28278 + Interview Questions in Maths in Class 12 Page 212 InterviewSolution

10551.	I : theunmberof waysof arranging4 boy and3girlsina rowalwaysbeginswitha boy endswitha girlsis 1440 . II: Thenumberof waysof arranging5 boyand 4girlsin a lineso thattherewill be aboy inthe begingand in theendingand intheendingis 10080
Answer» Only1 is ture onlyIIis true BothI andIIaretrue neither a norIItrue Answer :A

Discussion

10552.	How many diagonals can an n-gon (a polygon with n sides ) have ?
Answer» Solution :"A POLYGON of N-sides has n vertices". `:.` "The NUMBER of ST. LINES joining the n-vertices is" `""^nC_2`. `:.` "The number of diagonals is" `""^nC_2-n` `= (n!)/(2!(n-4)!)-n=(n(n-1))/2-n` `= (n^2-n-2n)/2=(n^2-3n)/2=(n(n-3))/2`

Discussion

10553.	If f(x)=1/9abs({:(cosx, 1, 0), (1, 2cosx, 1), (0, 1, 2cosx):}), " then " (d^(2)f)/(dx^(2))=
Answer» `cos3x` `cos(pi+3x)` `SIN3X` `sin(pi+3x)` ANSWER :B

Discussion

10554.	If three six faced dice are tossed together, then the probability that exactly two of the three numbers are equal is
Answer» `((K-1)(k-2))/(432)` `(k(k-1))/(432)` `(k^(2))/(432)` none Answer :A

Discussion

10555.	Find the mean and variance of first n natural numbers .
Answer» ANSWER :`=(N^(2)-1)/(12)`

Discussion

10556.	Find the maximum area of an isosceles triangle inscribed in the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1with its vertex at one end of the major axis.
Answer» ANSWER :`(3sqrt(3))/(4) `AB

Discussion

10557.	Evaluate int_((-pi)/4)^(pi/4)sin^(2)xdx
Answer» ANSWER :`(PI)/(4)-(1)/(2)`

Discussion

10558.	Find the coefficient of x^(7) in ((2+3x)^(3))/((1-3x)^(4)).
Answer» ANSWER :`8 (""^10C_3 . 3^7) + 36 (""^9C_3 . 3^6)+ 54(""^8C_3 . 3^5) + 27 (""^7C_3 . 3^4)`

Discussion

10559.	intsec^11theta tantheta d theta
Answer» SOLUTION :`intsec^11theta TANTHETA d THETA` =`intsec^11theta.sectheta.tantheta d theta` [PUT `sectheta=t` Then `sectheta.tanthetad theta=dt`] =`intt^10dt=1/11t^11+C=1/11sec^11theta+C`

Discussion

10560.	Find the maximum length of chord of the ellipse(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then findthe locus of midpoint of PQ
Answer» Solution :Let `P-=(2sqrt(3)COS theta, 2 sin theta)` and `Q-=(2sqrt(3)cos((pi)/(2)+theta),2SIN((pi)/(2)+theta))` or `Q-=(-2sqrt(2)sin theta, 2 cos theta)` `(PQ)^(2)=8(cos theta+sin theta)^(2)+4(sin theta-cos theta)^(2)=12+4 sin 2 theta` `:. (PQ)_("max")=4`

Discussion

10561.	Find the mean deviation about the mean for the data
Answer» ANSWER :`=157.92`

Discussion

10562.	Choose the correct option regarding energy of empty orbitals. {:(,n,l,m,s),((I),4,0,0,+(1)/(2)),((III),3,1,1,+(1)/(2)):}{:(,n,l,m,s),((II),3,2,0,-(1)/(2)),((IV),3,0,0,-(1)/(2)):}
Answer» `I GT IV` `II lt I` `II lt III` `I = III` ANSWER :A

Discussion

10563.	Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0
Answer» ANSWER :(i) 4 (II) 4 (iii) 2 (IV) 3 (v) 0

Discussion

10564.	The range of a random variable X = {1, 2, 3,….} and probabilities are given by P(X = k) = (3^(Ck))/(lfloork) forr k = 1, 2, 3… and C is a constant. Find the value of C.
Answer» ANSWER :`C = ln_(3)(ln_(E)2)`

Discussion

10565.	If (1 -x+ x^2)^n = a_0 +a_1x + a_2x^2+….+a_(2n)x^(2n) then a_0 + a_2 +a_4 + …….+a_(2n) =
Answer» `(3^N +1)/(2)` `(3^(n)-1)/(2)` `(3^(n+1))/(2)` `(2^(n-1))/(2)` ANSWER :A

