28278 + Interview Questions in Maths in Class 12 Page 539 InterviewSolution

26901.	Integrate the following functions x^3/sqrt(1-x^8)
Answer» SOLUTION :`int x^3/sqrt(1-x^8) DX = int x^3/sqrt(1-(x^4)^2) dx`. put `t = x^4`. Then `DT = 4x^3 dx` therefore REQUIRED INTEGRAL =`int 1/sqrt(1-t^2) 1/4 dt = 1/4 sin^-1 t+c` =`1/4 sin^-1 x^4 +c`

Discussion

26902.	If veca,vecb,vecc are unit vectors such that veca+vecb+vecc=vec0 , find the value ofvecavecb+vecbvecc+vecc*veca.
Answer» ANSWER :`(-3)/(2)`

Discussion

26903.	If the magnitude of the vector product of the vector hati+hatj+hatk with aunit vector along the sum of vector 2hati+4hatj-5hatkand lambda hati+2hatj+3hatk is equal to sqrt2, then find the value of 'lambda'
Answer» ANSWER :`lambda=1`

Discussion

26904.	A and B are two events such that P(A) ne 0. Find P(B\|A), if i. A is a subset of B , ii. AnnB = 0
Answer» ANSWER :i. 1, II. 0

Discussion

26905.	Form the values of the following in terms of a, b, c if alpha, beta are roots of ax^(2)+bx+c=0, c != 0 i) (1)/(alpha)+(1)/(beta) ii) (1)/(alpha^(2))+(1)/(beta^(2)) iii) alpha^(3)+beta^(3) iv) ((alpha)/(beta)-(beta)/(alpha))^(2) v) alpha^(4)beta^(7)+alpha^(7)beta^(4) vi) alpha^(2)+beta^(2) vii) (alpha^(2)+beta^(2))/(alpha^(-2)+beta^(-2)) viii) (alpha)/(beta^(2))+(beta)/(alpha^(2))
Answer» Answer :i) `(-b)/(a)` ii) `(b^(2)-2AC)/(C^(2))` III) `(3abc-b^(3))/(a^(3))` iv) `(b^(2)(b^(2)-4AC))/(a^(2)c^(2))` v) `bc^(4)((3ac-b^(2)))/(a^(7))` VI) `(b^(2)-2ac)/(a^(2))` vii) `(c^(2))/(a^(2))` viii) `(3abc-b^(3))/(ac^(2))`

Discussion

26906.	If A is 2xx2 matrix such that A^(2) =O then tr (A) is
Answer» 1 `-1` 0 none of these ANSWER :C

Discussion

26907.	Let f(x)={{:(x^(n)sin(1//x^(2))","xne0),(0","x=0):},(ninI). Then
Answer» `(pi)/(2)` `(pi)/(2sqrt(2))` `(pi)/(sqrt(2))` `sqrt(2)pi` Solution :For `NGT0, underset(xto0)LIMX^(N)sin(1//x^(2))=0xx(" any value between-1 to 1")=0` For `nlt0,underset(xto0)limx^(n)sin(1//x^(2))=ooxx(" any value between-1 to 1")=+-oo`

Discussion

26908.	Evaluate int Sin^(5) x dx
Answer» Answer :`-(sin^(4)xcccosx)/(5)-(4)/(15)sin^(2)xcosx-(8)/(15)cos+c`

Discussion

26909.	Find the area lying above x-axisand included between the circle x^(2)+ y^(2) = 8x and inside in the parabola y^(2) = 4x.
Answer» ANSWER :`4/3(8+3pi)`

Discussion

26910.	Which of the following functions is decreasing on (0, (pi)/(2)).
Answer» sin (2x) TAN X COS x cos (3X) Answer :C

Discussion

26911.	If the angles of elevation of two towers of heights h_(1) and h_(2) from the mid-point of the line joining their feet be (pi)/(3) and (pi)/(6), respectively, then (h_(1))/(h_(2)) = _________________
Answer» ANSWER :`3.00`

Discussion

26912.	If the line barr=hati+lambda(2hati-mhatj-3hatk) is parallel to the plane barr.(mhati+3hatj+hatk)=0, then m is equal to
Answer» 3 -3 1 -1 Answer :B

Discussion

26913.	Integration using rigonometric identities : int (x sin x)/((x cos x-sin x+5))dx=...+c
Answer» `log\|x cosx-sin x+5\|` `-log\|x cosx-sin x+5\|` `log\|x sinx-sin x+5\|` `-log\|x sinx-sin x+5\|` ANSWER :B

