28278 + Interview Questions in Maths in Class 12 Page 39 InterviewSolution

1901.	The parabola with drectrix x+2y-1=0 and focus (1,0) is
Answer» `4X^(2)-4xy+y^(2)-8x+4y+4=0` `4x^(2)+4xy+y^(2)-8x+4y+4=0` `4x^(2)+5xy+y^(2)-8x+4y+4=0` `4x^(2)-4xy+y^(2)-8x-4y+4=0` ANSWER :A

Discussion

1902.	Show that if A and B are square matrics such that AB=BA , then (A+B)^(2)=A^(2)+2AB+B^(2).
Answer» ANSWER :`=A^(2)+2AB+B^(2)=R.H.S`.

Discussion

1903.	If A=[{:(8,0),(4,-2),(3,6):}]andB=[{:(2,-2),(4,2),(-5,1):}], then find the matrix X , such that 2A+3X=5B.
Answer» Answer :`[{:(-2,(-10)/(3)),(4,(14)/(3)),((-31)/(3),(-7)/(3)):}]`

Discussion

1904.	If a gt b and e is the eccentricity of the ellipsethen the equation of the normal at the end of the latusrectum in the first quadrant is
Answer» `x-ey+ae^(3)=0` `x+ey-ae^(3)=0` `x+ey+ae^(3)=0` `x-ey-ae^(3)=0` ANSWER :D

Discussion

1905.	If S = 0, S' =0 are two touching circles then angle between their radical axis and the common tangent at the at their points of contanct is
Answer» `30^@` `60^@` `0^@` `90^@` ANSWER :C

Discussion

1906.	Evalute the following integrals int (cos 6x- cos 4x)/(sin 6x - sin 4x) dx
Answer» ANSWER :`(1)/(5) ` LOG \| cos 5X \| + c

Discussion

1907.	Three vertices of a rectangle are (3,2),(-4,2) and (-4,5). Plot the points and find the coordinates of thefourth vertex.
Answer» `(-1,13,13)` `(3,-3,-1)` `(7,1,-5)` `(3,-3,-5)` ANSWER :D

Discussion

1908.	Construct truth tables for the following and indicate which of these are tautologies (p rarr ~~p) rarr~~p
Answer» SOLUTION :

Discussion

1909.	Let f: R be a function. We say that f has PROPERTY 2 if lim_(hto0)(f(h)-f(0))/(h^2) exists and is finite. Then which of the following options is/are correct ?
Answer» `f(x)=sinx` has PROPERTY 2 `f(x)=x^(2//3)` has PROPERTY 1 `f(x)=\|x\|` has PROPERTY 1 `f(x)x\|x\|` has PROPERTY 2 Solution :it is given, that `f:rtoR` and property 1, `underset(hto0)(lim)(f(h)-f(0))/(SQRT(\|h\|))` exists and finite, and property 2, `underset(hto0)(lim)(f(h)-(f(0)))/(h^(2))` exists and finite. OPTION a, `P2:underset(hto0)(lim)(h^(2//3)-0)/(sqrt(\|h\|))=underset(hto0)(lim)(1)/(h)((sinh)/(h))=`doesn't exist. option b, `P1:underset(hto0)(lim)(\|h\|-0)/(sqrt(\|h\|))=underset(hto0)(lim)(\|h\|)/(h)={{:(1,"if "hto0^(+)),(-1," if "hto0^(-)):}` so `underset(hto0)(lim)(f(h)-f(0))/(h^(2))` does not exist.