Discussion

10566.	Evalute the following integrals int (7x -4)/((x -1)^(2)(x+2)) dx
Answer» ANSWER :`2log\|x-1\|-(1)/(x-1)2log\|x+2\|+c`

Discussion

10567.	i. Solve 5x-3 lt 17 when x is a real number. ii. Mark the solutions on a number line.
Answer» ANSWER :i.`X LT 4`

Discussion

10568.	Find the realtionship between a and b so that the function f defined by f(x)={(ax+1","," if "xle3),(bx+3","," if "xgt3):} is continuous at x=3
Answer» ANSWER :`a=b+2/3`

Discussion

10569.	If f:RrightarrowR is an even function having derivatives of all orders, then an odd function among the following is
Answer» `F''` `f'''` `f'+ f''` `f''+ f'''` ANSWER :B

Discussion

10570.	What is the distance (in units) between the two planes 3x+5y+7z=3 and 9x+15y+21z=9:
Answer» 0 3 6/sqrt 83 6 Answer :A

Discussion

10571.	int sqrt(1 - 2x - x^(2)) dx =
Answer» `SIN^(-1) ((x1)/(sqrt(2))) + ((X + 1)/(2)) sqrt(1 - 2x - x^(2)) `+ c `sin^(-1) ((x + 1)/(2)) + ((x + 1)/(2)) sqrt(1 -2x - x^(2)) + c` `sin^(-1)((x- 1)/(sqrt(2))) + ((x - 1)/(2)) sqrt(1 - 2x - x^(2)) + c ` `sin^(-1)((x- 1)/(2)) + ((x- 1)/(2)) sqrt(1 - 2x - x^(2)) + c ` ANSWER :A

Discussion

10572.	Evaluate: int(xsin^(-1)x)/sqrt(1-x^(2))dx
Answer» ANSWER :`x-sqrt(1-x^(2))SIN^(-1)x+c`

Discussion

10573.	If alphaand beta are real them \|(alpha+i beta)/(beta+ialpha)\|=
Answer» LIES between 0 and 1 1 `GT 1` `0` ANSWER :B

Discussion

10574.	For integers m and n, both greater than 1, consider the following three statements P : m divides n, Q : m divides n^(2) , R : m is prime then
Answer» <P>`Q ^^ R RARR P` `P ^^ Q rarr R` `Q rarr R` `Q rarr P` ANSWER :A

Discussion

10575.	Find Lt_(x to a) [(sqrt(a + 2x) - sqrt(3x))/(sqrt(3a + x)-2sqrt(x))]
Answer» ANSWER :B::C

Discussion

10576.	If int (7^((1)/(x)))/(x^(2))dx=m*7^((1)/(x)) thenm....
Answer» `(-1)/(LOG7)` `-log7` `-1` `(1)/(7)` ANSWER :A

Discussion

10577.	int_(0)^(2) f(x) dx = …..., where f(x) =max {x, x^(2)}.
Answer» `(8)/(3)` `(13)/(6)` `(17)/(6)` `(19)/(6)` Answer :A

Discussion

10578.	The sumof all 4-digitnumbers that canbe formedusingthedigits2,3,4,5,6withoutrepetitionis
Answer» 533820 532280 533280 532380 Answer :C

