28278 + Interview Questions in Maths in Class 12 Page 82 InterviewSolution

4051.	Find the radius of the circle escribed to the triangle ABC (Shown in the figure below) on the side BC ifangleNAB=30^(@), angleBAC=30^(@), AB=AC=5.
Answer» `((10sqrt(2)+5sqrt(3)-5)(2-SQRT(3)))/(2sqrt(2))` `((10sqrt(2)+5sqrt(3)+5))/(2sqrt(2))(2-sqrt(3))` `((10sqrt(2)+5sqrt(3)-5))/(2sqrt(2))(2+sqrt(3))` `((10sqrt(2)+5sqrt(2)+1))/(2sqrt(3))(sqrt(3)-1)` Answer :A

Discussion

4052.	Using determinants find equation of line passess from point (1,2) and (3,6)
Answer» ANSWER :`thereforey=2x`

Discussion

4053.	Find int (1)/( sin x cos^(3) x) dx
Answer» ANSWER :`I = log_(e) ( TAN X) + ( tan^(2) x )/(2) + C`

Discussion

4054.	If a,b,c ge 4are integers, not all equal, and 4abc = (a + 3) (b + 3) (c + 3), then what is the value of a + b + c ?
Answer» ANSWER :16

Discussion

4055.	If f(x) =(sin [x])/([x])" at "[x] ne 0 and f(x)=0" at "then " underset(x to 0)"Lt" f(x)=
Answer» 0 1 `-1` does not exist Answer :D

Discussion

4056.	IfA =({:( 1,1,1),( 1,omega ^(2) , omega ),( 1 ,omega , omega ^(2)) :})where omega is a complex cube root of unity then adj -Aequals
Answer» `(OMEGA ^(2) -omega ) VEC A ` ` (omega -omega ^(2) ) oversetto A ` ` -oversetto A ` ` oversetto A ` ANSWER :B

Discussion

4057.	Find the equation of normal to the parabola y^(2) = 4x and whose slopeis 2.
Answer» ANSWER :`RARR 2x-y -12=0`

Discussion

4058.	The projections of a line segment on x, y and z axes are respectively 3, 4 and 12. The length of the line segment is
Answer» 5 `4sqrt(10)` `3sqrt(17)` 13 Answer :D

Discussion

4059.	Let n be a positive integer. Find the maximum number of non congruent triangles whose side lengths are integers less than or equal to n.
Answer» ANSWER :`{((N(n+2)(2n+5))/(24),"n is EVE"),(((n+1)(n+3)(2n+1))/(24),"n is ODD"):}`

Discussion

4060.	A fair die is tossed twice. The probability of getting 4, 5 or 6 on the first toss and 1,2,3 or 4 on the second toss is
Answer» `7//36` `5//36` `1//3` `35//36` ANSWER :C

Discussion

4061.	Evaluate the following improper integrals with infinite limits on the basis of their definition : (a) int_(2)^(oo)(xdx)/(sqrt((x^(2)-3)^(3))), (b) int_(1)^(oo)(dx)/(x+x^(3)), (c ) int_(0)^(oo)(xdx)/(sqrt((4x^2+1)^(3))), (d) int_(1)^(oo)(dx)/(x^(2)(1+x)), (e) int_(-oo)^(oo)(dx)/(x^(2)-6x+10), (f) int_(0)^(oo)e^(-x)sinxdx
Answer» Answer :(b) `(1)/(2)1n2;` (C ) `1;` (d) `1-1n2;` (e ) `pi;(F)(1)/(2)`.

Discussion

4062.	If the coordinate axes are the bisectors of the angle between the pairs of lines ax^(2) + 2hxy + by^(2) = 0 , where h^(2) gt ab anda ne b, then
Answer» `a + B = 0` `H = 0` `h NE 0 , a + b = 0` ` a + b ne 0` ANSWER :B

Discussion

4063.	If 4 fair coins are tossed find the probability of getting 2 heads and 2 talls.
Answer» ANSWER :`(3)/(8)`

Discussion

4064.	""^20C_0 + ""^20C_1 + ""^20C_2+…….+""^20C_10 =
Answer» `[2^19 - 1/2. ""^18C_10]` `[2^19 +1/2.""^20C_10]` `2^19-1/4. ""^18C_10]` `[2^19 - 1/4 . ""^6C_3]` ANSWER :B

Discussion

4065.	Does the graph below represent a function or a relation? (##CEN_GRA_C01_S01_002_Q01.png" width="80%">
Answer» Solution :Vertical LINE X = 2 meets the above graph at (2, 1) and (2, 2). Hence the graph does not represent a FUNCTION.