Discussion

1910.	If the coefficients of variation of two distributions are 40 and 20 and their variances are 144 and 64 respectively, then the mean of their arithmetic means is
Answer» 40 12 30 35 Answer :D

Discussion

1911.	If2,3 aretworootsofthereciprocalequation6x^5 - 29 x^4 +2x^3 +2x^2 -29 x+6=0 thenthe otherrootsare
Answer» `1,-2,3` `-1,-2,-3` `-1,1/2,1/3` `1,1/2,1/3` ANSWER :C

Discussion

1912.	If int (f(x)dx)/(log sin x)= log sin x, then f(x)=....
Answer» `SIN X` `COS x` `log sin x` `cot x` Answer :D

Discussion

1913.	If two dice are rolled then the probability of getting both even or sum 10 is
Answer» `(4)/(18)` `(5)/(18)` `(7)/(18)` `(1)/(3)` ANSWER :B

Discussion

1914.	If there are 25 railway stations on a railway line, how many types of single second class tickets must be printed, so as to enable a passenger to travel from one station to another.
Answer» ANSWER :`""^(25)P_2`

Discussion

1915.	A particle P moves on the line y=x, xle0 with constant speed u m//sec. Another particle Q revolves along the circke (x-1)^(2)+y^(2)=1/9 with constant speed (omega)/3m//sec. In anticlockwise directio, let at t=0, both P and Q simultaeously started, P from the point (0,0) and Q from he point (2/3,0). Further at any time instant t sec, let the distance of theri separation is r(t)m. Also it was observed that at time t_(0) sec, both P and Q are at their closest distance of approach, denoted by r_("minimum")m, then choose the correct statements from among the following
Answer» <P>`[12r_("minimum")]=4` (where [.] denotes the greatest integer function) `t_(0)=(7pi)/(4omega)`sec `t_(0)=(pi)/(2omega)` sec `2r(t)(dr(t))/(dt)\|_(t=(7pi)/(2omega)sec)=(16omega)/(3pi)m^(2)//sec` Solution :Eg. of common normal `y-0=-1(x-1)` `y=-x+1,(x-1)^(2)+y^(2)=1/3` `x+y-1=0,2y^(2)=1/9` `x-1=y,y^(2)=1/(3sqrt(2))` Clearly SHORTEST distance of approach is along common normal whose equation is `x+y=1=0`. So, when they are at their CLOSEST distance `P` must be at `(1/2,1/2)` and `Q` must be at `(1- 1/(3sqrt(2)),1/(3sqrt(2)))` covering angle `(7pi)/4` on the circle . Since `P` and `Q` happened to be at these points at same time so we have `t_(0)=(7pi)/(4w)=1/(sqrt(2u))` also at this instance `t_(0),r_("min")=(3-sqrt(2))/(3sqrt(2))IMPLIES[12r_("min")]=[6sqrt(2)-4]=4` Also at any time instant `t_(1)` co-ordinate of `P,Q` are `((ut)/(sqrt(2)),(ut)/(sqrt(2)))` at `Q(1+(cos(omegat))/3,+sin((omegat)/3))` `:.r^(2)(t)=((ut)/(sqrt(2))-1 - (cos(omegat))/3)^(2)+((ut)/(sqrt(2))-(sin(omegat))/3)^(2)`

Discussion

1916.	If omegane1 is a cube root ofunity, then the sum of the series S=1+2omega+3omega^(2)+…..+3nomega^(3n-1) is
Answer» `(3N)/(omega-1)` `3n(omega-1)` `(omega-1)/(3n)` `0` ANSWER :A

Discussion

1917.	The value of a.a' is
Answer» 0 `a` a+a'` NONE of these Solution :We KNOW that `a.a'=0`

Discussion

1918.	Match the items from List-I that of List-II A bag contains 4 red , 3 white and 5 blue balls. Three balls are drawn at a time randomly from the bag. The correct answer is
Answer» `{:(A,B,C,D),(v,II, iii, IV):}` `{:(A,B,C,D),(iv,i, v, ii):}` `{:(A,B,C,D),(iv,i, v, iii):}` `{:(A,B,C,D),(v,iii, iv, i):}` ANSWER :B

Discussion

1919.	If veca=3hati-hatj+2hatk and vecb=hati-3hatk then veca.vecb is
Answer» 3 -3 4 None of these Answer :B

Discussion

1920.	f(x)= {(3x-8,"If " x le 5),(2k,"if" x gt 5):} is continuous, find k
Answer» a.`(7)/(2)` B.`(4)/(7)` C.`(3)/(7)` d.`(2)/(7)` Answer :A