Discussion

10579.	Matchthe followingcolumnsandchoosethe correctanswer. {:(,"Column I",,,"Column II"),((A), (1 - x) ^(-n),,(1),(x)/(x + 1)),((B),(1-x) ^(-n),,(2), 1- nx + (n(n+1))/(2!) x ^ 2 -... if \|x\| lt 1),((C), If x gt 1", then " 1 +(1)/(x) +(1)/(x^2) + ..." is",,(3), 1 + nx + (n(n+1))/(2!) x ^ 2+ ... if \|x\| lt 1),((D), if\|x\| gt 1", then" 1 - (2 )/(x^2) + (3)/(x^4)- (4)/(x^6) + ...,,(4),(x)/(x-1)),(,,,(5), (x^4)/((x^2 + 1)^2)),(,,,(6),(x^4)/((x^2 -1)^2)):}
Answer» `{:(""(A),(B),(C ),(D)),(1, 3, 4,5 ):}` `{:(""(A), (B), (C ), (D)),(2, 3,4, 5):}` `{:(""(A), (B), (C ), (D)),(3, 2, 4, 5):}` `{:(""(A), (B), (C ), (D)),(2, 3, 1, 5):}` Solution :(a)`(1 -x ) ^(-n )= 1+nx+ (n(n + 1 ))/(2 !)x ^ 2+…, if\|x\|lt1` (b) `(1 + x ) ^ (-n )= 1- nx+ (n (n + 1 ))/(2! )x ^2 - …, if \|x\|lt1` (c )`1 +(1)/(x)+ (1)/(x^ 2 )+ … = (1)/(1 - (1)/(x)) = (x ) /(x - 1 ) , ifx gt1` ` [ becausea+ ar+ ar ^ 2 + ...=(a )/( 1 - r ), if \|r\|lt1 ]` (d)`1 -(2)/(x^ 2 )+ (3)/ (x ^ 4)- (4)/(x ^ 6)+ ... = ( 1+ (1)/(x^ 2 ))^ (-2) ` ` = ((x^ 2 )/(1 + x ^ 2)) ^ 2 ` `= (x ^4)/((1 + x ^ 2 )^ 2 ) , if \|x\| gt 1`

Discussion

10580.	Let {:f(x)= {(abs(x+1):,xlt1),(1-x:,x le 1):} and {:f(x)= {(x-2:, xlt0),(x+3:, x ge0):}. Then the function h - fg is given by :
Answer» `{:{(x^2+x+2:, xlt-1),(x^2-x-2:,-1le x lt 0),(x^2+ 4x+3:,0lexlt1),(-x^2 -2X +3:, xgt1):}` `{:{(-x^2 + x +2 :,x lt-1),(x^2 - x -2 :,-1 LE x LT0),(x^2-4x +3:,0 le xlt 1),(-x^2 - 2x + 3:,x ge1):}` `{:{(-x^2+x+2:,xlt-1),(x^2-x-2:,-1 le xlt0),(x^2 + 4x +3 :, 0 le x le 1),(-x^2 - 2x +3:, x ge 1):}` None of these Answer :C

Discussion

10581.	Let S_(1) = x ^(2) - y ^(2) + 2y - sqrt2 -1 and S_(2) = 4x ^(2) + 9y^(2) - 18y -27 be such that S_(1) =0 and S_(2) =0 intersect in four real points Q, R, S and T and let P be the point (2^(3//4),1) show that PQ + PR+PS +PT = 4, 2 sqrt ((36+9 sqrt2)/(13)).
Answer» ANSWER :PQ + PR+PS +PT = 4, 2 sqrt ((36+9 sqrt2)/(13)).`

Discussion

10582.	If A, B, C are the sets of all values of x, for which x^(2)-5x-14 is positive, -6x^(2)+2x-3 is negative and 4x-5x^(2)+2 is negative respectively, then A cap B cap C=
Answer» (-2, 7) `phi` `((2-sqrt(14))/5, (2+sqrt(14))/5)` R Answer :C

Discussion

10583.	A determinant of second order is made with the elements 0 and 1. What is the probability that the determinant made is (i) non-negative (ii) non-zero
Answer» Answer :`(i) (13)/(16)` `(ii) (3)/(8)`

Discussion

10584.	Statement-1: For every natural number n ge 2, (1)/(sqrt1)+(1)/(sqrt2)+…..(1)/(sqrtn) gt sqrtn Statement-2: For every natural number n ge 2, sqrt(n(n+1) lt n+1
Answer» ANSWER :A

Discussion

10585.	If [{:(3,1,-1),(0,1,2):}]then AA ' is a ……… matrix.
Answer» Symmetric Skew symmetric Orthogonal None of these Answer :A

Discussion

10586.	A pair of perpendicular lines passes through the origin and also through the points of intersection of the curve x^(2) + y^(2) = 4 with x + y = a , where a gt 0 . Then a is equal to
Answer» 2 3 4 5 Answer :A