Discussion

26914.	Evaluate the following integrals int (ax^2 + bx + c)dx
Answer» Solution :`int (ax^2 +BX+ c) DX = ax^3/3 +bx^2/2 +CX + c^.` (`c^.` is an arbitrary CONSTANT)

Discussion

26915.	Fundamental theorem of definite integral : If I_(n)=int_(0)^(pi/4)tan^(n)dx then lim_(ntooo)n(I_(n)+I_(n+2))=.......
Answer» 1 `(1)/(2)` `OO` 0 Answer :A

Discussion

26916.	If A+ B+C= 180^(@) " then " cos 2A+ cos 2B + cos 2C+ 1=
Answer» `1+ 4 sin A sin B sin C ` `1-2 sin A sin B sin C ` `2+2 sin A sin B sin C ` `4SIN A sin B COS C ` ANSWER :A

Discussion

26917.	How many factors of 10,000 end with a 5 on the right ?
Answer» SOLUTION :We have `1000 = 2^4xx5^4` `:." The factors of 10000 ending with 5 are"5,5xx5=25,5xx5xx5xx5=125` `5xx5xx5xx5=625` `:. "There are 4 factors ending with 5"`.

Discussion

26918.	Let 'A' is (4xx4) matrix such that the sum of elements in each row is 1. Find out sum of the all the elements in A^(10).
Answer» ANSWER :4

Discussion

26919.	For the ellipse given by ((x - 3)^(2))/(25) + ((y - 2)^(2))/(16) = 1, match the equations of the lines given in List I with those on the List Ii. {:("List I","List II"),(i."The equation of the minor axis",p. 3 x = 34),(ii."The equation of a latusrectum",r. x + y = 9),( ,s. x = 6),( ,f. x = 3),( ,u. 3y = 34):}
Answer» <P>I,P,S Q,U,F Q,P,F Q,P,S Answer :d

Discussion

26920.	Let A(2 sec theta,3 tan theta) and B (2 sec phi 3 tan phi ) where theta+phi=(pi)/(2), be two points on the hyperbola (x^2)/(4)-(y^2)/(9)=1 If (alpha, beta) is the point of intersection of normals to the hyperbola at A and B, then beta=
Answer» `(-13)/(3)` `(13)/(3)` `(3)/(13)` `(-3)/(13)` ANSWER :A

Discussion

26921.	If P is a complex number whose modulus is one, then the equation( (1 + iz)/(1- iz) )^4 = P has
Answer» real and equal ROOTS real and DISTINCT roots TWO real and two complex roots all complex roots Answer :D

Discussion

26922.	Find the probability of throwing at most 2 sixes in 6 throws of a single die.
Answer» ANSWER :`(35)/(18)((5)/(6))^(4)`

Discussion

26923.	IF mx ^2+ 7xy -3y^2+ 4x+ 7y+2is resolvableintotwolinearfactorsthen m=oftwplinearfactors thenthe factorsare
Answer» 7 4 2 `-5` ANSWER :C