Discussion

1921.	Integrate the following functions : tan^(-1)(sqrtx)
Answer» ANSWER :`(x+1)TAN^(-1)(SQRTX)-sqrtx+c`

Discussion

1922.	Pulmonary surfactant is :-
Answer» AMINO acid Steriod Phospholipid Glycolipid Answer :A

Discussion

1923.	If(2x ^ 3+x ^ 2- 5 ) /( x ^4-25 )=(Ax +B)/( x ^ 2- 5 )+(Cx + 1 ) /( x ^ 2+5 ),then(A, B, C)equalsto
Answer» ` (1, 1, 1 ) ` ` (1, 1 , 0 ) ` ` (1, 0, 1 ) ` ` (1, 2, 1 ) ` Solution : ` (2 x ^3 + x ^ 2-5 ) /(x ^4 -25 )=(Ax +B)/( x ^ 2- 5 )+(CX + 1 ) /(x ^ 2+ 5 ) ` ` rArr(Ax + B )(x ^ 2+5 )+(x + 1 )(x ^ 2- 5 )=2X ^ 3+x ^ 2- 5 ` ` rArr A + C = 2 , 5B - 5 =- 5 ` ` 5A - 5C =0 rArr B =0 ` ` rArrA = C ` `thereforeA = C = 1` `therefore( A, B, C )=(1, 0, 1 ) `

Discussion

1924.	If f'(x)=3x^(2)-(2)/(x^(3)) and f(1)=0 then find f(x).
Answer» ANSWER :`X^(3)+(1)/(x^(2))-2`

Discussion

1925.	Only 3 students A, B, C appear at a competetive examination. The probability of A coming first isthree times that of B and the probaility of B coming first is 3 times that of C. Find the probability of each coming first.
Answer» ANSWER :`(9)/(13), (3)/(13), (1)/(13)`

Discussion

1926.	If the lines barr = (2, -3, 7) + k(2, a, 5), k epsilon Rand barr = (1, 2, 3) + k(3, -a, a), k epsilon R are perpendicular to each other then a = ......
Answer» 2 -6 1 -1 Answer :D

Discussion

1927.	If Arg (3z-2i) = pi//2 then the locus of z = x +iy is
Answer» `x^(2) + y^(2) - 3x - 2 = 0 , y = 0` x = 0 such that `y GT (2)/(3)` `x^(2) + y^(2) + 2x - 4y = 0` such that `y lt 0 , x^(2) + y^(2) gt 1` `x^(2) + y^(2) + 2x - 4y = 0` such that `2x - y + 4 gt 0` ANSWER :B

Discussion

1928.	Match theequationgiven in List - I to the curve, it represents on Argand plane, given in List - II (Here z is a complex number and omega is a non real cube root of unity)
Answer» `{:(P, Q, R, S),(4, 1, 2, 3):}` `{:(P, Q, R, S),(3, 4, 1, 2):}` `{:(P, Q, R, S),(1, 3, 2, 4):}` `{:(P, Q, R, S),(2, 4, 3, 1):}` ANSWER :B

Discussion

1929.	If 3 cards are drawn from a pack of 52 cards at random, then the probability of getting cards from one suit and one card from another suit is
Answer» <P>`(.^(4)C_(2)XX.^(13)C_(2)xx.^(13)C_(1))/(.^(52)C_(3))` `(.^(4)P_(2)xx.^(13)C_(2)xx.^(13)C_(1))/(.^(52)C_(3))` `(.^(13)C_(2)xx.^(13)C_(1))/(.^(52)C_(3))` `(.^(13)C_(2)xx.^(13)C_(1))/(.^(52)C_(3))` Answer :B

Discussion

1930.	The pH of the water in Lake Michigan was tested at 13 locations along the illions shoreline. The data is presented in the scatterplot above. Which of the following best represents the mode of the pH in the collected data?
Answer» 7.2 7.3 7.4 7.5 Answer :A