Discussion

10587.	Let n be a positive integer if 1le1gt K len such that (sin^(2)nx)/(sin^(2)x)=a_(@)+sum_(1ge i lt klen) a_(1,k) cos 2 (k-1) for all real number x with x not an integer multiple of pi, then the value of a_(1,k) is
Answer» SOLUTION :`s=sin2x+sin4x+……+sin2nx` `=(sin nx-sin(n+1)x)/(sinx)` `C=cos2x+cos4c+………..+cos2nx` `=(sin nx cos (n+1)x)/(sinx)` `((sin^(2)nx)/(sin^(2)nx))^(2)=((sin n XSIN(n+1)x)/(sinx))^(2)+((sin n cos(n+1)x)/(sinx))^(2)=s^(2)+c^(2)` On the other hand `s^(2)+c^(2)=(sin2x+sin4x+...........sin2nx)^(2)+(cos2x+cos4x+.............+cos2nx)^(2)` `=n+sum_(1le 1lt k le n) (2sin 2 xsin 2 kx +2cos 2 x cos 2kx)` `=nn+2 sum_(1le 1 lt k le n)cos2(k-1)x` `IMPLIES a_(1,k)=2`

Discussion

10588.	A biased die is such that P(4) = (1)/(10) and other scores being equally likely. The die is tossed twice. If X is the 'number of fours seen', then find the variance of the random variable X.
Answer» ANSWER :0.18

Discussion

10589.	The position vectors of P and Q are respectively a and b. If R is a point on PQ such that PR = 5PQ, then the position vector of R is
Answer» 5b - 4a 5b + 4a 4b - 5a 4b + 5a Solution :Given, PR = 5 PQ It means R DIVIDES PQ externally in the ratio 5 : 4. `therefore` Position VECTOR of `R=(5b-4a)/(5-4)=5b-4a`

Discussion

10590.	int_(2)^(4) (sqrt(x^(2)-4))/(x^(4))dx=
Answer» `3/32` `SQRT(3)/32` `3/8` `sqrt(3)/8` ANSWER :B

Discussion

10591.	Integration by partial fraction : If int sin5x cos 3x dx=-(cos8x)/(16)+A then A=...
Answer» `(sin 2X)/(16)+C` `-(COS2X)/(4)+C` C None of these Answer :B

Discussion

10592.	Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0) , B (4, 5) and C(6, 3).
Answer» ANSWER :7

Discussion

10593.	Let a, b be roots of x^(2) + 2x + 5 . 71 = 0. "Let" A_(n) be alpha^(n) + beta^(n) , "where " n in N. "If" A_(n+1) + kA_(n-1) - A_(1) A_(n) = 0 then k is equal to ______
Answer» ANSWER :`5 . 71`

Discussion

10594.	Statement-1: Number of solutions of the equation cos(x-1) = (\|x-1\|)/(10) are 6. Statement -2: Number of solutions of the equation f(x) = g(x) is equal to the number of points of intersection of graph y = f(x) and y = g(x)
Answer» Statement -1 is true, statement -2 is True and Statement -2 is a CORRECT EXPLANATION for statement -1. Statement -1 is true, statement -2 is True and Statement -2 is NOT a correct explanation for statement -1. Statement -1 is True , Statement -2 is FALSE Statement -1 is False, Statement -2 is True Answer :A

Discussion

10595.	If "cosec"theta+cottheta=c, then what is costheta equal to ?
Answer» `(c)/(c^(2)+1)` `(c)/(c^(2)-1)` `(c^(2)-1)/(c^(2)+1)` None of the above Solution :Let`"COSEC "theta+cottheta=c` `RARR(1)/(SINTHETA)+(costheta)/(sintheta)=crArr(1+costheta)/(sintheta)=c` `rArr(1+(2" cos"^(2)(theta)/(2)-1))/(2"SIN"(theta)/(2)"cos"(theta)/(2))=crArr(2" cos"^(2)(theta)/(2))/(2"sin"(theta)/(2)"cos"(theta)/(2))=c` `rArr"cot"(theta)/(2)=crArrcostheta=(1-(1)/(c^(2)))/(1+(1)/(c^(2)))=(c^(2)-1)/(c^(2)+1)` `(becausecostheta=(1-TAN^(2)((theta)/(2)))/(1+tan^(2)((theta)/(2))))` `rArr"tan"(theta)/(2)=(1)/(c)`

Discussion

10596.	A bag contains 5 red and 3 blue balls . If three balls are drawn one by one without replacement from the bag then the probability of drawing exactly two red balls of the three balls , the first ball being red is
Answer» `1/3` `4/7` `5/14` `5/28` ANSWER :C

