28278 + Interview Questions in Maths in Class 12 Page 547 InterviewSolution

27301.	The radius of the sphere x^(2)+y^(2)+z^(2)=12x+4y+3z is
Answer» `13/2` 13 26 52 Answer :A

Discussion

27302.	Does there exist a function which is continuous everywhere but not differentiable at exactly two points ? Justify your answer.
Answer» ANSWER :x=1 and x=2

Discussion

27303.	Statement 1 : The function f(x)=(3x-1)4x^(2)-12x+5\|cospix is differentiable at x=(1)/(2), (5)/(2). because Statement 2 : cos (2n +1)(pi)/(2)= 0 AA n in 1=l.
Answer» STATEMENT - 1 is True, Statement - 2 is True, Statement - 2 is a correct EXPLANATION for Statement - 6 Statement - 1 is True, Statement - 2 is True, Statement - 2 is NOT a correct explanation for Statement - 6 Statement - 1 is True, Statement - 2 is False Statement - 1 is False, Statement - 2 is True Answer :A

Discussion

27304.	If the matrix A is both symmetric and skew symmetric ,then ……..
Answer» is a DIAGONAL matrix is a ZERO matrix is a SQUARE matrix None of these Answer :B

Discussion

27305.	A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs. 5 and that from a shade is Rs. 3. Assuming that the manufacturer can sell all the lamps and shades that he produces,how should he schedule his daily production in order to maximise his profit ?
Answer» ANSWER :Maximum profit is Z = RS. 32 when he manufacture 4 pedestal LAMPS and 4 wooden shades.

Discussion

27306.	The minimum ..............
Answer» Solution :Equation of normal to `y=tan X` at `(alpha, tan alpha)` `y-tan alpha= (-1)/(sec^(2) alpha) (x-alpha)` `tan alpha. (sec^(2) alpha)=(2+pi/4-alpha)` `tan alpha (1+tan^(2) alpha)= (2+pi/4-alpha)` `alpha=pi/4` `implies` minimum DISTANCE = distance between `(pi/4, 1)` and `(2+pi/4, 0)` - RADIUS `=SQRT(5)-1`

Discussion

27307.	If f(x)=lim_(nrarroo) ((x^(2)+ax+1)+x^(2n)(2x^(2)+x+b))/(1+x^(2n)) and lim_(xrarrpm1) f(x) exists, then The value of a is
Answer» `-1` 1 0 2 Solution :`f(x)=UNDERSET(nrarroo)(lim)((x^(2)+ax+1)+x^(2n)(2X^(2)+x+b))/(1+x^(2n))` `={{:(x^(2)+ax+1",",\|x\|lt1),(2x^(2)+x+b",",\|x\|gt1),((-a+b+3)/(2)",",x=-1),((a+b+5)/(2)",",x=1):}` `underset(xrarr-1)(lim)f(x)" exists if"` `underset(xrarr -1)(lim)f(x)=underset(xrarr-1^(+))(lim)f(x)` `rArr""underset(xrarr-1^(-))(lim)(2x^(2)+x+b)=underset(xrarr-1^(+))(lim)(x^(2)+ax+1)` `rArr""2-1+b=1-a+1` `rArr""a+b=1"(i)"` `underset(xrarr1)(lim)f(x)" exists if"` `underset(xrarr1^(-))(lim)f(x)=underset(xrarr1^(+))(lim)f(x)` `rArr""underset(xrarr1^(-))(lim)(x^(2)+ax+1)=underset(xrarr1^(+))(lim)(2x^(2)+x+b)` `rArr 1+a+1=2+1+b` `rArr a-b=1"(ii)"` `"Solving Eqs. (i) and (ii), we GET a = 1 and b=0."`

Discussion

27308.	A box contains 1 white and 3 black balls. Two balls ar drawn at random. Describe the sample space associated with this experiment.
Answer» SOLUTION :`S={(W, B_1), (W, B_2), (W, B_3), (B_1, B_2), (B_1, B_3), (B_2, B_3)}`

Discussion

27309.	Solve (i) 2 sin x+ tan x=0 (ii)7 cos^(2) theta+3 sin^(2) theta=4 (iii) cos x + sec x=2 (iv)Solve tan x + tan 2x+tan 3x=0 (v) sin x sin 3x=1//2 (vi)cot(pi)/(3) cos (vii)Solve sec x-1=sqrt(2-1)tan x 2nx=sqrt(3)
Answer» Answer :(i) `npi, 2(3k+1)(pi)/(3)` (ii) `2npipx(pi)/(3),2npipm(2pi)/(3)` (iii)`2npi` (IV)`(npi)/(3),npipmtan^(-1)(1)/SQRT(2)` (v)`(2n+1)(pi)/(4),(6kpm1)(pi)/(6)` (VI)`x=m pm 1//6, m in I` (vii)`2npi+(pi)/(4)`