Discussion

1931.	Evaluate : int(x^(2) sin^(-1)x)/((1-x^(2))^((3)/(2)))dx
Answer» Answer :`(x.sin^(-1)x)/(sqrt(1-x^(2))) + (1)/(2) log\|1-x^(2)\|-(1)/(2)(sin^(-1)x)^(2) + C`

Discussion

1932.	If x^(a)(x^(a+1))^(a)(x^(a))^(1-a)=x^(k), then k=
Answer» `2a+1` `a+a^(2)` `3A` `3a+1` SOLUTION :`X^(a)x^(a^(2)+a)x^(a-a^(2))=x^(a+a^(2)+a+a-a^(2)=x^(3a))`.

Discussion

1933.	The relation R defined in the set of real number R is as follow : R {(x,y) : x - y + sqrt2 is an irrational number} Is R transitive relation ?
Answer» SOLUTION :N/A

Discussion

1934.	Assume int _(0) ^(pi) ln sin theta d theta =- pi ln 2then prove that int _(0) ^(pi) theta ^(3) ln sin theta d theta =(3pi)/(2) int_(0) ^(pi) theta ^(2) ln ( sqrt2 sin theta) d theta.
Answer» ANSWER :`( SQRT2 SIN THETA) d theta`

Discussion

1935.	Using L' Hospital' s rule prove that lim_(x to (pi)/(2)) (sec x - tan x ) = 0
Answer» ANSWER :1

Discussion

1936.	If f(x)=2x^(4)-13x^(2)+ax+b is divisible by x^(2)-3x+2, then (a, b) is equal to
Answer» `(-9,-2)` (6, 4) (9, 2) (2, 9) ANSWER :C

Discussion

1937.	Write{x:x =can be written as a sum of two odd integers } set in the form of lists?
Answer» SOLUTION :`{2,4,6,8,10,………}`

Discussion

1938.	If Delta_(1)=\|(x,b,b),(a,x,b),(a,a,x)\|" and "Delta_(2)=\|(x,b),(a,x)\|, then
Answer» `Delta_(1)=3(Delta_(2))^(2)` `(d)/(dx)(Delta_(1))=3Delta_(2)` `(d)/(dx)(Delta_(1))=3Delta_(2)^(2)` `Delta_(1)=3Delta_(2)^(3//2)` Solution :`a+ar+ar^(2)+ar^(3)+ar^(4)=40` `(1)/(a)+(1)/(ar)+(1)/(ar^(2))+(1)/(ar^(3))+(1)/(ar^(4))=10implies(1)/(a^(2)R^(4))(a+ar+ar^(2)+ar^(3)+ar^(4))=10impliesa^(2)r^(4)=4impliesar^(2)=pm2` `\|S\|=\|a^(5).r^(10)\|=\|(pm2)^(5)\|`

Discussion

1939.	The minimum value of 2x+5 subject to 3x-1ge1 is_____.
Answer» ANSWER :The MINIMUM VALUE is 5.

Discussion

1940.	If f(x) is a polynomial of degree m(ge1), then which of the following is not true ?
Answer» `(d^(n)y)/(dx^(n))=0`, for all `NGTM` f is DERIVABLE at all `X in R` f is continuous at all `x in R` None of these. ANSWER :D

Discussion

1941.	If the normals from any point to the parabola x^(2)=4y cuts the line y=2 in points whose abscissae are in A.P., then the slope of the tangents at the 3 conormal points are in
Answer» AP GP HP none Answer :A

Discussion

1942.	Match the following {:("Line", "Intercepts"),(I. 3x+4y=6, (a) -13//2","-13//3),(II. 5x-2y+10=0, (b)5"," 5//3),(III."joining the points (2, -1), (-1, 2)", (c) -2","5),(IV."Joining the points (4, -7), (1, -5)", (d) 2"," 3//2):}
Answer» C, d, a, B c, b, a, d d, c, b, a a, b, c, d ANSWER :C

