14949 + Interview Questions in Maths in Class 11 Page 24 InterviewSolution

1151.	Simplify the following (21)/(4) sqrt(-48) -5 sqrt(-27)
Answer» ANSWER :`6sqrt3i`

Discussion

1152.	(i) If the axes are rotated through an angle 30^(0) , then find the coordinates of (1,2) in the new system . (ii) If the axes are rotated through an angle 30^(0), then find the coordinates of (-2, 4) in the new system. (iii) When the axes are rotated through an angle (pi)/(2) , find the new coordinates of the point (alpha, 0)
Answer» Answer :(i) `((SQRT(3) + 2)/( 2), (-1 + sqrt(3))/( 2))` (ii) `(2 - sqrt(3), 1 + 2 sqrt(3))` (iii) `(0, - ALPHA)`

Discussion

1153.	P(n):n^2 - n +41 , for n = ……, it is not prime number .
Answer» 1 2 3 41 Answer :D

Discussion

1154.	If the centroid of the tetrahedron is (0, -1, (5)/(2)) and three vertices are (-2, 3, 4), (3, -4, 2), (2, -5, 1) then the fourth vertex is
Answer» (-3, 2, 3) (1, 0, 5) (0, -1, 5) (5, -1, 0) Answer :a

Discussion

1155.	Evaluate(sqrt3+ sqrt2 )^6- ( sqrt3- sqrt2)^6 .
Answer» ANSWER :396`SQRT6`

Discussion

1156.	Let bara = 2bari -barj+bark , barb=bari+2barj-bark , barc=bari+barj-2bark be the three vectors. A vector in the plane of barb, barc "and whose projection on " bara " of magnitude " sqrt(2/3) is
Answer» `2bari+3barj-3bark` `2bari+3barj+3bark` `2bari+barj-5bark` `bari+barj-bark` ANSWER :A

Discussion

1157.	The probability of intersection of two events A and B is always less than or equal to those favorable to the event A.
Answer» ANSWER :A

Discussion

1158.	Find the rth term from the end in (x+a)^(n).
Answer» ANSWER :`=""^(N) C_(n - r+1) .X^(r-1) .a^(n-r+1)`.

Discussion

1159.	Which of the following has its middle term independent of x?
Answer» `(x+1/x)^10` `(x+1/x)^9` `(x^2+1/x)^9` `(x^2+1/x)^10` ANSWER :A

Discussion

1160.	If A=[a_(ij)] is scalar matrix then the trace of A is
Answer» `sum_(i)a_(IJ)` `sum_(i)a_(ij)` `sum_(i)sum_(J)a_(ij)` `sum_(i)a_(II)` ANSWER :D

Discussion

1161.	If the vectors bara = (1,x,-2), barb = (x,3,-4) are mutually perpendicular, then x =
Answer» -2 2 4 -4 Answer :A

Discussion

1162.	Descibe the sample space :A coin is tossed twice . If the second thrownIf the second throw results in a tail , a die is thrown.
Answer» Answer :S={HH,HTI,HT2,HT3,HT4,HT5,H16,T T1,T T2,T T3,T T4, T T5, T T6}`

Discussion

1163.	If bara,barb,barc " are unit vectors, then " abs(bara-barb)^(2)+abs(barb-barc)^(2) +abs(barc-bara)^(2) does not exceed
Answer» 4 9 8 6 Answer :B

Discussion

1164.	Show that the solutions Cos p theta = Sin q theta from two series each of which is an A.P. Find also the common difference of each A.P (p ne pm q)
Answer» ANSWER :2

Discussion

1165.	Find the range of the following functions given by f(x)= (3)/(2-x^(2))
Answer» ANSWER :`[(3)/(2), OO)`

Discussion

1166.	What is dripping out from a conical funnel at a uniform rate of 2cm^(3)//sec through a tiny hole at the vertex at the bottom. When the slant height of the water is 4cm. Find the rate of decrease of slant height of the water given that the vertical angle of the funnel is 120^@.
Answer» ANSWER :`1/(3PI)` cm/sec

Discussion

1167.	If lamdax^(2)+6xy+9y^(2)+4x+12y+3=0 represents a pair of straight liens then lamda=
Answer» `-3` `-4` 1 5 Answer :C

Discussion

1168.	Solve the equation for0 le x le 2pi. 2 sin x-1 =0
Answer» ANSWER :`pi/6, (5PI)/(6)`

Discussion

1169.	Determine whether p,q and "If p, then q " are true or false in each case given below : 3 >2
Answer» <P> ANSWER :`{:(p,Q,p =>q),(T,T,T):}`