Discussion

27310.	If x,y,a,b,c,d are real and x+iy= sqrt((a+ib)/(c+id))" then"(x^(2)+y^(2))^(2)=
Answer» `(a^(2)+B^(2))/(C^(2)+d^(2))` `(a^(2)-b^(2))/(c^(2)-d^(2))` `(a^(2)-c^(2))/(b^(2)-d^(2))` `(a^(2)+b^(2))/((c+d)^2)` ANSWER :A

Discussion

27311.	If the scalar product of the vector hati+hatj+2hatk with the unti vector along mhati+2hatj+3hatk is equal to 2, then one of the value of m is
Answer» 3 4 5 6 Solution :`(hati +hatj +2 hatk). ((mhati +2hatj +3hatk )/( SQRT(m^(2)+2^(2)+3^(2))))=2` `implies m+2+6=2sqrt(13+m^(2))` `implies (m+8)^(2)=4(13+m^(2))` `implies m^(2)+16M+64 =4M^(2)+52` ` implies 3m^(2)-16m - 12=0 ` `implies(3m+2)(m-6)=0` `implies m=6,-(2)/(3)`

Discussion

27312.	Areabounded by curvey= tan pi x , x in [-1/4 ,1/4] and X-axisis …..
Answer» `(LOG 2)/(2 PI)` `(log 2)/(2)` `log 2` `(LOG2)/(pi)` ANSWER :D

Discussion

27313.	A sequence of positive (a _(1), a _(2)…a _(n)) is called good if a _(1) =a_(1) +a _(2) + …+ a _(i-1) for all 2 le I le n. What is the maximum possible value of n for a good sequence such that a _(n) = 9216?
Answer» ANSWER :12

Discussion

27314.	Find the derivative of 1/(1 - t^2) with respect to1 + t^(2).
Answer» `(1 -t^2)^(2)` `(1 -t^2)^(-2)` `(1 + t^2)^(-1)` `(1 -t^2)^(2)` ANSWER :A

Discussion

27315.	A window in the form of a rectangle , is surmounted by a semicircular opening . Thetotal perimeter of the window is 10 m Findthe dimensions of the rectangular part of the window to admit maximum light through the whole opening .
Answer» ANSWER :`=2X=(20)/(pi+4)`m and BREADTH `=y=(10)/(pi+4)`m.

Discussion

27316.	O( 0, 0 ) , A ( 6 , 0 ) , B (0 , 4 )arethreepoints.IfPisa pointsuchthatthearea ofthequadrilateralPABCis10sq.Unit,thenthelocusofPis
Answer» `X ^ 2 -9y ^ 2 =0 ` `y ^ 2-9 x ^ 2=0 ` `9x ^ 2-y ^ 2=0 ` `9 y ^ 2-x ^ 2=0 ` ANSWER :A

Discussion

27317.	If A, B, C are mutually exclusive and exhaustive events such that P(B) = (3)/(2)P(A), P(C) = (1)/(3)P(B) then P(A) =
Answer» ANSWER :`2 : 1`

Discussion

27318.	An ellipse has eccentricity 1/2 and the focus at the point P(1/2,1). Its one directrix is the common tangent, nearer to the point P, to the hyperola x^(2)-y^(2)=1 and the circle x^(2)+y^(2)=1. Find the equation of the ellipse.
Answer» ANSWER :`(2x-1)^(2) +4(y-1)^(2)=(x-1)^(2)`

Discussion

27319.	P is a point on the circle x^2+y^2=1. Line OP, where O is origin, and x=1meets at Q. L_1 is a line parallel to x-axis drawn from Q. A line is drawn parallel to x-axis from P meeting x = 1 at R. OR meets L_1 at S. Then locus S is:
Answer» circle parabola ellipse hyperbola Answer :B

Discussion

27320.	Compute the volume of the solid generated by revolving about the x-axis the figure bounded by the parabola y= 0.25 x^(2) + 2 and the straight line 5x -8y + 14=0
Answer» ANSWER :`(891)/(1180)PI`

