28278 + Interview Questions in Maths in Class 12 Page 532 InterviewSolution

26551.	Evaluate the integrals by using substitution int_(0)^(pi/2)sqrt(sinphi)cos^(3)phidphi
Answer»

Discussion

26552.	Evaluate int_(pi/6)^(pi/3)(dx)/(1+sqrt(tanx))
Answer» ANSWER :`(PI)/(12)`

Discussion

26553.	Differentiate the functions(log x)^(x) + x^(log x)
Answer» Answer :`(LOGX)^(x-1)[1 + LOG x.log (log x)]+ 2X^(log x-1) XX log x`

Discussion

26554.	If (a^(n + 1) + b^(n + 1))/(a^(n) + b^(n)) is the arithmetic mean between a and b, then n =
Answer» 2 `-2` 0 2 Answer :C

Discussion

26555.	Integrate the functions (sqrt(tanx))/(sinxcosx)
Answer» ANSWER :`2sqrt(TANX)+C`

Discussion

26556.	Match the following
Answer» a,B,c b,c,a c,a,b a,c,a Answer :B

Discussion

26557.	Write the general form of the equation of a line. Write the condition on its coefficients.
Answer» SOLUTION :NA

Discussion

26558.	Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x-3,find fof.
Answer» SOLUTION :N/A

Discussion

26559.	Match the following
Answer» a,B,C b,c,a c,a,b a,c,b Answer :C

Discussion

26560.	(1)/(x(x - 1 ) (x + 2 ) …. (x+ n))= (A_0 )/( x )+(A _ 1 )/(x + 1 )+…….. ( A _ n) /(x +n ) ,0leile r rArr A _ ris equalto
Answer» ` ( -1) ^ r(r!)/( (n - r) !) ` ` (-1) ^r (r!)/(r!(n-r )!) ` ` (1)/(r!(n-r)!)` `(r!)/((n-r)!)` Solution : ` (1)/(x (x +1)(x+2)… (x+n))= (A_0)/(x)+ (A_1)/((x+1)) + … + (A_n)/(x+n) ,0le ILE r ` ` rArr(1)/(x(x+1)(x+2)…(x+r)…(x+n)) = (A_0)/(x)+ (A_1)/((x+1))+ …. + (A_n)/(x+n ) ` ` (1)/(x(x+1)(x+2)… (x+r - 1 )(x + r + 1 )… (x + n))`= `rArr(A_0 (x + r ))/(x)+ (A_1(x+r))/(x+1) + ... + (A_r(x+r))/((x+r)) +(A_(r +1)(x+r))/(x + r + 1 )+... + (A_n(x+r))/(x + n) ` ` rArr (1)/(x(x+1)(x+2)...(x+n)) = (A_0 (x + r ))/(x)+ (A_1(x+r))/(x + 1 )+... + A_r + A _ (r + 1 )((x + r ))/((x+r + 1)) + ... + A_n((x + r ))/((x + n)) ` Substituting`x =- r `in ABOVEEQUATION, we GET, ` rArr(1)/((-r)(- r + 1 ) (-r + 2 )... (-r + r - 1 )(-r + r + 1 )... (-r + n)) ` `= 0 + 0+ ...+ A _ r + 0 ` `thereforeA_r= (1 ) /((-1) ^r r (r -1) ... (-1).(1) (2) ... (-r + n)) ` ` A _r =((-1) ^r)/((r) (r - 1 )...(1).(1)(2)...(n-r )) ` `= ((-1) ^r ) /(r! (n - r) ! ) `

Discussion

26561.	On the set Q^(+) of all positive rational number define an operation * on Q^(+)by ab =(ab)/(2) forall a,b in Q^(+) Show that (i) is a binary operation on Q^(+)(ii) * is commutative (iii)* is associative Find the identify element in Q^(+) for * Whast is the inverseof a in Q^(+)?
Answer» SOLUTION :`ae=a RARR e=2` `ab=2 rarr(ab)/(2)=2 rarr b=4/a rarr a^(-1) =(4)/(a)`

Discussion

26562.	If sqrt(x^(2) + y^(2))=a. e^(tan^(-1)((y)/(x))), a gt 0 then the value of y''(0) is…….
Answer» `(a)/(2) E^(-(PI)/(2))` `AE^((pi)/(2))` `(-2)/(a) e^(-(pi)/(2))` Does not exist Answer :C

