28278 + Interview Questions in Maths in Class 12 Page 105 InterviewSolution

5201.	Obtain the following integrals : int (sinx+cosx)/(sqrt(1+sin (2x)))dx
Answer» ANSWER :`:. I=x+C`

Discussion

5202.	int(cotx cot(x + alpha) +1)dx=
Answer» `COT alphalog(ABS((sinx)/(sin(x+ ALPHA))))+c` `logabs(sinx sin(x + alpha))+x+c` `log abs(sinx COS(x+ alpha))+x + c` `tan alphalog(abs((cosx)/(sin(X+alpha))))+c` Answer :A

Discussion

5203.	Find the values of x and y, if 2{:[(1,3),(0,x)]+{:[(y,0),(1,2)]={:[(5,6),(1,8)]:}
Answer» ANSWER :X =3, y = 3

Discussion

5204.	Construct a 3xx4 matrix , whose elements are given by : (i)a_(ij)=(1)/(2)\|3i+j\| (ii)a_(ij)=2i-j
Answer» ANSWER :(i) `=[{:(1,(1)/(2),0,(1)/(2)),((5)/(2),2,(3)/(2),1),(4,(7)/(2),3,(5)/(2)):}]` (II) `=[{:(1,0,-1,-2),(3,2,1,0),(5,4,3,2):}]`

Discussion

5205.	Let f(x)=2 tan^(-1)((1-x)/(1+x))
Answer» STATEMENT-1 True statement -1 is True,Statement -2is True statement -2 is a correct explanation for Statement-5 Statement-1 True statement -1 is True,Statement -2is True statement -2 is not a correct explanation for Statement-5 Statement-1 True statement -1 is True,Statement -2is False Statement-1 is False ,Statement -2 is True SOLUTION :`f(x)=2tan^(-1)""(1-x)/(1+x)(tan^(-1)-tan^(-1)x)"-="pi/2-2tan^(-1)""x` `rArr f(x)=-(2)/(1+x^2)lt0 for all x in [0,1]` `rArr f(x)` decreases on [0,1] `rArr ` Range of `f=[f(1),f(0)]=[0,pi//2]` Hence both the STATEMENTS are ture and statement are ture and statement -2 is a correct explanation of statement - 1

Discussion

5206.	H_(2)S gas is not evolved when SO_(3)^(2-) ion reacts with following reagents.
Answer» An+dil.`H_(2)SO_(4)` Al + conc. NaOH Al + dil. HCl None of these Solution :`SO_(3)^(2-)+2Al+2OH^(-)+3H_(2)OrarrS^(2-)+2[Al(OH)_(4)]^(-)` `H_(2)S` does not evolve as LIBERATED `H_(2)S` is neutralised by NaOH and `Na_(2)S` is FORMED.

Discussion

5207.	Coffiecient of x^3 in the expansion of e^(-bx)
Answer» `(-b^3)/6` `(b^3)/6` `(b^3)/3` `(-b^3)/3` ANSWER :A

Discussion

5208.	If the standard deviation of 0,1,2,3,4,5,6,7,8,9 is K, then the standard deviation of 10,11,12,…,19 is
Answer» K K +10 `K + SQRT(10)` 10 K Answer :A

Discussion

5209.	Lines L_(1) : y-c=0 and L_(2) : 2x+y=0 intersect the line L_(3) : y+2=0 at P and Q respectively. The bisector of the acute angle between L_(1) and L_(2) intersects L_(3) at R. Statement I The ratio PR : RQ equals 2sqrt(2) : sqrt(5). Because Statement II In any triangle, bisector of an angle divides the triangle into two similar triangles.
Answer» STATEMENT I is true, Statement II is also true, Statement II is correct explanation of Statement I Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I Statement I is true , Statement II is false Statement I is false , Statement II is true Solution :It is not necessary that the bisector of an angle will DIVIDE the triangle into TWO similar triangles, therefore, statements II is false. Now, we verify Statement I. `DeltaOPQ`, `OR` is the internal bisector of `/_POQ`. `:. (PR)/(RQ)=(OP)/(OQ)` `IMPLIES(PR)/(RQ)=(sqrt(2^(2)+2^(2)))/(sqrt(1^(2)+2^(2)))=(2sqrt(2))/(sqrt(5))`