Discussion

26924.	Evaluate sum_(i=0)^(n-1) sum_(j= 1 + i)^(n+1)""^(n)C_(i) ""^(n+1)C_(j) .
Answer» Solution :Let ` P = sum_(i=0)^(n-1) sum_(j= 1 + i)^(n+1)""^(n)C_(i) ""^(n+1)C_(j)` . `sum_(j=1)^(n-1)""^(n)C_(0)""^(n+1)C_(j) +sum_(j= 2)^(n+1)""^(n)C_(i) ""^(n+1)C_(j)+ sum_(j= 3)^(n+1) ""^(n)C_(2)""^(n+1)C_(j) + ...+ sum_(j = n)^(n+1) ""^(n)C_(n-1) ""^(n+1)C_(j)` `""^(n)C_(0) sum_(j=1)^(n-1)""^(n)C_(j)+""^(n)C_(1) +sum_(j= 2)^(n+1)""^(n+1)C_(j) ""^(n+1)C_(2)+ sum_(j= 3)^(n+1) ""^(n+1)C_(j) + ...+ ""^(n)C_(n-1)sum_(j = n)^(n+1)""^(n+1)C_(j)` `""^(n)C_(0)(""^(n +1)C_(j) + ""^(n+1)C_(2) + ""^(n+1)C_(3) + ...+ ""^(n+1)C_(n+1))` ` + ""^(n)C_(1) (""^(n+1)C_(2)+""^(n+1)C_(3) + ""^(n+1)C_(4)+ ...+ ""^(n+1)C_(n+1))` ` + ""^(n)C_(2) (""^(n+1)C_(3)+""^(n+1)C_(4) + ""^(n+1)C_(5)+ ...+ ""^(n+1)C_(n+1))` ` + ...+ ""^(n)C_(n-1)(""^(n +1)C_(n) + ""^(n+1)C_(n+1))` `= ""^(n+1)C_(1)""^(n)C_(0) + ""^(n+1)C_(2) (""^(n)C_(0) + ""^(n)C_(1)) + ""^(n+1)C_(3) (""^(n)C_(0) + ""^(n)C_(1) + ""^(n)C_(2))` ` + ...+ ""^(n+1)C_(n+1) (""^(n)C_(0) + ""^(n)C_(1) + ""^(n)C_(2)+ ...+ ""^(n)C_(n-1))` `(""^(n)C_(0) + ""^(n)C_(1)) ""^(n)C_(0)+ (""^(n)C_(1) + ""^(n)C_()) ( ""^(n)C_(2)+ ""^(n)C_(1))+ (""^(n)C_(2) + ""^(n)C_(3)) (""^(n)C_(0) + ""^(n)C_(1) + ""^(n)C_(2))` `+ ...+ (""^(n)C_(n) + ""^(n)C_(n-1))(""^(n)C_(0) + ""^(n)C_(1)+ ""^(n)C_(2) + ...+ ""^(n)C_(n-1)) + n` `(""^(n)C_(0))^(2) + (""^(n)C_(1))^(2) + (""^(n)C_(2))^(2) + ...+ (""^(n)C_(n-1))^(2)` ` + {""^(n)C_(0) ""^(n)C_(1) + ""^(n)C_(0) ""^(n)C_(2) + ""^(n)C_(0) ""^(n)C_(3)` `+...+""^(n)C_(0) ""^(n)C_(n-1) + ...+ ""^(n)C_(n-2) + ""^(n)C_(n-1)} + 2^(n) - 1 + n` ` (""^(n)C_(0) + ""^(n)C_(1) + ""^(n)C_(2) + ...+ ""^(n)C_(n-1))^(2) + 2^(n) - 1 + n` `= (2^(n) -1)^(2) + 2^(n) -1 + n = 2 ^(2N) - 2^(n) + n`

Discussion

26925.	A hyperbola has one focus at (1, 2) , its corresponding directrix is x + y = 1 and eccentricity is 2. Then
Answer» <P>`{:(P,Q,R,S),(2,1,3,4):}` `{:(P,Q,R,S),(3,4,1,2):}` `{:(P,Q,R,S),(1,2,4,3):}` `{:(P,Q,R,S),(4,3,2,1):}` SOLUTION :N/A

Discussion

26926.	Let A=[{:((1)/(6),(-1)/(3),(-1)/(6)),((-1)/(3),(2)/(3),(1)/(3)),((-1)/(6),(1)/(3),(1)/(6))]. If A^(2016l)+A^(2017m)+A^(2018n)=(1)/(alpha)A, for every l,m,n in N, then the value of alpha is
Answer» `(1)/(6)` `(1)/(3)` `(1)/(2)` `(2)/(3)` ANSWER :B

Discussion

26927.	int_0^1x(1-x)^ndx
Answer» Solution :`I=int_0^1x(1-X)^ndx` =`int_0^1(1-x)x^ndx` =`int(x^n-x^(n+1))DX` =`[x^(n+1)/(n+1)-x^(n+2)/(n+2)]_0^1` =`1/(n+1)-1/(n+2)=1/((n+1)(n+2))`

Discussion

26928.	I= int "arc" sin x dx.
Answer» Answer :`X "ARC" SIN x+ sqrt( 1-x^(2) ) +C`.

Discussion

26929.	The value of ""^(2)P_(1) + ^(3)P_(1) + ...... + ^(n)P_(1) equal to
Answer» `(N^(2) - n + 2)/2` `(n^(2) + n + 2)/2` `(n^(2) + n - 2)/2` `(n^(2) - n - 2)/2` ANSWER :D

Discussion

26930.	If x sin (a + y) + sin a cos (a + y)= 0, then prove that (dy)/(dx)= (sin^(2) (a + y))/(sin a)
Answer» ANSWER :`(SIN^(2) (a + y))/(sin a)`