Discussion

26563.	Differentiate cotx-secx-log_10x
Answer» SOLUTION :`y=cotx-secx-log_10x` `dy/dx=-cosec^2x-secx CDOT tanx-1/xlog_10e`

Discussion

26564.	Line x =0 divides the region mentioned above in two parts,The ratio of the area left-hand side of the line to that of right-hand side of the line is-
Answer» ` (2+PI ): pi ` ` (2-pi) :pi ` ` 1:1 ` `(pi+2) :pi ` ANSWER :D

Discussion

26565.	Find dy/dx,if y=12(1-cost),x=10(t-sint).pi/2lttltpi/2
Answer» SOLUTION :`dy/dx=12[0+sint)=12sint,dx/dt=10(1-cost)thereforedy/dx=(dx//dt)/(dx//dt)=(12sint)/(10(1-cost))=(6xx2sin(1//2)COS(1//2))/(5xx2sin^2(1//2))=6/5cot(1//2)`

Discussion

26566.	Find the coefficient of x^6 in the expansion of (1+ x^2 - x^3)^8
Answer» ANSWER :84

Discussion

26567.	Solve (dy)/(dx)=(y(x-2y))/(x(x-3y))
Answer» ANSWER :`KX^(2)E^(-X)/(y)`

Discussion

26568.	overset(sqrt(3))underset(1)int (dx)/(1+x^(2))=.....
Answer» `(PI)/(3)` `(2pi)/(3)` `(pi)/(6)` `(pi)/(12)` Answer :D

Discussion

26569.	Ifcos^(-1)((x)/(5)) + "cosec"^(-1) ((5)/(4)) =ppi/2then x=…….
Answer» 1 3 5 4 Answer :D

Discussion

26570.	If a vector vecr is in the direction of X- axis then find its direction cosines.
Answer» ANSWER :(1,0,0) (-1,0,0)

Discussion

26571.	Compute P(A/B) if P (B)= 0.5 and P(AnnB) = 0.32
Answer» <P> SOLUTION :P(A/B)=(P`(ANNB))/(P(B))` =0.32/0.5=32/50=16/25

Discussion

26572.	If a plane passes through the point (1, 1, 1) and is perpendicular to the line (x - 1)/3 = (y - 1)/0 = (z - 1)/4, then its perpendicular distance from the origin is -
Answer» `3/4` `4/3` `7/5` `1` SOLUTION :Equation of the PLANE which PASSES through (1,1,1) and dr's of its normal are 3,0,4 is- `3(x - 1) + 0(y - 1) + 4(Z -1) = 0` `3X + 4z - 7 = 0` Perpendicular distance from the origin is- `=\|(-7)/5\| = 7/5`.

Discussion

26573.	The parabolas y^(2)=4x,x^(2)=4y divide the square region bounded by the lines x = 4, y = 4 and the co-ordinate axes. If S_(1),S_(2),S_(3) are respectively the areas of these parts numbered from top to bottom then S_(1):S_(2):S_(3) is
Answer» `2:1:1` `1:1:1` `1:2:1` `1:2:3` ANSWER :B

Discussion

26574.	Negation of the statement (p ^^ r) rarr (r vv q) is
Answer» <P>`(p ^^ r) ^^ (~r ^^ ~Q)` `~(p ^^ r) RARR ~(r VV q)` `~(p vv r) rarr ~(r ^^ q)` `(p ^^ r) vv (r ^^ q)` Answer :A

Discussion

26575.	IfA=[{:(1,2),(4,2):}], then show that \|2A\|=4\|A\|.
Answer»

Discussion

26576.	sum _(k =1) ^(3) cos ^(2) (2k -1) pi/12 is equal to
Answer» 0 `1/2` `-1/2` `3/2` ANSWER :D

Discussion

26577.	If veca,vecb,vecc are unit vectors such that veca+vecb+vecc = vec0, find the value of veca.vecb+vecb.vecc+vecc.veca.
Answer» Solution :`veca+vecb+vecc` = 0 `IMPLIES(veca+vecb+vecc)^2` = 0 `\|veca\|^2+\|vecb\|^2+\|vecc\|^2 + 2(veca.vecb+vecb.vecc+vecc.veca)` = 0 `implies 2(veca.vecb+vecb.vecc+vecc.veca)` = -(1+1+1) `(THEREFORE \|veca\|^2` = `\|vecb\|^2` = `\|vecc\|^2` =1 `implies veca.vecb+vecb.vecc+vecc.veca` = -3/2.