Discussion

1943.	State which of the following statement is true?
Answer» If `y^(2)=x` then y amy be regarded as a FUNCTION of x . The function `f(x)=(x^(2))/(x) and phi (x) =x` are identical A constant function is an onto function if its codomain contains only ELEMENT. Let `CC` be the set of all complex number and the function `f:RR rarr RR, g: CC rarr CC` be DEFINED by , `f(x)=x^(2) and g(x)=x^(2)` . STATE with reasons whether `f=g` or not. Answer :C

Discussion

1944.	Let P and Q be two sets defined as follows: P-{z sub C :(1 +i)z ge 0} Q = {z in C, z/(1+i) ge 0}, then
Answer» <P>P = Q `P SUBE Q, P NE Q` `Q sube P, P ne Q` `P ne Q` ANSWER :D

Discussion

1945.	If a matrix has 5 elements, what are the possible orders it can have?
Answer» ANSWER :`1 XX 5` or `5 xx 1`

Discussion

1946.	Find the shortest distance vecr=hati+2hatj+3hatk+lambda(hati-3hatj+2hatk)and vecr=4hati+5hatj+6hatk+mu(2hati+3hatj+hatk).
Answer» ANSWER :` SQRT(26) `UNIT `~~`5 unit

Discussion

1947.	tan ^(-1) "" (1)/(2)+ tan ^(-1) "" (2)/(11) = tan ^(-1)""(3)/(4)
Answer» ANSWER :R.H.S

Discussion

1948.	Ifveca , vec ball are unit vector, then the greatest value of\|veca +vecb\| + \|veca-vecb\| is
Answer» `2 SQRT2` sqrt2 2 4sqrt2 Answer :A

Discussion

1949.	If g=120, what is a+b+c?
Answer» ANSWER :`300^(@)`

Discussion

1950.	An infinite G.P has first 13 term as a and sum 5 , then
Answer» `a LT - 10` `-10 lt a lt 0` `0 lt a lt 10` `a GT 10` Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

The parabola with drectrix x+2y-1=0 and focus (1,0) is

Show that if A and B are square matrics such that AB=BA , then (A+B)^(2)=A^(2)+2AB+B^(2).

If A=[{:(8,0),(4,-2),(3,6):}]andB=[{:(2,-2),(4,2),(-5,1):}], then find the matrix X , such that 2A+3X=5B.

If a gt b and e is the eccentricity of the ellipsethen the equation of the normal at the end of the latusrectum in the first quadrant is

If S = 0, S' =0 are two touching circles then angle between their radical axis and the common tangent at the at their points of contanct is

Evalute the following integrals int (cos 6x- cos 4x)/(sin 6x - sin 4x) dx

Three vertices of a rectangle are (3,2),(-4,2) and (-4,5). Plot the points and find the coordinates of thefourth vertex.

Construct truth tables for the following and indicate which of these are tautologies (p rarr ~~p) rarr~~p

Let f: R be a function. We say that f has PROPERTY 2 if lim_(hto0)(f(h)-f(0))/(h^2) exists and is finite. Then which of the following options is/are correct ?

If the coefficients of variation of two distributions are 40 and 20 and their variances are 144 and 64 respectively, then the mean of their arithmetic means is

If2,3 aretworootsofthereciprocalequation6x^5 - 29 x^4 +2x^3 +2x^2 -29 x+6=0 thenthe otherrootsare

If int (f(x)dx)/(log sin x)= log sin x, then f(x)=....

If two dice are rolled then the probability of getting both even or sum 10 is

If there are 25 railway stations on a railway line, how many types of single second class tickets must be printed, so as to enable a passenger to travel from one station to another.

If omegane1 is a cube root ofunity, then the sum of the series S=1+2omega+3omega^(2)+…..+3nomega^(3n-1) is

The value of a.a' is

Match the items from List-I that of List-II A bag contains 4 red , 3 white and 5 blue balls. Three balls are drawn at a time randomly from the bag. The correct answer is

If veca=3hati-hatj+2hatk and vecb=hati-3hatk then veca.vecb is

f(x)= {(3x-8,"If " x le 5),(2k,"if" x gt 5):} is continuous, find k

Integrate the following functions : tan^(-1)(sqrtx)

Pulmonary surfactant is :-

If(2x ^ 3+x ^ 2- 5 ) /( x ^4-25 )=(Ax +B)/( x ^ 2- 5 )+(Cx + 1 ) /( x ^ 2+5 ),then(A, B, C)equalsto

If f'(x)=3x^(2)-(2)/(x^(3)) and f(1)=0 then find f(x).