Discussion

1170.	Find the point equidistant from the four points (-1,1,3),(2,1,2),(0,5,6) and (3,2,2).
Answer» ANSWER :4

Discussion

1171.	Find the distance from the origin to each of the point: (2,2,3)
Answer» ANSWER :`SQRT17`

Discussion

1172.	Ifsin alpha + sin beta = a , cos alpha + cos beta = b " thencos ( alpha + beta ) =
Answer» `SIN((alpha-beta)/2)=+-sqrt((a^(2)+b^(2))/4)` `cos((alpha-beta)/2)=sqrt((a^(2)+b^(2))/2)` `tan((alpha-beta)/2)=+-sqrt((4-a^(2)-b^(2))/(a^(2)+b^(2)))` `tan((alpha-beta)/2)=+-sqrt((4+a^(2)+b^(2))/(a^(2)+b^(2)))` ANSWER :C

Discussion

1173.	Insert three numbers between 1 and 256 so that the following sequence is a G.P ?
Answer» ANSWER :256

Discussion

1174.	Let bara,barb and barc be non-zero vectors such that (baraxxbarb)xxbarc=1/3absbarbabsbarcbara. If theta is the acute angle between the vectors barb and barc then sintheta equals to
Answer» `2/3` `(SQRT2)/3` `1/3` `(2SQRT2)/3` ANSWER :D

Discussion

1175.	Evaluate the following limits : lim_(x to 0) (tan 3x- 2x)/(3x-sin^(2) x)
Answer» ANSWER :`1/3`

Discussion

1176.	The transformed equation of 4x^(2) + 9y^(2) - 8x + 36y + 4 = 0when the axes are translated to (1, -2) is ax^(2) + by^(2) = c . Then desending order of a, b, c
Answer» C, B, a c, a, b a, b, c a, c, b Answer :A

Discussion

1177.	((n),(r)) = (""^(n)P_(r))/(K), then K = ......
Answer» `R !` `(n-n) !` `(n-n) ! R!` `(r-1)!` ANSWER :A

Discussion

1178.	Two rays in the first quadrant x+y=absa and ax-y=1 " interset each other in the interval " a in (a_0,oo)," the value of " a_0 is
Answer» ANSWER :A-s;B-p,Q;C-r;D-p,q,s

Discussion

1179.	Find the 9th term in the expansion of ( 3x - (1)/( 2x ) )^(8), x ne 0.
Answer» ANSWER :`256 x^8`

Discussion

1180.	If sqrt(3) cos theta - sin theta = 1 then theta =
Answer» `2 k PI + (pi)/(2), k in Z` `2 k pi + (pi)/( 3) , k in Z` `2 k pi + (pi)/( 6) , k in Z` `2 k pi + (pi)/( 4) , k in Z` Answer :A

Discussion

1181.	(vec(a) + vec(b)) xx (vec(a)-vec(b)) + (vec(b) + vec(c )) xx (vec(b)-vec(c )) + (vec(c )+ vec(a)) xx (vec(c ) -vec(a))=
Answer» `2(vec(a) XX vec(B) +vec(b) xx vec(C ) + vec(c ) xx vec(a))` `-2 (vec(a) xx vec(b) + vec(b) xx vec(c ) + vec(c ) xx vec(a))` `(vec(a) xx vec(b) + vec(b) xx vec(c )+ vec(c ) xx vec(a))` `-(vec(a) xx vec(b) + vec(b) xx vec(c ) + vec(c ) xx vec(a))` Answer :B

Discussion

1182.	Ifp_1, p_2, p_3arethe lengthsof the altitudesfromthe verticesofDelta ABCto the oppositesides,then( a cot A)/(p_1) + ( b cot B)/( p_2)+( c cot C)/(p_3)=
Answer» ` (1)/ ( R ) ` ` (1)/( R) ` ` (1)/( r^(3))` ` 2` ANSWER :D

Discussion

1183.	Find the multiplicative inverse of each of the following complex numbers when it exists. (i)/(1+i)
Answer» ANSWER :`1-i`

Discussion

1184.	If A = { x : (-2)/(5) le x le (pi-2)/(5)}, B = { y : - 1 le y le 1} and f(x)= cos (5x+2) then the mapping f: A rarr B is
Answer» One-one but not onto. onto but not one-one. Both one-one and onto Neither one-one nor onto Answer :C

Discussion

1185.	Let bara=2bari+barj+bark,barb=bari+2barj-bark and a unit vector barc be coplaner. If barc is perpendiclar to bara then barc=
Answer» `1/(SQRT2)(-barj+bark)` `1/(SQRT3)(-bari-barj-bark)` `1/(SQRT5)(bari-2barj)` `1/(sqrt3)(bari-barj-bark)` ANSWER :D