Discussion

26578.	{:("Column A","", "Column B"),("The average of three number if the greatest is 20",,"The average of the numbers if the greatest is 2"):}
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

26579.	Value of lim _(hto0) (int _(0)^(x-he ^(-1//h))dx - int _(0)^(pi) x ^(2)e^(-x ^(2))dx )/(he^(-1//h)) in equal to:
Answer» `PI (1-pi^(2)) E ^(-pi^(2))` `2PI (1- pi^(2)) e ^(-pi^(2))` `pi (1-pi)e ^(-pi)` `pi ^(2) e ^(-pi ^(2))` ANSWER :D

Discussion

26580.	If overline(a), overline(b), overline(c) are non-collinear vectors such that for some scalars x, y, z, xoverline(a)+yoverline(b)+zoverline(c)=overline(0), then
Answer» `x=0, yne0,zne0` `XNE0, y=0, zne0` `xne0, yne0, z=0` `x=0, y=0, z=0` ANSWER :D

Discussion

26581.	By using the properties of definite integrals, evaluate the integrals int_(0)^(pi)log(1+cosx)dx
Answer» ANSWER :`-pilog2`

Discussion

26582.	If the tangent at the point (1,2) on the ellipse 3x^(2)+4y^(2)=19is also a tangent to the parabola y^(2)-kx=0 then k =
Answer» `(57)/(16)` `(-57)/(64)` `(57)/(64)` `(-57)/(16)` ANSWER :D

Discussion

26583.	number of ways in which 4 prizes can be distributed among 5 students If no student gets all the prizes is
Answer» 625 620 1024 1020 Answer :B

Discussion

26584.	Let two independent eventsA and Bsuch that P(A)=0.3,P(B)=0.6.Find P(A and B)
Answer» <P> SOLUTION :GIVEN that P (A) = 0.3 and P(B) = 0.6therefore `P(A^c)`= 1-P(A) = 1-0.3=0.7 `P(B^c)` = 1-P(B) = 1-0.6=0.4 =P(A)P(B) =`0.3xx0.6`=0.18

Discussion

26585.	Solve ((1)/(2))^(logx^(2))+2gt3.2^(log(-x))
Answer» Answer :`n in(-OO,-1)uu((-1)/(10),0)`

Discussion

26586.	I : The coefficient of x^2 in (sqrtx^3 + 2//x)^6 is 60. II : The coefficient ofx^(-6) in (x^4 -1//x^2)^15 is -1365.
Answer» only I is true only II is true both I and II are true neither I nor II true Answer :C

Discussion

26587.	Find the equation of the circle passing through the origin, having its centre on the line x+y=4 and intersecting the circle x^2+y^2-4x+2y+4=0 orthogonally.
Answer» ANSWER :`x^2+y^2-4x-4y=0`

Discussion

26588.	The vertices of a triangle are A(1,0,0),B(0,2,0),C(0,0,3). If the direction ratios of the line joining the orthoceutre and circumcentre of the triangle are a, b, -111, the a+b is equal to
Answer» 5 10 15 25 Answer :C

Discussion

26589.	Show that each of the followingexpressions is a soluton of the corresponding given differential equation (i) y=2x^(2),xy'=2y (ii) y=ae^(x)+be^(-x), y''-y=0
Answer» ANSWER :(i) XY (II) 0

Discussion

26590.	Consider the functin f (x) = (ln x)/(8) - ax +x ^(2) and a ge 0 is a real constant :
Answer» Answer :ATO Q; BtoS; C TOP; DtoR`

Discussion

26591.	lim_( xto oo) ((x^2+5x+3)/(x^2+x+3))^x
Answer» `E^4` `e^2` `e^3` `e` ANSWER :A

Discussion

26592.	If bar(P),bar(Q),bar(R) and bar(S) are points whose position vectors are bar(i)-bar(k),-bar(i)+2bar(j),2bar(i)-3bar(k)and 3bar(i) - 2bar(j) - bar(k), then find component of bar(RS) on bar(PQ).
Answer» ANSWER :`4//3`