Discussion

26931.	Let f(x)=min{x,x^2}, for every x in R. Then
Answer» f (x) is CONTINUOUS for all x f (x) is diffentiable for all x `f'(x) =1` for `x GT 1` f (x) is not DIFFERENTIABLE at TWO VALUES of x Answer :B

Discussion

26932.	int_(0)^([x])(2^(x))/(2^[x])dx=
Answer» `- ([2X])/(LN 2)` `([2x])/(ln 2)` `- ([X])/(ln 2)` `([x])/(ln 2)` ANSWER :D

Discussion

26933.	Match the statement in Column I with those in Column II. [Note : Here z takes values in the complex plane and Im z and Re z denote, respectively, the imagi- nary part and the real part of z]. {:(,Column -I, Column -II),((A),"The set of points z satisfying"\|z-iz\|\|=\|z+i\|z\|\|,(P)" an ellipse with eccentricity"4/5),((B),"The set of points z satisfying"\|z+4\|+\|z-4\|=10" is contained in or equal to",(Q)"the set of points z satisfying "Im z = 0 ),((C),"If " \|w\|=2",then the set of points "z=w-1/w" is contained in or equal to",(R)"the set of points z satisfying "\|Im z \|ge1),(,,(S)"the set of points z satisfying "\|Re z \|le2),((D),"If" \|w\|=1",then the set of points"z=w+1/w" is contained in or equal to ",(T) " the set of points z satisfying"\|z\|le3):}
Answer» ANSWER :A::B::C::D

Discussion

26934.	From the set of all families having three children, a family is picked at random If one child of the family is a son. find the probablilty that he has two sisters.
Answer» Solution :The ONE child of the FAMILY is a son. We have to find the probability that he has two sisters. We have the following mutually exclusive EVENTS : BGG,GBG,GGB. `THEREFORE` The required probability `=P(B)xxP(G)xxP(G)+P(G)xxP(B)+P(G)+P(G)xxP(G)xxP(B)` `=1/2xx1/2xx1/2+1/2xx1/2xx1/2+1/2xx1/2xx1/2=3/8`

Discussion

26935.	A die is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?
Answer» ANSWER :`(2)/(5)`

Discussion

26936.	The value of n for which 704 + (1)/(2) (704) + (1)/(4)(704) + ….. Upto n terms = 1984 - (1)/(2) ( 1984) + (1)/(4) (1984) …. Upto n terms is
Answer» 5 4 4 10 Answer :A

Discussion

26937.	Integrate the following function : intsqrt((1-x)/(1+x))dx
Answer» ANSWER :`SIN^(-1)x+sqrt(1-x^(2))+C`

Discussion

26938.	Iff(x) = x+\|x\|+ cos([ pi ^(2) ]x) and g(X)=sin x,where [.]denotesthegreatestintegerfunction, then
Answer» f(X)+ G(x)iscontinuouseverywhere , then f(x) + g(x) is differentiableeverywhere `f(x) xxg(x) ` is DIFFERENTIABLE EVERYWHERE `f(x) xx g(x) ` is continuousbut not differentiableat x=0 ANSWER :A::C

Discussion

26939.	Let A = R - {3} and B =R -{1}. Consider the function f : A to B defined by f (x) = ((x -2)/(x -3)). Is f one-one and onto ? Justify your answer.
Answer» ANSWER :YES

Discussion

26940.	If two dice are thrown the probability that atleast one of the dice shows a number greater than or equal to 4 is
Answer» `9//36` `3//4` `1//9` `4//9` ANSWER :B

Discussion

26941.	Integrate the functions 1/(1+cotx)
Answer» ANSWER :`x/2-1/2logabs(cosx+sinx)+C`

Discussion

26942.	f (x) = lim _(x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +1),n in N and g (x) =tan ((1)/(2)sin ^(-1)((2f (x))/(1+f ^(2) (x)))), then The number of points where g (x) is non-differentiable AA x in R is:
Answer» 1 2 3 4 Answer :D

Discussion

26943.	If \|(z_1 z- z_2)/(z_1 z+z_2)\|=k, (z_1 , z_2 ne 0) then
Answer» for `K =1` LOCUS of Z is straight line for `k cancel(in) {1,0}z` lieson a circle for `k=0` z represents a point for `k=1,z` lies on the perpendicular bisector of the segment JOINING `(z_2)/(z_1) and (z_2)/(z_1)` Answer :A::B::C::D