Discussion

27321.	Integrate the following functions : intxsqrt(x^(4)+1)dx
Answer» Answer :`(x^(2))/(4)SQRT(x^(4)+1)+(1)/(4)log\|x^(2)+sqrt(x^(4)+1)\|+C`

Discussion

27322.	A pair of dice is thrown. Find the probability of getting a sum of at least 9 if 5 appears on at least one of the dice.
Answer» Solution :A PAIR of DICE is thrown. LET A be the event of GETTING at least 9 POINT and B, the event that 5 appears on at least one of the dice. `therefore` B={(1,5),(2,5),(3,5),(4,5),(5,5),(5.6),(5,1),(5,2),(5,3),(5,4),(5,6)} A={(3,6),(4,5),(5,4),(6,3),(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}`therefore A capB`={(4,5),(5,4),(5,5),(5,6),(6,5) `thereforeP(A\|B)=P((A capB))/(P(B))=(5/36)/(11/36)=5/11`

Discussion

27323.	STATEMENT-1 : Number of solution oflog \|x\| = theta^(x) is twoand STATEMENT-2 :Iflog_(30) 3 - a , log_(30) 5 = b "then" log_(30) 8 = 3 (1 - a - b) .
Answer» Statemant-1 is TRUE , STATEMENT-2 is True, Statement -2 is a correct EXPLANATION for Statement-1 Statemant-1 is True , Statement-2 is True, Statement -2 is NOTa correct explanation for Statement-1 Statement-1 is True, Stetement-2 is False. Statement-1 is False, Statement-2 is True Answer :4

Discussion

27324.	int e^(3x) " cos 2x dx "
Answer» Answer :`(E^(3x))/(13) ( 3 sin2x +3 cos 2X)+c`

Discussion

27325.	A fair coin and an unbiased die are tossed. Let A be the event head appears on the coin' and B be the event 3 on the die. Check whether A and B are independent events or not.
Answer» ANSWER :A and B are INDEPENDENT

Discussion

27326.	The quadratic equation whose one root is (-3+I sqrt7)/(4) is
Answer» `2X^(2)-3x+2=0` `2x^(2)+3x-2=0` `2x^(2)-3x-2=0` `2x^(2)+3x+2=0` ANSWER :D

Discussion

27327.	""^21C_0 + ""^21C_1 + ""^21C_2 + ……..+ ""^21C_10 =
Answer» `2^10` `2^20` `2^21` `2^19` ANSWER :B

Discussion

27328.	If [{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6):}] , then find values of x,y,z and w.
Answer» ANSWER :`=4`

Discussion

27329.	If int e ^(x) ((2tan x)/(1+tan x)+ cosec ^(2)(x+(pi)/(4)))dx =e ^(x). g(x)+k, then g ((5pi)/(4))=
Answer» 0 1 `-1` `2` ANSWER :B

Discussion

27330.	Obtain following definite integrals : overset(2)underset(1)int (1)/(sqrt((x-1)(2-x)))dx
Answer» ANSWER :`:.1 =PI`

Discussion

27331.	If omega is an imaginary cube root of 1, then (1+omega-omega^(2))^(5)+(1-omega+omega^(2))^(5)=
Answer» `16` `8` `9` `32` ANSWER :D

Discussion

27332.	Find int_(0)^(pi)(x)/(a^(2)-cos^(2)x)dx
Answer» ANSWER :`(PI^(2))/(2asqrt(a^(2)-1))`

Discussion

27333.	An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?
Answer» ANSWER :`(3)/(7)`

Discussion

27334.	Find the second order derivative of the following functions tan^(-1)x
Answer» SOLUTION :`y=tan^-1xdy/dx=1/(1+x^2)IFF(d^2y)/(dx^2)=(-1)/(1+x^2)^2(0+2X)=(-2x)/(1+x^2)^2`

Discussion

27335.	Domainof definitation of thefunctionf(X )= (3)/(4-x^2)+ log_(10)(x^3 -x)is
Answer» `(-1,0) UU (1,2)` `(1,2)uu (2,OO)` `(-1,0) uu (1,2) uu (2,oo)` `(1,2)` ANSWER :C

Discussion

27336.	The normal at P(8, 8) to the parabola y^(2) = 8x cuts it again at Q then PQ =
Answer» 10 `10sqrt(5)` `5sqrt(10)` 50 Answer :B