Discussion

26593.	T_(n) =sum _( r =2n )^(3n-1) (r)/(r ^(2) +n ^(2)), S_(n) = sum _(r =2n+1)^(3n) (r )/(r ^(2) + n ^(2)), thenAA n in {1,2,3...}:
Answer» `T_(n ) GT 1/2 LN 2` ` S_(n) LT 1/2 ln 2` ` T_(n) lt 1/2 ln 2` ` S_(n)gt 1/2 ln 2` Answer :A::B

Discussion

26594.	x(x^(2) - 1)(dy)/(dx) = 1, y = 0 when x = 2.
Answer» Answer :`y = 1/(2) log (X^(2) - 1)/(x^(2)) -(1)/(2) log(3)/(4)`

Discussion

26595.	Let A = ((2.1,2.7,1.3),(3.1,3.2,1.7),(2.1,2.5,2.9)). The sum of values of x for which A - xI_(3) is singular is _______
Answer» ANSWER :10.57

Discussion

26596.	Let f(x) =x^(2) , x in (-1,2) Then show that f(x) has exactly one point of local minimabut global maximum Is not defined.
Answer»

Discussion

26597.	C_0 - 2^3 . C_1 +3^2. C_2 - …. + (-1)^n (n+1)^2 . (C_n)=
Answer» 0 `2^n` `(2^(n+1)-1)/(n+1)` none Answer :A

Discussion

26598.	int_(0)^(pi//2) (sin 8x.log(cot x))/(cos 2 x)dx=
Answer» 0 1 `1//2` `pi//2` ANSWER :A

Discussion

26599.	lim_(n rarr oo) ((2)/(3) + ((2)/(3))^(2) + ((2)/(3))^(3) + ……. + ((2)/(3))^(n)) is :
Answer» 1 2 `1//2` NONE of these ANSWER :B

Discussion

26600.	How many roots foes the following equation possess 3 ^(\|x\|) (\|2-x\|\|)=2 ?
Answer» 2 3 4 6 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

Evaluate the integrals by using substitution int_(0)^(pi/2)sqrt(sinphi)cos^(3)phidphi

Evaluate int_(pi/6)^(pi/3)(dx)/(1+sqrt(tanx))

Differentiate the functions(log x)^(x) + x^(log x)

If (a^(n + 1) + b^(n + 1))/(a^(n) + b^(n)) is the arithmetic mean between a and b, then n =

Integrate the functions (sqrt(tanx))/(sinxcosx)

Match the following

Write the general form of the equation of a line. Write the condition on its coefficients.

Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x-3,find fof.

Match the following

(1)/(x(x - 1 ) (x + 2 ) …. (x+ n))= (A_0 )/( x )+(A _ 1 )/(x + 1 )+…….. ( A _ n) /(x +n ) ,0leile r rArr A _ ris equalto

On the set Q^(+) of all positive rational number define an operation * on Q^(+)by a*b =(ab)/(2) forall a,b in Q^(+) Show that (i) * is a binary operation on Q^(+)(ii) * is commutative (iii)* is associative Find the identify element in Q^(+) for * Whast is the inverseof a in Q^(+)?

If sqrt(x^(2) + y^(2))=a. e^(tan^(-1)((y)/(x))), a gt 0 then the value of y''(0) is…….

Differentiate cotx-secx-log_10x

Line x =0 divides the region mentioned above in two parts,The ratio of the area left-hand side of the line to that of right-hand side of the line is-

Find dy/dx,if y=12(1-cost),x=10(t-sint).pi/2lttltpi/2

Find the coefficient of x^6 in the expansion of (1+ x^2 - x^3)^8

Solve (dy)/(dx)=(y(x-2y))/(x(x-3y))

overset(sqrt(3))underset(1)int (dx)/(1+x^(2))=.....

Ifcos^(-1)((x)/(5)) + "cosec"^(-1) ((5)/(4)) =ppi/2then x=…….

If a vector vecr is in the direction of X- axis then find its direction cosines.