Discussion

26944.	Solve the inequation sqrt(x^(2)-3x-10) gt (8-x).
Answer» ANSWER :`((74)/(13), INFTY)`

Discussion

26945.	A and B are two points on the hyperbola O is the centre. If OA is perpendicular to OB then (1)/(OA)^(2)+(1)/(OB)^(2) is equal to
Answer» `(1)/(a^(2))+(1)/(B^(2))` `(1)/(a^(2))-(1)/(b^(2))` `(1)/(b^(2))-(1)/(a^(2))` `a^(2)+b^(2)` ANSWER :b

Discussion

26946.	Evaluate int_(0)^((pi)/(4)) [sin x + [cos x + [tan x + [sec x]]]] dx
Answer» ANSWER :`(PI)/(4)`

Discussion

26947.	sintheta= ( x + Y)/( 2 sqrt(xy))is possible
Answer» all realx,y `X , ygt 0` `x=y ne 0` no realx,y Answer :C

Discussion

26948.	To double the covering range of a TV transmittion tower, its height should be multiplied by :
Answer» `(1)/(sqrt(2))` 2 4 `sqrt(2)` SOLUTION :NA

Discussion

26949.	The total number of 5 digit numbers formed using the digits 2, 4, 6, 7, 8 if the digits are no repeated is
Answer» 5! `5^(5)` 6! `5^(2)` ANSWER :B

Discussion

26950.	Analyze the roots of the following equations: (i)2x^(3) - 9x^(2) + 12x - (9//2) = 0 (ii) 2x^(3) - 9x^(2) + 12x - 3 = 0
Answer» Solution :Let `f(x) = 2X^(3) - 9x^(2) + 12x - (9//2)`. Then `f(x) = 6X^(2) - 18x +12` `= 6(x^(2)-3x+2) = 6(x- 1)(x-2)` Now `f'(x) = 0 rArr` x = 1 and x = 2 Also `f(1) = 2 - 9 + 12 - (9//2) gt 0` and`f(2) = 16 - 36 + 24 - (9//2) lt 0` HENCE, the graphs of the function `y= f(x)is as shown in the figure. (##CEN_ALG_C02_SLV_026_S01.png" width="80%"> As shown in the figure, the graph CUTS the x-axis at three distinct points Hence, equation`f(x) = 0` has three distinct roots. (ii) For `2x^(3) - 9x^(2) + 12x - 3 = 0,` `f(x) = 2x ^(3) - 9x + 12x - 3` `f'(x)= 0` `rArr6x^(2) - 18x + 12 = 0` or6 (x - 1) (x - 2) = 0 `rArr`x = 1and x = 2 Also ` f(1)= 2 - 9 + 12 - 3 = 2` and `f(2) = 16 - 36 + 24 - 3 = 1` Hence, the graphof y = f(x) is as shown in the figure. Thus , from the graph, we can see thatf(x) = 0 has only one real root, though y = f(x) has two turning points .

Discussion

Explore topic-wise InterviewSolutions in .

Integrate the following functions x^3/sqrt(1-x^8)

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

If the magnitude of the vector product of the vector hati+hatj+hatk with aunit vector along the sum of vector 2hati+4hatj-5hatkand lambda hati+2hatj+3hatk is equal to sqrt2, then find the value of 'lambda'

A and B are two events such that P(A) ne 0. Find P(B|A), if i. A is a subset of B , ii. AnnB = 0

If A is 2xx2 matrix such that A^(2) =O then tr (A) is

Let f(x)={{:(x^(n)sin(1//x^(2))","xne0),(0","x=0):},(ninI). Then

Evaluate int Sin^(5) x dx

Find the area lying above x-axisand included between the circle x^(2)+ y^(2) = 8x and inside in the parabola y^(2) = 4x.

Which of the following functions is decreasing on (0, (pi)/(2)).

If the angles of elevation of two towers of heights h_(1) and h_(2) from the mid-point of the line joining their feet be (pi)/(3) and (pi)/(6), respectively, then (h_(1))/(h_(2)) = _________________

If the line barr=hati+lambda(2hati-mhatj-3hatk) is parallel to the plane barr.(mhati+3hatj+hatk)=0, then m is equal to

Integration using rigonometric identities : int (x sin x)/((x cos x-sin x+5))dx=...+c

Evaluate the following integrals int (ax^2 + bx + c)dx

Fundamental theorem of definite integral : If I_(n)=int_(0)^(pi/4)tan^(n)dx then lim_(ntooo)n(I_(n)+I_(n+2))=.......