Discussion

1186.	If S_(1) = {2}, S_(2) = { (3)/(2) , (4)/(2) }, S_(3) = { (4)/( 4) , (5)/(4) , (6)/( 4) } , S_(4) = { (5)/( 8) , (6)/( 8) , (7)/(8) , (8)/( 8) } ,….. then the sum of numbers in S_(20) is
Answer» `(1220)/( 2^(20))` `(1563)/( 2^(19) -1)` `(1445)/( 2^(18))` `(1576)/( 2^(21))` Answer :A

Discussion

1187.	If a straight line perpendicular to 2x-3y+7=0 forms a triangle with the coordinate axes whose area is 3 sq. units, then the equation of the straight line(s) is
Answer» `3x+2y=+-4` `3x+2y=+-6` `3x+2y=+-8` `3x+2y=+-2` ANSWER :B

Discussion

1188.	If omega is a cube root of unity, then omega + omega^(2)=…..
Answer» ANSWER :`-1`

Discussion

1189.	If vec(a)= -vec(i) + vec(j) + vec(k), vec(b)= vec(i)-vec(j) + vec(k), vec(c )= vec(i) + vec(j)-vec(k), then the vectors vec(a) xx vec(b), vec(b) xx vec(c ), vec(c ) xx vec(a) are
Answer» collinear mutually perpendicular linearly dependent linearly independent Answer :D

Discussion

1190.	sec^(2)(Tan^(-1)2)+cosec^(2)(Cot^(-1)3)=
Answer» 5 10 15 20 Answer :C

Discussion

1191.	Let f(x)=(x-1)^(4)(x-2)^(n) , n inN. Then f(x) has
Answer» a maximum at x= 1 if N is odd a maximum at x=1 if n is EVEN a MINIMUM at x=1 ifis even a minima at x=2if n is even Answer :A::C::D

Discussion

1192.	What universal set would you propose for each of the following : The set of squares.
Answer» ANSWER :The SET of all the QUADRILATERAL in the PLANE.

Discussion

1193.	If f(x)=ax^(5)+bx^(3)+cx+d is odd then
Answer» `a=0` `b=0` `c=0` `d=0` ANSWER :D

Discussion

1194.	If theta is angle between pair of lines x^(2)-3xy+lambday^(2)+3x-5y+2=0 then "cosec"^(2) theta
Answer» 10 20 5 15 Answer :A

Discussion

1195.	Point R (h, k) divides a line segment between the axes in the ratio 1:2 Find equation of the line.
Answer» ANSWER :`2KX + HY = 3KH`

Discussion

1196.	Which of the following relations are functions? Give reason {(3,3) (4,2) (5,1) (6,0) (7,7)}
Answer» ANSWER :It is a FUNCTION

Discussion

1197.	How many permutations can be there with x^(3).y^(2) z^(4)? How many of these arrangements, all z are not together?
Answer» ANSWER :1260, 1200

Discussion

1198.	If x+1/x=2 cos20^(@) then x^(3)+1/x^(3)=
Answer» `1//2` 1 `1//4` `1//8` ANSWER :B

Discussion

1199.	Natural numbers are written as 1, (2,3), (4,5,6).. Show that the sum of number in the nth group is (n)/(2) (n +1) .
Answer» ANSWER :C

Discussion

1200.	If they are in A.P, find the possible values of n
Answer» SOLUTION :n=7 or [4]

Discussion

Explore topic-wise InterviewSolutions in .

Simplify the following (21)/(4) sqrt(-48) -5 sqrt(-27)

P(n):n^2 - n +41 , for n = ……, it is not prime number .

If the centroid of the tetrahedron is (0, -1, (5)/(2)) and three vertices are (-2, 3, 4), (3, -4, 2), (2, -5, 1) then the fourth vertex is

Evaluate(sqrt3+ sqrt2 )^6- ( sqrt3- sqrt2)^6 .

Let bara = 2bari -barj+bark , barb=bari+2barj-bark , barc=bari+barj-2bark be the three vectors. A vector in the plane of barb, barc "and whose projection on " bara " of magnitude " sqrt(2/3) is

The probability of intersection of two events A and B is always less than or equal to those favorable to the event A.

Find the rth term from the end in (x+a)^(n).

Which of the following has its middle term independent of x?

If A=[a_(ij)] is scalar matrix then the trace of A is

If the vectors bara = (1,x,-2), barb = (x,3,-4) are mutually perpendicular, then x =

Descibe the sample space :A coin is tossed twice . If the second thrownIf the second throw results in a tail , a die is thrown.