Compute P(A/B) if P (B)= 0.5 and P(AnnB) = 0.32

If a plane passes through the point (1, 1, 1) and is perpendicular to the line (x - 1)/3 = (y - 1)/0 = (z - 1)/4, then its perpendicular distance from the origin is -

The parabolas y^(2)=4x,x^(2)=4y divide the square region bounded by the lines x = 4, y = 4 and the co-ordinate axes. If S_(1),S_(2),S_(3) are respectively the areas of these parts numbered from top to bottom then S_(1):S_(2):S_(3) is

Negation of the statement (p ^^ r) rarr (r vv q) is

IfA=[{:(1,2),(4,2):}], then show that |2A|=4|A|.

sum _(k =1) ^(3) cos ^(2) (2k -1) pi/12 is equal to

If veca,vecb,vecc are unit vectors such that veca+vecb+vecc = vec0, find the value of veca.vecb+vecb.vecc+vecc.veca.

{:("Column A","", "Column B"),("The average of three number if the greatest is 20",,"The average of the numbers if the greatest is 2"):}

Value of lim _(hto0) (int _(0)^(x-he ^(-1//h))dx - int _(0)^(pi) x ^(2)e^(-x ^(2))dx )/(he^(-1//h)) in equal to:

If overline(a), overline(b), overline(c) are non-collinear vectors such that for some scalars x, y, z, xoverline(a)+yoverline(b)+zoverline(c)=overline(0), then

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi)log(1+cosx)dx

If the tangent at the point (1,2) on the ellipse 3x^(2)+4y^(2)=19is also a tangent to the parabola y^(2)-kx=0 then k =

number of ways in which 4 prizes can be distributed among 5 students If no student gets all the prizes is

Let two independent eventsA and Bsuch that P(A)=0.3,P(B)=0.6.Find P(A and B)

Solve ((1)/(2))^(logx^(2))+2gt3.2^(log(-x))

I : The coefficient of x^2 in (sqrtx^3 + 2//x)^6 is 60. II : The coefficient ofx^(-6) in (x^4 -1//x^2)^15 is -1365.

Find the equation of the circle passing through the origin, having its centre on the line x+y=4 and intersecting the circle x^2+y^2-4x+2y+4=0 orthogonally.

The vertices of a triangle are A(1,0,0),B(0,2,0),C(0,0,3). If the direction ratios of the line joining the orthoceutre and circumcentre of the triangle are a, b, -111, the a+b is equal to

Show that each of the followingexpressions is a soluton of the corresponding given differential equation (i) y=2x^(2),xy'=2y (ii) y=ae^(x)+be^(-x), y''-y=0

Consider the functin f (x) = (ln x)/(8) - ax +x ^(2) and a ge 0 is a real constant :

lim_( xto oo) ((x^2+5x+3)/(x^2+x+3))^x

If bar(P),bar(Q),bar(R) and bar(S) are points whose position vectors are bar(i)-bar(k),-bar(i)+2bar(j),2bar(i)-3bar(k)and 3bar(i) - 2bar(j) - bar(k), then find component of bar(RS) on bar(PQ).

T_(n) =sum _( r =2n )^(3n-1) (r)/(r ^(2) +n ^(2)), S_(n) = sum _(r =2n+1)^(3n) (r )/(r ^(2) + n ^(2)), thenAA n in {1,2,3...}:

x(x^(2) - 1)(dy)/(dx) = 1, y = 0 when x = 2.

Let A = ((2.1,2.7,1.3),(3.1,3.2,1.7),(2.1,2.5,2.9)). The sum of values of x for which A - xI_(3) is singular is _______

Let f(x) =x^(2) , x in (-1,2) Then show that f(x) has exactly one point of local minimabut global maximum Is not defined.

C_0 - 2^3 . C_1 +3^2. C_2 - …. + (-1)^n (n+1)^2 . (C_n)=

int_(0)^(pi//2) (sin 8x.log(cot x))/(cos 2 x)dx=

lim_(n rarr oo) ((2)/(3) + ((2)/(3))^(2) + ((2)/(3))^(3) + ……. + ((2)/(3))^(n)) is :

How many roots foes the following equation possess 3 ^(|x|) (|2-x||)=2 ?

On the set Q^(+) of all positive rational number define an operation * on Q^(+)by ab =(ab)/(2) forall a,b in Q^(+) Show that (i) is a binary operation on Q^(+)(ii) * is commutative (iii)* is associative Find the identify element in Q^(+) for * Whast is the inverseof a in Q^(+)?