Discussion

4066.	A company produces two types of leather belts A and B on which the profits are Rs. 40 and Rs. 30 per belt respectively. Each belt of type A requires twice as much time as required by a belt to type B.If all belts were of type B the company could produce 1000 belts per day. But the supply of leather is sufficient only for 800 belts per day. Belt A requires a fancy buckle and only 400 fancy buckles are available per day. For belt of type B only 700 buckles are available per day. How should the company manufacture the two types of belts in order to have maximum overall profit?
Answer» SOLUTION :NA

Discussion

4067.	Let R be the relation in the set N given byR = {(a,b) : a = b -2, b gt 6}. Choose the correct answer.
Answer» `(2, 4) in R` `(3, 8) in R` `(6, 8) inR` `(8, 7) in R` Answer :C

Discussion

4068.	The sequence 9, 18, 27, 36, 45, 54,….. consists of successive mutiple of 9. This sequence is then altered by multiplying every other term by -1, starting with the first term, to prduce the new sequence -9, 18, -27,36,-45, 54,…….. If the sum of the first n terms of this new sequence is 180, determine n.
Answer» ANSWER :40

Discussion

4069.	A line passes through two points A(2,-3,-1) and B(8,-1,2). The coordinates of a point on this lie at distance of 14 units from a are
Answer» `(14,-1,5)` `(-10,-7,-7)` `(10,7,7)` `(-4,-1,-5)` Answer :B

Discussion

4070.	Let PQ be a focal chord of the parabola y^2=4ax. The tangents to the parabola at P and Q meet at a point lying on the line y=2x +a, a gt0. Length of chord PQ is:
Answer» 7a 5a 2a 3a Answer :B

Discussion

4071.	The value of I= int_(0)^(pi) (xdx)/( 4 cos^(2) x +9 sin^(2) x ) is
Answer» `PI^(2) //12` `pi^(2)//4` `pi^(2) //6` `pi^(2) //3` Answer :A

Discussion

4072.	Write the general solution of the differential equations : dy/dx=cosx-x
Answer» SOLUTION :`dy/DX=cosx-xrArry=int(cosx-x)dx`

Discussion

4073.	Letf(x)={{:(-1+sinK_(1)pix",", "x is rational."), (1+cosK_(2)pix",", x):} If f(x) is a periodic function, then
Answer» EITHER `K_(1),K_(2) in` RATIONAL or `K_(1),K_(2) in` IRRATIONAL `K_(1),K_(2) in " rational only "` `K_(1),K_(2) in " irrational only "` `K_(1),K_(2) in " irrational such that " K_(1)/K_(2)` is rational ANSWER :B

Discussion

4074.	Transform each of the following equations into ones in which the coefficients of the third highest power of x is zero . x^3+2x^2+x+1=0
Answer» ANSWER :`x^3-x^2 +1=0 , 27 x^3 +27 x^2 +23=0`

Discussion

4075.	At what points, the function f(x)=sinx-cosx,0ltxlt2pi, attains local maxima and minima.
Answer» ANSWER :MAXIMUM VALUE=`-SQRT2` Manumum value=`-sqrt2`

Discussion

4076.	Matrices of different order can not be subtracted .
Answer» ANSWER :1

Discussion

4077.	inttan^5theta sec^4theta d theta
Answer» SOLUTION :`inttan^5theta sec^4theta d THETA` =`inttan^5theta.(1+tan^2theta).sec^2thetad theta` [PUT `tantheta=1` Then `sec^2thetad theta=DT`] =`intt^5.(1+t^2).dt=int(t^5+t^7)dt` =`1/6t^6+1/8t^8+C=1/6tan^6theta+1/8tan^8theta+C`

Discussion

4078.	For the following probability distribution determine standard deviation of the random variable X.
Answer» ANSWER :0.7

Discussion

4079.	The solution of y = x(dy)/(dx) + a sqrt(1+((dy)/(dx))^(2)) is
Answer» y = MX + C `y = mx + asqrt(1+m^(2))` y = mx `y = asqrt(1+m^(2))` ANSWER :B

Discussion

4080.	If only one common tangent can be drawn to the circles x^2+y^2-2x-4y-20=0 and (x+3)^(2)+(y+1)^(2)=p^(2)," then p="
Answer» 20 16 49 10 Answer :D