Discussion

5210.	In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them :(a) 7x + 5y + 6z + 30 = 0 and 3x - y-10z + 4 = 0(b) 2x + y + 32 - 2 = 0 and x - 2y + 5 = 0(c) 2x - 2y + 4z + 5 = 0 and 3x - 3y + 6z-1 = 0(d) 2x – y + 3z-1 = 0 and 2x - y + 3z + 3 = 0(e) 4x + 8y + z - 8 = 0 and y + z - 4 = 0
Answer» ANSWER :(a) `therefore theta=cos^(-1)(2/5)` (B) `=0` (c) `=2/3` `therefore` NORMAL of the PLANES are parallel `therefore` Given planes are parallel (d)`therefore` Normal of the planes are parallel `therefore` Given planes are parallel (e) `therefore theta=45^@`

Discussion

5211.	Differentiate w.r.t.x the function in Exercises 1 to 11. sin^(3)x+ cos^(6)x
Answer» Answer :`3 SIN X COS x(sin x-2 cos^(4)x)`

Discussion

5212.	If alpha, beta, gamma are roots of x^(3) +4x+1=0, then (alpha+beta)^(-1) +(beta+gamma)^(-1) +(gamma+alpha)^(-1) equals
Answer» 2 3 4 5 Answer :C

Discussion

5213.	Arrange the following according to their values in ascending order A) int_(0)^(1) sqrt(1-x^(2))dx B) int_(0)^(1) (1)/(sqrt(1-x^(2)))dx C) int_(0)^(1//sqrt(3))(1)/(1+x^(2))dx
Answer» A, B, C C, B, A C, A, B A, C, B Answer :C

Discussion

5214.	thetangent andnormaltothetangentto theellipse(x^(2))/(a^(2))+(y^(2))/(b^(2))=1at thepoint(3,(-9)/(2)),thenthe area( in sq units ) oftheDeltaPQRIs
Answer» `(16)/(3)` `(14)/(3)` `(34)/(15)` `(68)/(15)` Solution :Equationof givenellipse is ` 3x^(2) +5y^(2)=32` bnow,the slopeof tangent andnormalat POINT `P(2,2)` totheellipse(i) areresectively `m_(T)=(dy)/(dx)\|_(""(2,2))and m_(N)=-(dx)/(dy)\|_((2,2)"")` ondiferntiatingellipse(i) w.R.tx, weget `6x+10y(dy)/(dx)=0implies (dy)/(dx)=-(3x)/(5y)` `SoM_(T) =-(3x)/(5y)\|_((2,2)"")=-(3)/(5) andm_(N) = (5y)/(3Y)\|_((2,2)"")=(5)/(3)` Nowequationof tangentand normal tothegivenellipse(i) atpointP(2,2) are `(y-2)=-(3)/(5)(x-2)` and `(y-2)=(5)/(3)(x-2)` RESPECTIVLY. It isgiventhat pointif INTERSECTIONOF tangentandnormalare Qand RAt X- axisRespectively. so, `Q((16)/(3),0) and R((4)/(5) ,0)` `therefore ` Area of`DeltaPQR =(1)/(2)(QR)xx"height "` `=(1)/(2) xx(68)/(15)xx2=(68)/(15) sq units ` `[ :'QR= sqrt(((16)/(3)-(4)/(5))^(2))=sqrt(((68)/(15))^(2))` = (68)/(15)` andheight= 2]

Discussion

5215.	Integration by partial fraction : int(x-1)/((x-3)(x-2))dx=....
Answer» `LOG(x-3)-log(x-2)+C` `log(x-3)^(2)-log(x-2)+c` `log(x-3)+log(x-2)+c` `log(x-3)^(2)+log(x-2)+c` ANSWER :B

Discussion

5216.	Solve the inequation (sqrt(6+x-x^(2)))/(2x+5) ge (sqrt(6+x-x^(2)))/(x+4).
Answer» ANSWER :`[-2, -1] CUP {3}`

Discussion

5217.	If A is square matrix of order 2 and A^2+A+2I=0 then
Answer» A can not be a skew-symmetric MATRIX `\|A+l\|=0` A is ONE SINGULAR and `A^(-1)=(A+l)^(-1)` `\|A\|\|A+l\|=2` ANSWER :A

Discussion

5218.	Number of words consisting of two vowels and two consonants which can be made out of the letters of word "DEVASTATION" is
Answer» 126 198 1512 1638 Solution :DVSTIN, EAAIO : `(.^(5)C_2 XX .^(4)C_(2))4 ! + .^(5)C_(2) (4!)/(2!) + .^(4)C_(2) (4!)/(2!) + 1 + (4!)/(2!2!)`