Discussion

27337.	Prove thefollowing inequalities. (i) 1+x^(2) gt (x sin x + cos x) " for " x in [0,oo) (ii) sin x- sin 2x le 2x """forall" x in [0, (pi)/(3)] (iii) (x^(2))/(2)+ 2x+3 le (3-x)e^(x) """for all" x le 0 (iv) 0 le x sin x-(sin^(2)x)/(2) le (1)/(2) (pi -1) " for " 0 le x le (pi)/( 2)
Answer»

Discussion

27338.	A card from pack of 52 cards is lost. From the remaining cards of pack, two cards are drawn and are found to be spades. Find the probability of the missing card to be a spade.
Answer» ANSWER :`(11)/(50)`

Discussion

27339.	int e^(Sinx).(x Cos x-tanx.Secx)dx=
Answer» `e^(Sinx)(x-Sec x)+C` `e^(SIN x)(x+Sec x)+c` `e^(Sinx)(x+Cos x)+c` `e^(Sinx)(x-Cos x)+c` ANSWER :1

Discussion

27340.	Find the area of the region bounded by the curces: y = 6x -x ^(2) and y=x ^(2) - 2x.
Answer» Answer :`=21 (1)/(3)` SQ. UNIT

Discussion

27341.	Consider the function defined on [0, 1] to R, f(x) =(sin x - x cos x)/x^(2) if x ne 0 and f(0)=0, then the function f(x)
Answer» has a REMOVABLE discontinuity at `x=0` has a NON removable FINITE discontinuity at x=0 has a removable infinite discontinuity at x=0 is continous at x=0 Answer :D

Discussion

27342.	Let f(x)=" max "{sin x, cos x, (1)/(2)}. Determine the area of the region bounded by y=f(x), x-axis and x=2pi
Answer» ANSWER :`(5pi)/(12)+SQRT(2)+sqrt(3)`

Discussion

27343.	Computes the area of the surface formed by revolving one branch of the lemniscate rho=a sqrt(cos 2 varphi) about the straight line varphi = (pi)/(4)
Answer» ANSWER :`=2PI a^(2)`

Discussion

27344.	Integrate the following functions sqrt(1-4x-x^2)
Answer» Solution :`int SQRT(1-4x-x^2) dx` =`int sqrt(1-(x^2+4x))dx` =`int sqrt(1-(x^2+4x+4-4) dx` =`int sqrt(1-(x+2)^2+4) DX` =`int sqrt((sqrt5)^2-(x+2)^2) dx` `(x+2)/2 sqrt((sqrt)^2-(x+2)^2) + (sqrt5)^2/2 sin^-1((x+2)/sqrt5) +C` `(x+2)/2 sqrt(1-4x-x^2)+ 5/2 sin^-1((x+2)/sqrt5)+c`

Discussion

27345.	A class of problems that requires one to use permutations and combinations for computing probability has at its heart notion of sets and subsets. They are generally an abstract formulation of some concrete situation and require the application of counting techniques. A is a set containing 10 elements. A subset P_(1) of A is chosen and the set A is chosen and the set A is reconstructed by replacing the elements of P_(1). A subset P_(2) of A is chosen and again the set A is reconstructed by replacing the elements of P_(2). This process is continued by choosing subsets P_(1), P_(2), ... P_(10). The probability that P_(1)capP_(2)cap...P_(10)=phi is
Answer» `(1023)^(10)/(2^(100))` `(1025)^(10)/(4^(100))` `(1023)^(10)/(4^(100))` `(1025)^(10)/(2^(100))` ANSWER :A

Discussion

27346.	If P(AnnB)=(1)/(4), P(barAnnbarB)=(1)/(5) and P(A)=P(B)=P then the value of P=
Answer» `(11)/(40)` `(21)/(40)` `(13)/(40)` `(17)/(40)` ANSWER :B

Discussion

27347.	A class of problems that requires one to use permutations and combinations for computing probability has at its heart notion of sets and subsets. They are generally an abstract formulation of some concrete situation and require the application of counting techniques. A is a set containing 10 elements. A subset P_(1) of A is chosen and the set A is chosen and the set A is reconstructed by replacing the elements of P_(1). A subset P_(2) of A is chosen and again the set A is reconstructed by replacing the elements of P_(2). This process is continued by choosing subsets P_(1), P_(2), ... P_(10). The probability that P_(i)capP_(j)=phi" "AA" "i nej,i,j=1,2,....,10 is
Answer» `(11^(10))/(4^(100))` `(10^(11))/(2^(100))` `(11^(10))/(2^(100))` `(10^(11))/(4^(100))` ANSWER :C