Discussion

4081.	The value of int_(0)^([x]) (2^t)/( 2^([t]) ) dt
Answer» `[X] LOG 2` `([x])/(log 2)` `(1)/(2) ([x])/(log 2)` `(1)/( 4) ([x])/( log 2)` ANSWER :B

Discussion

4082.	Prove that if the function f(x)=sin x+cos a x is a periodic, than a is a rational number.
Answer» ANSWER :`(2N)/(K)`

Discussion

4083.	If (3hati+4hatj+9hatk) and (a hati-3hatj+1hatk) are perpendicualr to each other then a = ………………
Answer» 1 `-1` 7 `-7` ANSWER :A

Discussion

4084.	Let pi_(1) be the plane passing through the points (0,1,2), (1,0,-2), (-2, 1,0) and p_(2) be the plane passing through the point (1, 2,3) and perpendicular to the planes x + y + z =1 and 2x-3y + z =5. If theta is the acute angle between the planes pi_(1) and pi_(2) then cos theta=
Answer» `(sqrt14)/(9)` `(PI)/(3)` `(13)/(3 sqrt22)` `(pi)/(4)` ANSWER :A

Discussion

4085.	If f(x) = {:{ ( (1- sqrt2e sinx)/(pi-4x) ,if x ne pi/4), ( a , if x = pi/4) :} is continous atpi/4 thana is equal to
Answer» 4 2 1 `1//4` ANSWER :D

Discussion

4086.	If the limiting points of the system of circles x ^(2) + y ^(2) + 2gx+ lamda (x ^(2) + y ^(2) + 2fy +k) =0, where lamdais a parameter, subtend a right angle at the origin, then klf ^(2)=
Answer» `-1` 1 2 none of these ANSWER :C

Discussion

4087.	Find the number of 4 letter words that can be formed using the letters of the word MIXTURE which do not contain the letter X
Answer» ANSWER :360

Discussion

4088.	The parameter on which the value of thedeterminant \|[1, a, a^2],[cos (p-d) x ,cos p x, cos (p+d) x],[sin (p-d) x, sin p x, sin (p+d) x]\|does not depend upon is
Answer» a p d x Answer :B

Discussion

4089.	If (pi)/(2) lt alpha (3pi)/(2) , the modulus argument form of (1 + cos 2 alpha) + isin 2 alpha is
Answer» `-2COS ALPHA{COS(alpha-pi)+ISIN(alpha-pi)}` `2cos alpha{cos(alpha)+isinalpha)` `2cos alpha{cos(-alpha)+isin(-alpha)}` `-2cos alpha{cos(pi-alpha)+isin(pi-alpha)}` ANSWER :A

Discussion

4090.	From the equations which representsthe following Pair of lines x = y , x + 2y + 5 = 0
Answer» Solution :x = y , x + 2y + 5 = 0 `therefore` (x =-y) ( x + 2y + 5 )= 0 or, `x^2 + 2XY + 5x - XY - 2y^2 - 5y = 0 or, `x^2 - 2y^2 + xy + 5x - 5y = 0 which REPRESENTS a PAIR of lines.

Discussion

4091.	A pair of dice is thrown. If the two numbers appearing are different , find the probability thet the sum of points exceeds 8.
Answer» SOLUTION :Let B be the event that sum of the POINTS exceeds 8. `THEREFORE` B={ (3,6),(4,5),(5,4),(6,3),(5,6),(6,5),(4,6),(6,4) } `therefore P (B) = absB/absS=8/30`

Discussion

4092.	A pair of dice is thrown. If the two numbers appearing are different , find the probability thet the sum of point is 8.
Answer» <P> Solution :A pair of DICE is THROWN as two NUMBERS are different We have `absS=30` Let A be the event thet the sum of points on the dice is 8, where the number on the dice are different. `therefore` A={(2,6),(3,5),(5,3),(6,2)} `P(A)=absA/absS=4/30`

Discussion

4093.	If(1 ) /(x ^ 4+x ^ 2+ 1 )= (Ax +B)/(x ^ 2+ x +1 )+ (Cx+D)/( x ^ 2 - x+1 ) ,thenC +Disequal to
Answer» ` - 1 ` ` 1 ` ` 2` ` 0` SOLUTION : ` ( 1 ) /(X ^4 + x ^ 2+ 1 )= ( Ax + B) /(x ^ 2+ x+ 1 ) + (Cx +D)/(x ^ 2- x+ 1) ` ` RARR ( Ax +B)( x ^ 2- x+ 1 )+(Cx+ D)(x ^ 2+ x+ 1 )= 1 ` Let, `x ^ 2 +1 =x ` `rArrx ^ 2+ 1 - x=0 ` `0+(Cx + D )(2x )= 1` `rArr2 Cx^ 2+2Dx =1 ` `rArr2C ( x-1 )+ 2Dx= 1` ` rArr2x ( C + D)- 2C = 1` `rArr2x ( C + D)- 2 c =0.x+ 1` `thereforeC + D =0 `