If A+ B+C= 180^(@) " then " cos 2A+ cos 2B + cos 2C+ 1=

How many factors of 10,000 end with a 5 on the right ?

Let 'A' is (4xx4) matrix such that the sum of elements in each row is 1. Find out sum of the all the elements in A^(10).

Let A(2 sec theta,3 tan theta) and B (2 sec phi 3 tan phi ) where theta+phi=(pi)/(2), be two points on the hyperbola (x^2)/(4)-(y^2)/(9)=1 If (alpha, beta) is the point of intersection of normals to the hyperbola at A and B, then beta=

If P is a complex number whose modulus is one, then the equation( (1 + iz)/(1- iz) )^4 = P has

Find the probability of throwing at most 2 sixes in 6 throws of a single die.

IF mx ^2+ 7xy -3y^2+ 4x+ 7y+2is resolvableintotwolinearfactorsthen m=oftwplinearfactors thenthe factorsare

Evaluate sum_(i=0)^(n-1) sum_(j= 1 + i)^(n+1)""^(n)C_(i) ""^(n+1)C_(j) .

A hyperbola has one focus at (1, 2) , its corresponding directrix is x + y = 1 and eccentricity is 2. Then

Let A=[{:((1)/(6),(-1)/(3),(-1)/(6)),((-1)/(3),(2)/(3),(1)/(3)),((-1)/(6),(1)/(3),(1)/(6))]. If A^(2016l)+A^(2017m)+A^(2018n)=(1)/(alpha)A, for every l,m,n in N, then the value of alpha is

int_0^1x(1-x)^ndx

I= int "arc" sin x dx.

The value of ""^(2)P_(1) + ^(3)P_(1) + ...... + ^(n)P_(1) equal to

If x sin (a + y) + sin a cos (a + y)= 0, then prove that (dy)/(dx)= (sin^(2) (a + y))/(sin a)

Let f(x)=min{x,x^2}, for every x in R. Then

int_(0)^([x])(2^(x))/(2^[x])dx=

From the set of all families having three children, a family is picked at random If one child of the family is a son. find the probablilty that he has two sisters.

A die is thrown twice and the sum of the numbers appearing is observed﻿ to be 6. What is the conditional probability that the number 4 has appeared at least﻿ once?﻿

The value of n for which 704 + (1)/(2) (704) + (1)/(4)(704) + ….. Upto n terms = 1984 - (1)/(2) ( 1984) + (1)/(4) (1984) …. Upto n terms is

Integrate the following function : intsqrt((1-x)/(1+x))dx

Iff(x) = x+|x|+ cos([ pi ^(2) ]x) and g(X)=sin x,where [.]denotesthegreatestintegerfunction, then

Let A = R - {3} and B =R -{1}. Consider the function f : A to B defined by f (x) = ((x -2)/(x -3)). Is f one-one and onto ? Justify your answer.

If two dice are thrown the probability that atleast one of the dice shows a number greater than or equal to 4 is

Integrate the functions 1/(1+cotx)

f (x) = lim _(x to oo) (x ^(2) + 2 (x+1)^(2n))/((x+1) ^(2n+1) + x^(2) +1),n in N and g (x) =tan ((1)/(2)sin ^(-1)((2f (x))/(1+f ^(2) (x)))), then The number of points where g (x) is non-differentiable AA x in R is:

If |(z_1 z- z_2)/(z_1 z+z_2)|=k, (z_1 , z_2 ne 0) then

Solve the inequation sqrt(x^(2)-3x-10) gt (8-x).

A and B are two points on the hyperbola O is the centre. If OA is perpendicular to OB then (1)/(OA)^(2)+(1)/(OB)^(2) is equal to

Evaluate int_(0)^((pi)/(4)) [sin x + [cos x + [tan x + [sec x]]]] dx

sintheta= ( x + Y)/( 2 sqrt(xy))is possible

To double the covering range of a TV transmittion tower, its height should be multiplied by :

The total number of 5 digit numbers formed using the digits 2, 4, 6, 7, 8 if the digits are no repeated is

Analyze the roots of the following equations: (i)2x^(3) - 9x^(2) + 12x - (9//2) = 0 (ii) 2x^(3) - 9x^(2) + 12x - 3 = 0

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

A die is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?