Discussion

27348.	Giventhat prod_(n=1)^(n) cos ""(x)/(2^(n))=(sin x)/(2^(n) sin ((x)/(2^(n)))) and f(x) ={{:( lim_( n to oo) sum _( n=1) ^(n) (1)/(2^(n))tan((x)/(2^(n))), x in (0, pi)-{(pi)/(2)}),((2)/(pi),x=(pi)/(2)):} thenwhichoneof the followingistrue ?
Answer» F(x)has NON- removablediscontinuityoffinite typeat `x=(PI)/(2).` f(x)has removeabledisconinutyat `x=(pi)/(2)` `f(x) ` is CONTINUOUS at `x=(pi)/(2)` f(x) hasnon- removable discontinuousofinfintetypeat`x=(pi)/(2)` . Answer :C

Discussion

27349.	A class of problems that requires one to use permutations and combinations for computing probability has at its heart notion of sets and subsets. They are generally an abstract formulation of some concrete situation and require the application of counting techniques. A is a set containing 10 elements. A subset P_(1) of A is chosen and the set A is chosen and the set A is reconstructed by replacing the elements of P_(1). A subset P_(2) of A is chosen and again the set A is reconstructed by replacing the elements of P_(2). This process is continued by choosing subsets P_(1), P_(2), ... P_(10). The number of ways of choosing subsets P_(1), P_(2),...P(10) is
Answer» `4^(100)` `2^(100)` `2^(20)` `4^(20)` Answer :B

Discussion

27350.	The midpoint of the chord 3x-y=10 w.r.t x^(2)+y^(2)=18 is
Answer» (3,-1) (5,5) (1,3) not existing Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

The radius of the sphere x^(2)+y^(2)+z^(2)=12x+4y+3z is

Does there exist a function which is continuous everywhere but not differentiable at exactly two points ? Justify your answer.

Statement 1 : The function f(x)=(3x-1)4x^(2)-12x+5|cospix is differentiable at x=(1)/(2), (5)/(2). because Statement 2 : cos (2n +1)(pi)/(2)= 0 AA n in 1=l.

If the matrix A is both symmetric and skew symmetric ,then ……..

The minimum ..............

If f(x)=lim_(nrarroo) ((x^(2)+ax+1)+x^(2n)(2x^(2)+x+b))/(1+x^(2n)) and lim_(xrarrpm1) f(x) exists, then The value of a is

A box contains 1 white and 3 black balls. Two balls ar drawn at random. Describe the sample space associated with this experiment.

Solve (i) 2 sin x+ tan x=0 (ii)7 cos^(2) theta+3 sin^(2) theta=4 (iii) cos x + sec x=2 (iv)Solve tan x + tan 2x+tan 3x=0 (v) sin x sin 3x=1//2 (vi)cot(pi)/(3) cos (vii)Solve sec x-1=sqrt(2-1)tan x 2nx=sqrt(3)

If x,y,a,b,c,d are real and x+iy= sqrt((a+ib)/(c+id))" then"(x^(2)+y^(2))^(2)=

If the scalar product of the vector hati+hatj+2hatk with the unti vector along mhati+2hatj+3hatk is equal to 2, then one of the value of m is

Areabounded by curvey= tan pi x , x in [-1/4 ,1/4] and X-axisis …..

A sequence of positive (a _(1), a _(2)…a _(n)) is called good if a _(1) =a_(1) +a _(2) + …+ a _(i-1) for all 2 le I le n. What is the maximum possible value of n for a good sequence such that a _(n) = 9216?

Find the derivative of 1/(1 - t^2) with respect to1 + t^(2).

A window in the form of a rectangle , is surmounted by a semicircular opening . Thetotal perimeter of the window is 10 m Findthe dimensions of the rectangular part of the window to admit maximum light through the whole opening .

O( 0, 0 ) , A ( 6 , 0 ) , B (0 , 4 )arethreepoints.IfPisa pointsuchthatthearea ofthequadrilateralPABCis10sq.Unit,thenthelocusofPis

If A, B, C are mutually exclusive and exhaustive events such that P(B) = (3)/(2)P(A), P(C) = (1)/(3)P(B) then P(A) =

An ellipse has eccentricity 1/2 and the focus at the point P(1/2,1). Its one directrix is the common tangent, nearer to the point P, to the hyperola x^(2)-y^(2)=1 and the circle x^(2)+y^(2)=1. Find the equation of the ellipse.