Discussion

4094.	If tantheta(P)/(q)"where"p,qgt0and if thetain(0,(pi)/(4))then sqrt((q+p)/(q-p))+sqrt((q-p)/(q+p)) is equal to
Answer» `(2sintheta)/(sqrt(sin2theta))` `(2sintheta)/(sqrt(COS2THETA))` `(2costheta)/(sqrt(cos2theta))` `(2costheta)/(sqrt(cos2theta))` Solution :`sqrt((q+p)/(q-p))+sqrt((q-p)/(q+p))=sqrt((1+p//q)/(1-p//q))+sqrt((1-p//q)/(1+p//q))` `=((1+p//q)+(1-p//q))/(sqrt(1-(p//q)^(2)))=(2)/(sqrt(1-tan^(2)THETA))=(2cos theta)/(sqrt(COS2 theta)).`

Discussion

4095.	int_(0)^(1) (tan^(-1)x)/(x) dx equals
Answer» `underset(0)overset(x)INT (x)/(sin x)dx` `(1)/(2)underset(0)overset(x)int (x)/(sin x)dx` `underset(0)overset(pi//2)int (sin x)/(x)dx` None of the above Answer :B

Discussion

4096.	lim_(xto0)"sin"(1)/(x) is
Answer» 0 1 `OO` DOEST not exist Answer :D

Discussion

4097.	Integrate the following function : int(4x+5)/(sqrt(2x^(2)+x-3))dx
Answer» Answer :`2sqrt(2x^(2)+X-3)+2sqrt2log\|(x+(1)/(4))+SQRT((x+(1)/(4))^(2)-((5)/(4))^(2))\|+C`

Discussion

4098.	If veca=overset(-)i-overset(-)j-overset(-)k and vecb=lambda hati-3hatj+hatk and the orthogonal projection of vecb" on "veca is 4/3 (hati-hatj-hatk), then lambda is equal to
Answer» 0 2 12 `-1` ANSWER :B

Discussion

4099.	If the vertices of a feasible region are O(0, 0), A(10, 0), B(0, 20), C(15, 15), then minimum value of a objective function Z = 10x - 20y + 30 is ………
Answer» -120 130 30 -370 Answer :D

Discussion

4100.	A bag contains 2 n + 1 coins. If is known thatn of these coins have a head on both sides, whereas the remaining n + 1 coins are fair. A coin is picked up at random from the bag and tosses. If the probabilitythat the toss resultsin a head is 31/42 , then n=
Answer» 10 11 12 13 Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

Find the radius of the circle escribed to the triangle ABC (Shown in the figure below) on the side BC ifangleNAB=30^(@), angleBAC=30^(@), AB=AC=5.

Using determinants find equation of line passess from point (1,2) and (3,6)

Find int (1)/( sin x cos^(3) x) dx

If a,b,c ge 4are integers, not all equal, and 4abc = (a + 3) (b + 3) (c + 3), then what is the value of a + b + c ?

If f(x) =(sin [x])/([x])" at "[x] ne 0 and f(x)=0" at "then " underset(x to 0)"Lt" f(x)=

IfA =({:( 1,1,1),( 1,omega ^(2) , omega ),( 1 ,omega , omega ^(2)) :})where omega is a complex cube root of unity then adj -Aequals

Find the equation of normal to the parabola y^(2) = 4x and whose slopeis 2.

The projections of a line segment on x, y and z axes are respectively 3, 4 and 12. The length of the line segment is

Let n be a positive integer. Find the maximum number of non congruent triangles whose side lengths are integers less than or equal to n.

A fair die is tossed twice. The probability of getting 4, 5 or 6 on the first toss and 1,2,3 or 4 on the second toss is

If the coordinate axes are the bisectors of the angle between the pairs of lines ax^(2) + 2hxy + by^(2) = 0 , where h^(2) gt ab anda ne b, then

If 4 fair coins are tossed find the probability of getting 2 heads and 2 talls.

