(2) Which of the above statements is true ?

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

If x+3y=16 is the perpendicular bisector of bar(AB)and A(5, 7), then B is

Form the differential equation of the family of circles having centre on y-axis and radius 5 units.

A cubic polynomial P is such that P(1) = 1, P(2) = 2, P(3) = 3 and P(4) = 5. Then P(6) is

State which of the following matrices is symmetric,slew symmetric, both or not either: [[0,1,2],[-1,0,3],[-2,-3,0]]

If (1+x+2x^(2)+4x^(3))^(10)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(30)x^(30). Find the value of a_(0)-a_(1)+a_(2)-a_(3)…+a_(30)

Differentiate sqrt(tanx

Two events A and B are such that P(B) = 0 . 55and P(AB') = 0 . 15 . Theprobability of occurenceof at least one of eventis

IFalpha, betaare therootsof theequationax^2 + bx +c=0 andalphalt -1,beta gt 1 then1 +(c )/(a)+ |(b)/(a)| is

Let f(x) = (x + x^(2) + ...+ x^(n)-n)/(x -1), x ne 1, the value of f (1)

At a party, each man danced with exactly four women and each woman danced with exactly three men. Nine men attended the party. How many women attended the party?

Which of following functions have the same graph?

Find the number of 4-digit number that can be formed using the digits 1,2,3,4,5,6 that are divisble by when repectiton is allowed

If A and B are conjugate points w.r.t to circle x^(2)+y^(2)=r^(2) then OA^(2)+OB^(2)=

Evaluate int_(0)^((1)/(sqrt(2)))(x^(3))/(sqrt(1-x^(2))) dx

The tangent at any point P of a curve C meeta the x-axis at Q whose abscissa is positive and OP = OQ where O is origin, if C is a family of parabola having vertex (alpha, beta) and latus- rectum = 4a, then find value of (4(alpha+beta))/a ?

If the system of linear equations ax+by+cz=0 cx+ay+bz=0 bx+cy+az=0 where a,b,c in R are non-zero and distinct , has a non-zero solution, then :

Solve the following in equations : i) sqrt(x+2) gt sqrt(8-x^(2)) ii) sqrt((x-3)(2-x)) lt sqrt(4x^(2)+12x+11) iii) sqrt(x^(2)-3x-10) gt 8-x

Let f(x)= x^(3)-x^(2) + x + 1 g(x) = max I {f(t), 0 le t le x}, 0 le x le 1= 3-x, 1 lt x le 2 Then in [0, 2] the points where g(x) is not differentiable is………

If sqrt(9x^(2)+6x+1) lt 2-x, then

If f(x)=x^2+1 , and g(x)=x-2 , find x such that f(g(x))=g(f(x))

Find the number of possible common tangents that exist for the following pairs of circles. x^(2) + y^(2) = 4, x^(2) + y^(2) - 6 x - 8y + 16 = 0

The value of Lim_(xto0) (5x^(2)+[x^(2)+1])^(((1)/(x^(2)+sin^(2)x))) is, [Note : [y] denotes greatest interger less than or equal to y.]

Three poles whose feet lie on a circle subtend angle alpha, beta, gamma respectively at the centre of the circle. If the height of the poles are in A.P. then cot alpha, cot beta, cot gamma are in

If p is any statement, then (^^~p) is a

If p is any statement, then (p^^~) is a

If y = mx + c is a normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 if C=

A = {1,2,3,4} , B = {1,5,9,11,15,16} f = {(1,5),(2,9),(3,1),(4,5),(2,11)} Is f a relation from A to B ? Give reason for your answer.

An electric bulb will last 190 days or more with a probability 0.7 and it will last for atmost 200 days with a probability of 0.8. The probability that the bulb will last between 190 and 200 days is

Consider the circlex^(2)+y^(2)_4x-2y+c=0 whose centre is A(2,1). If the point P(10,7) is such that the line segment PA meets the circle in Q with PQ=5 then c=

The set of allpointswhere f(x) = root(3)(x^(2)|x|)-|x|-1 is notdifferentiableis

int (dx)/((x+2)(x^(2)+1))=a log|1+x^(2)|+btan^(-1)x+(1)/(5)log|x+2|+C then ... Of the following is true. a) a=-(1)/(10), b=-(2)/(5)b) a=(1)/(10), b=-(2)/(5)c) a=-(1)/(10), b=(2)/(5)d) a=(1)/(10), b=(2)/(5)

Consider the parabola whose focus is at (0,0) and tangent at vertex is x-y+1=0 Tangents drawn to the parabola at the extremities of the chord 3x+2y=0 intersect at angle

The polars of any two points A and B wrt a circle, centre O meet at P. Then AP^(2)-BP^(2)=

Where line XY is parallel to line QU. If b=4x, e=x+2y and d=3y+8, find h.

Find the direction cosines of perpendicular from the origin to the plane vecr.(6hati-3hatj-2hatk)+1=0.

Distance between parallel lines r=2i+lambda(i+j+k) and r=-3j+mu(i+j+k) is

Let f be a function defined on R by f(x)=lim_(n to oo) (log (3+x)-x^(2n) sinx)/(1+x^(2n)) then

Assertion (A) : If alpha is a root of x^5=1 then the value of(1-alpha)(1-alpha^2)(1-alpha^3)(1-alpha^4)=5Reason (R) : If omega is n^(th) roots od unity then the values of (1-omega)(1-omega^2)(1-omega^3)…...(1-omega^(n-1))=n

Let a_(n)=i^((n+1)^2), where i=sqrt(-1)" and "n=1, 2, 3,"………..". Then the value of a_(1)+a_(3)+a_(5)+"……….."+a_(25) is

Show that the function f(x)=x^(3)+1/(x^(3)) is decreasing function in the interval [-1,1]-{0}.

"The maximum or the minimum of the objective function occurs only at the corner points of the feasible region". This theorem is know as fundamental theorem of