P is a point on the circle x^2+y^2=1. Line OP, where O is origin, and x=1meets at Q. L_1 is a line parallel to x-axis drawn from Q. A line is drawn parallel to x-axis from P meeting x = 1 at R. OR meets L_1 at S. Then locus S is:

Compute the volume of the solid generated by revolving about the x-axis the figure bounded by the parabola y= 0.25 x^(2) + 2 and the straight line 5x -8y + 14=0

Integrate the following functions : intxsqrt(x^(4)+1)dx

A pair of dice is thrown. Find the probability of getting a sum of at least 9 if 5 appears on at least one of the dice.

STATEMENT-1 : Number of solution oflog |x| = theta^(x) is twoand STATEMENT-2 :Iflog_(30) 3 - a , log_(30) 5 = b "then" log_(30) 8 = 3 (1 - a - b) .

int e^(3x) " cos 2x dx "

A fair coin and an unbiased die are tossed. Let A be the event head appears on﻿ the coin' and B be the event 3 on the die. Check whether A and B are﻿ independent events or not.﻿

The quadratic equation whose one root is (-3+I sqrt7)/(4) is

""^21C_0 + ""^21C_1 + ""^21C_2 + ……..+ ""^21C_10 =

If [{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6):}] , then find values of x,y,z and w.

If int e ^(x) ((2tan x)/(1+tan x)+ cosec ^(2)(x+(pi)/(4)))dx =e ^(x). g(x)+k, then g ((5pi)/(4))=

Obtain following definite integrals : overset(2)underset(1)int (1)/(sqrt((x-1)(2-x)))dx

If omega is an imaginary cube root of 1, then (1+omega-omega^(2))^(5)+(1-omega+omega^(2))^(5)=

Find int_(0)^(pi)(x)/(a^(2)-cos^(2)x)dx

An urn contains 10 black and 5 white balls. Two balls are drawn from the﻿ urn one after the other without replacement. What is the probability that both drawn﻿ balls are black?﻿

Find the second order derivative of the following functions tan^(-1)x

Domainof definitation of thefunctionf(X )= (3)/(4-x^2)+ log_(10)(x^3 -x)is

The normal at P(8, 8) to the parabola y^(2) = 8x cuts it again at Q then PQ =

Prove thefollowing inequalities. (i) 1+x^(2) gt (x sin x + cos x) " for " x in [0,oo) (ii) sin x- sin 2x le 2x """forall" x in [0, (pi)/(3)] (iii) (x^(2))/(2)+ 2x+3 le (3-x)e^(x) """for all" x le 0 (iv) 0 le x sin x-(sin^(2)x)/(2) le (1)/(2) (pi -1) " for " 0 le x le (pi)/( 2)

A card from pack of 52 cards is lost. From the remaining cards of pack, two cards are drawn and are found to be spades. Find the probability of the missing card to be a spade.

int e^(Sinx).(x Cos x-tanx.Secx)dx=

Find the area of the region bounded by the curces: y = 6x -x ^(2) and y=x ^(2) - 2x.

Consider the function defined on [0, 1] to R, f(x) =(sin x - x cos x)/x^(2) if x ne 0 and f(0)=0, then the function f(x)

Let f(x)=" max "{sin x, cos x, (1)/(2)}. Determine the area of the region bounded by y=f(x), x-axis and x=2pi

Computes the area of the surface formed by revolving one branch of the lemniscate rho=a sqrt(cos 2 varphi) about the straight line varphi = (pi)/(4)

Integrate the following functions sqrt(1-4x-x^2)

If P(AnnB)=(1)/(4), P(barAnnbarB)=(1)/(5) and P(A)=P(B)=P then the value of P=

Giventhat prod_(n=1)^(n) cos ""(x)/(2^(n))=(sin x)/(2^(n) sin ((x)/(2^(n)))) and f(x) ={{:( lim_( n to oo) sum _( n=1) ^(n) (1)/(2^(n))tan((x)/(2^(n))), x in (0, pi)-{(pi)/(2)}),((2)/(pi),x=(pi)/(2)):} thenwhichoneof the followingistrue ?

The midpoint of the chord 3x-y=10 w.r.t x^(2)+y^(2)=18 is

A fair coin and an unbiased die are tossed. Let A be the event head appears on the coin' and B be the event 3 on the die. Check whether A and B are independent events or not.

An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?