Only 3 students A, B, C appear at a competetive examination. The probability of A coming first isthree times that of B and the probaility of B coming first is 3 times that of C. Find the probability of each coming first.

If the lines barr = (2, -3, 7) + k(2, a, 5), k epsilon Rand barr = (1, 2, 3) + k(3, -a, a), k epsilon R are perpendicular to each other then a = ......

If Arg (3z-2i) = pi//2 then the locus of z = x +iy is

Match theequationgiven in List - I to the curve, it represents on Argand plane, given in List - II (Here z is a complex number and omega is a non real cube root of unity)

If 3 cards are drawn from a pack of 52 cards at random, then the probability of getting cards from one suit and one card from another suit is

The pH of the water in Lake Michigan was tested at 13 locations along the illions shoreline. The data is presented in the scatterplot above. Which of the following best represents the mode of the pH in the collected data?

Evaluate : int(x^(2) sin^(-1)x)/((1-x^(2))^((3)/(2)))dx

If x^(a)*(x^(a+1))^(a)*(x^(a))^(1-a)=x^(k), then k=

The relation R defined in the set of real number R is as follow : R {(x,y) : x - y + sqrt2 is an irrational number} Is R transitive relation ?

Assume int _(0) ^(pi) ln sin theta d theta =- pi ln 2then prove that int _(0) ^(pi) theta ^(3) ln sin theta d theta =(3pi)/(2) int_(0) ^(pi) theta ^(2) ln ( sqrt2 sin theta) d theta.

Using L' Hospital' s rule prove that lim_(x to (pi)/(2)) (sec x - tan x ) = 0

If f(x)=2x^(4)-13x^(2)+ax+b is divisible by x^(2)-3x+2, then (a, b) is equal to

Write{x:x =can be written as a sum of two odd integers } set in the form of lists?

If Delta_(1)=|(x,b,b),(a,x,b),(a,a,x)|" and "Delta_(2)=|(x,b),(a,x)|, then

The minimum value of 2x+5 subject to 3x-1ge1 is_____.

If f(x) is a polynomial of degree m(ge1), then which of the following is not true ?

If the normals from any point to the parabola x^(2)=4y cuts the line y=2 in points whose abscissae are in A.P., then the slope of the tangents at the 3 conormal points are in

Match the following {:("Line", "Intercepts"),(I. 3x+4y=6, (a) -13//2","-13//3),(II. 5x-2y+10=0, (b)5"," 5//3),(III."joining the points (2, -1), (-1, 2)", (c) -2","5),(IV."Joining the points (4, -7), (1, -5)", (d) 2"," 3//2):}

State which of the following statement is true?

Let P and Q be two sets defined as follows: P-{z sub C :(1 +i)z ge 0} Q = {z in C, z/(1+i) ge 0}, then

If a matrix has 5 elements, what are the possible orders it can have?

Find the shortest distance vecr=hati+2hatj+3hatk+lambda(hati-3hatj+2hatk)and vecr=4hati+5hatj+6hatk+mu(2hati+3hatj+hatk).

tan ^(-1) "" (1)/(2)+ tan ^(-1) "" (2)/(11) = tan ^(-1)""(3)/(4)

Ifveca , vec ball are unit vector, then the greatest value of|veca +vecb| + |veca-vecb| is

If g=120, what is a+b+c?

An infinite G.P has first 13 term as a and sum 5 , then

Construct truth tables for the following and indicate which of these are tautologies (p rarr p) rarrp

If x^(a)(x^(a+1))^(a)(x^(a))^(1-a)=x^(k), then k=