If bara,barb,barc " are unit vectors, then " abs(bara-barb)^(2)+abs(barb-barc)^(2) +abs(barc-bara)^(2) does not exceed

Show that the solutions Cos p theta = Sin q theta from two series each of which is an A.P. Find also the common difference of each A.P (p ne pm q)

Find the range of the following functions given by f(x)= (3)/(2-x^(2))

What is dripping out from a conical funnel at a uniform rate of 2cm^(3)//sec through a tiny hole at the vertex at the bottom. When the slant height of the water is 4cm. Find the rate of decrease of slant height of the water given that the vertical angle of the funnel is 120^@.

If lamdax^(2)+6xy+9y^(2)+4x+12y+3=0 represents a pair of straight liens then lamda=

Solve the equation for0 le x le 2pi. 2 sin x-1 =0

Determine whether p,q and "If p, then q " are true or false in each case given below : 3 >2

Find the point equidistant from the four points (-1,1,3),(2,1,2),(0,5,6) and (3,2,2).

Find the distance from the origin to each of the point: (2,2,3)

Ifsin alpha + sin beta = a , cos alpha + cos beta = b " thencos ( alpha + beta ) =

Insert three numbers between 1 and 256 so that the following sequence is a G.P ?

Let bara,barb and barc be non-zero vectors such that (baraxxbarb)xxbarc=1/3absbarbabsbarcbara. If theta is the acute angle between the vectors barb and barc then sintheta equals to

Evaluate the following limits : lim_(x to 0) (tan 3x- 2x)/(3x-sin^(2) x)

The transformed equation of 4x^(2) + 9y^(2) - 8x + 36y + 4 = 0when the axes are translated to (1, -2) is ax^(2) + by^(2) = c . Then desending order of a, b, c

((n),(r)) = (""^(n)P_(r))/(K), then K = ......

Two rays in the first quadrant x+y=absa and ax-y=1 " interset each other in the interval " a in (a_0,oo)," the value of " a_0 is

Find the 9th term in the expansion of ( 3x - (1)/( 2x ) )^(8), x ne 0.

If sqrt(3) cos theta - sin theta = 1 then theta =

(vec(a) + vec(b)) xx (vec(a)-vec(b)) + (vec(b) + vec(c )) xx (vec(b)-vec(c )) + (vec(c )+ vec(a)) xx (vec(c ) -vec(a))=

Ifp_1, p_2, p_3arethe lengthsof the altitudesfromthe verticesofDelta ABCto the oppositesides,then( a cot A)/(p_1) + ( b cot B)/( p_2)+( c cot C)/(p_3)=

Find the multiplicative inverse of each of the following complex numbers when it exists. (i)/(1+i)

If A = { x : (-2)/(5) le x le (pi-2)/(5)}, B = { y : - 1 le y le 1} and f(x)= cos (5x+2) then the mapping f: A rarr B is

Let bara=2bari+barj+bark,barb=bari+2barj-bark and a unit vector barc be coplaner. If barc is perpendiclar to bara then barc=

If S_(1) = {2}, S_(2) = { (3)/(2) , (4)/(2) }, S_(3) = { (4)/( 4) , (5)/(4) , (6)/( 4) } , S_(4) = { (5)/( 8) , (6)/( 8) , (7)/(8) , (8)/( 8) } ,….. then the sum of numbers in S_(20) is

If a straight line perpendicular to 2x-3y+7=0 forms a triangle with the coordinate axes whose area is 3 sq. units, then the equation of the straight line(s) is

If omega is a cube root of unity, then omega + omega^(2)=…..

If vec(a)= -vec(i) + vec(j) + vec(k), vec(b)= vec(i)-vec(j) + vec(k), vec(c )= vec(i) + vec(j)-vec(k), then the vectors vec(a) xx vec(b), vec(b) xx vec(c ), vec(c ) xx vec(a) are

sec^(2)(Tan^(-1)2)+cosec^(2)(Cot^(-1)3)=

Let f(x)=(x-1)^(4)(x-2)^(n) , n inN. Then f(x) has

What universal set would you propose for each of the following : The set of squares.

If f(x)=ax^(5)+bx^(3)+cx+d is odd then

If theta is angle between pair of lines x^(2)-3xy+lambday^(2)+3x-5y+2=0 then "cosec"^(2) theta

Point R (h, k) divides a line segment between the axes in the ratio 1:2 Find equation of the line.

Which of the following relations are functions? Give reason {(3,3) (4,2) (5,1) (6,0) (7,7)}

How many permutations can be there with x^(3).y^(2) z^(4)? How many of these arrangements, all z are not together?

If x+1/x=2 cos20^(@) then x^(3)+1/x^(3)=

Natural numbers are written as 1, (2,3), (4,5,6).. Show that the sum of number in the nth group is (n)/(2) (n +1) .

If they are in A.P, find the possible values of n