""^20C_0 + ""^20C_1 + ""^20C_2+…….+""^20C_10 =

Does the graph below represent a function or a relation? (##CEN_GRA_C01_S01_002_Q01.png" width="80%">

Let R be the relation in the set N given byR = {(a,b) : a = b -2, b gt 6}. Choose the correct answer.

A line passes through two points A(2,-3,-1) and B(8,-1,2). The coordinates of a point on this lie at distance of 14 units from a are

Let PQ be a focal chord of the parabola y^2=4ax. The tangents to the parabola at P and Q meet at a point lying on the line y=2x +a, a gt0. Length of chord PQ is:

The value of I= int_(0)^(pi) (xdx)/( 4 cos^(2) x +9 sin^(2) x ) is

Write the general solution of the differential equations : dy/dx=cosx-x

Letf(x)={{:(-1+sinK_(1)pix",", "x is rational."), (1+cosK_(2)pix",", x):} If f(x) is a periodic function, then

Transform each of the following equations into ones in which the coefficients of the third highest power of x is zero . x^3+2x^2+x+1=0

At what points, the function f(x)=sinx-cosx,0ltxlt2pi, attains local maxima and minima.

Matrices of different order can not be subtracted .

inttan^5theta sec^4theta d theta

For the following probability distribution determine standard deviation of the random variable X.

The solution of y = x(dy)/(dx) + a sqrt(1+((dy)/(dx))^(2)) is

If only one common tangent can be drawn to the circles x^2+y^2-2x-4y-20=0 and (x+3)^(2)+(y+1)^(2)=p^(2)," then p="

The value of int_(0)^([x]) (2^t)/( 2^([t]) ) dt

Prove that if the function f(x)=sin x+cos a x is a periodic, than a is a rational number.

If (3hati+4hatj+9hatk) and (a hati-3hatj+1hatk) are perpendicualr to each other then a = ………………

Let pi_(1) be the plane passing through the points (0,1,2), (1,0,-2), (-2, 1,0) and p_(2) be the plane passing through the point (1, 2,3) and perpendicular to the planes x + y + z =1 and 2x-3y + z =5. If theta is the acute angle between the planes pi_(1) and pi_(2) then cos theta=

If f(x) = {:{ ( (1- sqrt2e sinx)/(pi-4x) ,if x ne pi/4), ( a , if x = pi/4) :} is continous atpi/4 thana is equal to

If the limiting points of the system of circles x ^(2) + y ^(2) + 2gx+ lamda (x ^(2) + y ^(2) + 2fy +k) =0, where lamdais a parameter, subtend a right angle at the origin, then klf ^(2)=

Find the number of 4 letter words that can be formed using the letters of the word MIXTURE which do not contain the letter X

The parameter on which the value of thedeterminant |[1, a, a^2],[cos (p-d) x ,cos p x, cos (p+d) x],[sin (p-d) x, sin p x, sin (p+d) x]|does not depend upon is

If (pi)/(2) lt alpha (3pi)/(2) , the modulus argument form of (1 + cos 2 alpha) + isin 2 alpha is

From the equations which representsthe following Pair of lines x = y , x + 2y + 5 = 0

A pair of dice is thrown. If the two numbers appearing are different , find the probability thet the sum of points exceeds 8.

A pair of dice is thrown. If the two numbers appearing are different , find the probability thet the sum of point is 8.

If(1 ) /(x ^ 4+x ^ 2+ 1 )= (Ax +B)/(x ^ 2+ x +1 )+ (Cx+D)/( x ^ 2 - x+1 ) ,thenC +Disequal to

If tantheta(P)/(q)"where"p,qgt0and if thetain(0,(pi)/(4))then sqrt((q+p)/(q-p))+sqrt((q-p)/(q+p)) is equal to

int_(0)^(1) (tan^(-1)x)/(x) dx equals

lim_(xto0)"sin"(1)/(x) is

Integrate the following function : int(4x+5)/(sqrt(2x^(2)+x-3))dx

If veca=overset(-)i-overset(-)j-overset(-)k and vecb=lambda hati-3hatj+hatk and the orthogonal projection of vecb" on "veca is 4/3 (hati-hatj-hatk), then lambda is equal to

If the vertices of a feasible region are O(0, 0), A(10, 0), B(0, 20), C(15, 15), then minimum value of a objective function Z = 10x - 20y + 30 is ………

A bag contains 2 n + 1 coins. If is known thatn of these coins have a head on both sides, whereas the remaining n + 1 coins are fair. A coin is picked up at random from the bag and tosses. If the probabilitythat the toss resultsin a head is 31/42 , then n=