Discussion

10597.	If the solution of the differential equation (dy)/(dx)-y((x^4+3x^2)/((x^2+1)^2))=(4x+3)e^(x^3/(x^2+1) is in the form y=f(x) (where f(0)=1), then f(A)+f(-1) is
Answer» `2sqrt3` `3sqrte` `4sqrte` `6sqrte` Solution :I.F.=`e^(-int(x^4+3X^2)/((x^2+1)^2) dx = e^((-x^3)/(x^2+1))` `RARR y e^((-x^3)/(x^2+1))=int(4x+3)dx` `rArr f(x)=y=(2x^2 + 3x +1)e^((x^3)/(x^2+1))` `rArr f(1)=6sqrte` & f(-1)=0 `rArr` f(-1)=0

Discussion

10598.	There are 10 pairs of shoes in a cup board from which 4 shoes are picked at random. The probability that there is atleast one pair is
Answer» `(99)/(323)` `(224)/(323)` `(2)/(5)` `(3)/(5)` Answer :A

Discussion

10599.	Recall that sinx + cosx =u (say) and sin x cosx =v (say) are connected by (sinx +cosx)^(2) = sin^(2)x + cos^(2)x+2sin cosx rArr u^(2) = 1+2v rArr v=(u^(2)-1)/(2) It follows that any rational integral function of sinx + cosx, and sinx cosx i.e., R(sinx + cosx, sinx cosx), or in our notation R(u,v) can be transformed to R(u, (u^(2)-1)/2). Thus, to solve an equation of the form R(u,v)=0, we form a polynomial equation in u and than look for solutions. The solution of sinx + cosx -2sqrt(2) =0 is completely described by
Answer» `x = 2NPI + pi/4, 2npi - (5PI)/12, 2npi + (11pi)/12, n in Z` `x= 2npi-pi/4, 2npi+pi/12, 2npi + (7pi)/12, n in Z` `x = 2npi+ pi/4, 2npi - pi/12, 2npi - (7pi)/12, n in Z` `x=2npi - pi/4, 2npi + pi/12, 2npi - (7pi)/12, n in Z` ANSWER :D

Discussion

10600.	Recall that sinx + cosx =u (say) and sin x cosx =v (say) are connected by (sinx +cosx)^(2) = sin^(2)x + cos^(2)x+2sin cosx rArr u^(2) = 1+2v rArr v=(u^(2)-1)/(2) It follows that any rational integral function of sinx + cosx, and sinx cosx i.e., R(sinx + cosx, sinx cosx), or in our notation R(u,v) can be transformed to R(u, (u^(2)-1)/2). Thus, to solve an equation of the form R(u,v)=0, we form a polynomial equation in u and than look for solutions. The number of solutions of the equation sin theta + costheta=1 + sintheta costheta in the interval [0,4pi] is
Answer» FOUR Six Eight FIVE ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

I : theunmberof waysof arranging4 boy and3girlsina rowalwaysbeginswitha boy endswitha girlsis 1440 . II: Thenumberof waysof arranging5 boyand 4girlsin a lineso thattherewill be aboy inthe begingand in theendingand intheendingis 10080

How many diagonals can an n-gon (a polygon with n sides ) have ?

If f(x)=1/9abs({:(cosx, 1, 0), (1, 2cosx, 1), (0, 1, 2cosx):}), " then " (d^(2)f)/(dx^(2))=

If three six faced dice are tossed together, then the probability that exactly two of the three numbers are equal is

Find the mean and variance of first n natural numbers .

Find the maximum area of an isosceles triangle inscribed in the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1with its vertex at one end of the major axis.

Evaluate int_((-pi)/4)^(pi/4)sin^(2)xdx

Find the coefficient of x^(7) in ((2+3x)^(3))/((1-3x)^(4)).

intsec^11theta tantheta d theta

Find the maximum length of chord of the ellipse(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then findthe locus of midpoint of PQ

Find the mean deviation about the mean for the data

Choose the correct option regarding energy of empty orbitals. {:(,n,l,m,s),((I),4,0,0,+(1)/(2)),((III),3,1,1,+(1)/(2)):}{:(,n,l,m,s),((II),3,2,0,-(1)/(2)),((IV),3,0,0,-(1)/(2)):}

The range of a random variable X = {1, 2, 3,….} and probabilities are given by P(X = k) = (3^(Ck))/(lfloork) forr k = 1, 2, 3… and C is a constant. Find the value of C.

If (1 -x+ x^2)^n = a_0 +a_1x + a_2x^2+….+a_(2n)x^(2n) then a_0 + a_2 +a_4 + …….+a_(2n) =

Evalute the following integrals int (7x -4)/((x -1)^(2)(x+2)) dx

i. Solve 5x-3 lt 17 when x is a real number. ii. Mark the solutions on a number line.

Find the realtionship between a and b so that the function f defined by f(x)={(ax+1","," if "xle3),(bx+3","," if "xgt3):} is continuous at x=3

If f:RrightarrowR is an even function having derivatives of all orders, then an odd function among the following is

What is the distance (in units) between the two planes 3x+5y+7z=3 and 9x+15y+21z=9:

int sqrt(1 - 2x - x^(2)) dx =

Evaluate: int(xsin^(-1)x)/sqrt(1-x^(2))dx

If alphaand beta are real them |(alpha+i beta)/(beta+ialpha)|=

For integers m and n, both greater than 1, consider the following three statements P : m divides n, Q : m divides n^(2) , R : m is prime then

Find Lt_(x to a) [(sqrt(a + 2x) - sqrt(3x))/(sqrt(3a + x)-2sqrt(x))]

If int (7^((1)/(x)))/(x^(2))dx=m*7^((1)/(x)) thenm....

int_(0)^(2) f(x) dx = …..., where f(x) =max {x, x^(2)}.

The sumof all 4-digitnumbers that canbe formedusingthedigits2,3,4,5,6withoutrepetitionis

Let {:f(x)= {(abs(x+1):,xlt1),(1-x:,x le 1):} and {:f(x)= {(x-2:, xlt0),(x+3:, x ge0):}. Then the function h - fg is given by :

Let S_(1) = x ^(2) - y ^(2) + 2y - sqrt2 -1 and S_(2) = 4x ^(2) + 9y^(2) - 18y -27 be such that S_(1) =0 and S_(2) =0 intersect in four real points Q, R, S and T and let P be the point (2^(3//4),1) show that PQ + PR+PS +PT = 4, 2 sqrt ((36+9 sqrt2)/(13)).

If A, B, C are the sets of all values of x, for which x^(2)-5x-14 is positive, -6x^(2)+2x-3 is negative and 4x-5x^(2)+2 is negative respectively, then A cap B cap C=

A determinant of second order is made with the elements 0 and 1. What is the probability that the determinant made is (i) non-negative (ii) non-zero

Statement-1: For every natural number n ge 2, (1)/(sqrt1)+(1)/(sqrt2)+…..(1)/(sqrtn) gt sqrtn Statement-2: For every natural number n ge 2, sqrt(n(n+1) lt n+1

If [{:(3,1,-1),(0,1,2):}]then AA ' is a ……… matrix.

A pair of perpendicular lines passes through the origin and also through the points of intersection of the curve x^(2) + y^(2) = 4 with x + y = a , where a gt 0 . Then a is equal to

Let n be a positive integer if 1le1gt K len such that (sin^(2)nx)/(sin^(2)x)=a_(@)+sum_(1ge i lt klen) a_(1,k) cos 2 (k-1) for all real number x with x not an integer multiple of pi, then the value of a_(1,k) is

A biased die is such that P(4) = (1)/(10) and other scores being equally likely. The die is tossed twice. If X is the 'number of fours seen', then find the variance of the random variable X.

The position vectors of P and Q are respectively a and b. If R is a point on PQ such that PR = 5PQ, then the position vector of R is

int_(2)^(4) (sqrt(x^(2)-4))/(x^(4))dx=

Integration by partial fraction : If int sin5x cos 3x dx=-(cos8x)/(16)+A then A=...

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0) , B (4, 5) and C(6, 3).

Let a, b be roots of x^(2) + 2x + 5 . 71 = 0. "Let" A_(n) be alpha^(n) + beta^(n) , "where " n in N. "If" A_(n+1) + kA_(n-1) - A_(1) A_(n) = 0 then k is equal to ______

Statement-1: Number of solutions of the equation cos(x-1) = (|x-1|)/(10) are 6. Statement -2: Number of solutions of the equation f(x) = g(x) is equal to the number of points of intersection of graph y = f(x) and y = g(x)

If "cosec"theta+cottheta=c, then what is costheta equal to ?

A bag contains 5 red and 3 blue balls . If three balls are drawn one by one without replacement from the bag then the probability of drawing exactly two red balls of the three balls , the first ball being red is

If the solution of the differential equation (dy)/(dx)-y((x^4+3x^2)/((x^2+1)^2))=(4x+3)e^(x^3/(x^2+1) is in the form y=f(x) (where f(0)=1), then f(A)+f(-1) is

There are 10 pairs of shoes in a cup board from which 4 shoes are picked at random. The probability that there is atleast one pair is