Discussion

5219.	Name the square matrix A=[a_(ij)] in which a_(ij)=0, i!=j.
Answer» ANSWER :DIAGONAL MATRIX

Discussion

5220.	int_(0)^(1)x(1-x)^(10)dx=
Answer» `(1)/(112)` `(1)/(132)` `(1)/(246)` `(1)/(92)` Answer :B

Discussion

5221.	int (a + b sin x )/((b+ a sin x )^(2))dx =
Answer» `(- COS X )/(b + a SIN x ) +C` `(cos x )/(b + a sin x )` + c `(sin x)/(b + a sin x )+ c` `(- sin x )/(b +a sin x )+ c ` Answer :A

Discussion

5222.	In the following cases, determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.(i) 2x – y + z = 6 and x + y + 2z = 7(ii) vecr.(hati-hatj+hatk) and vecr.(3hati+2hatj-hatk)-11=0(iii) x + y – 2z = 3 and 2x – 2y + z = 5(iv) 2x – 3y + 4z = 1 and -x + y = 4(v) vecr.(2hati+3hatj-6hatk)=5 and vecr.(hat i - 2 hatj+2hatk)=9
Answer» ANSWER :(i) `pi/3` (ii) `pi/2` (iii) `cos^(-1)((2)/(3sqrt6))` (IV) `cos^(-1)((5)/(sqrt(58)))` (v) `cos^(-1)((16)/(21))`

Discussion

5223.	Find the co-ordinates of the point where the line (x+1)/(2)=(y+2)/(3)=(z+3)/(4) cross the planel x + y + 4z = 6.
Answer» ANSWER :(1,1,1)

Discussion

5224.	Express with rational denominator(a+xsqrt(-1))/(a-xsqrt(-1))-(a-xsqrt(-1))/(a+xsqrt(-1))
Answer» SOLUTION :`(a=xsqrt(-1))/(a-xsqrt(-1))-(a-xsqrt(-1))/(a+xsqrt(-1))` `=(x+ix)/(a-ix)-(a-ix)/(a+ix)=((a+ix)^2-(a-ix)^2)/((a-ix)(a+ix))` `=(4aix)/(a^2-i^2x^2)=(4aix)/(a^2+x^2)`

Discussion

5225.	int_(0)^(pi//2) sin^(8) x. cos^(2)x dx=
Answer» `PI/(512)` `(3PI)/(512)` `(5PI)/(512)` `(7pi)/(512)` ANSWER :D

Discussion

5226.	There are two perpendicular lines, one touches to the circle x^(2) + y^(2) = r_(1)^(2) and other touches to the circle x^(2) + y^(2) = r_(2)^(2) if the locus of the point of intersection of these tangents is x^(2) + y^(2) = 9, then the value of r_(1)^(2) + r_(2)^(2) is.
Answer» ANSWER :9

Discussion

5227.	If (1 div 3p)/(3), (1-p)/(4), (1-2p)/(2) are the probabilities of 3 mutually exclusive events then find the set of all values of p.
Answer» Answer :`therefore (1)/(3) LE p le (1)/(2)`

Discussion

5228.	The total numberof relation fromtheset{p,q} to the set{e,f} is-
Answer» 16 32 56 4

Discussion

5229.	A random veriable X takes the values 0,1 and 2. If P(X =1) = P(X=2) and P(X =0) = 0.4 , then the mean of random veriable X is
Answer» 0.2 0.7 0.5 0.9 Answer :D

Discussion

5230.	A plane passes through the points (1, 1, 1). If b, c, a are the direction ratios of a normal to the plane where a, b, c (a lt b lt c) are the prime factors of 2001, then the equation of the plane is:
Answer» `29x + 31y + 3z = 63` `23x + 29Y – 29z = 23` `23x + 29y + 3z = 55` `31x + 37Y + 3z = 71` Solution :The equation of the plane is `b(x-1)+c(y-1)+a(z-1)=0` Now, `2001=3xx23xx29` `THEREFORE a lt b ltc rArr a = 3, b=23 and c=29` Substituting the VALUES of a, b, c in (i), we obtain `23x+26y+3z=55` as the equation of the required plane.

Discussion

5231.	The solution of (dy)/(dx) = (x log x^(2) + x)/(sin y + y cos y) is
Answer» `y SIN y = X^(2) log x + c` `y sin y = x^(2) + c` `y sin y = x^(2) + log x + c` `y sin y = x log x+ c` ANSWER :A

Discussion

5232.	Two unbiased dice are thrown. The probability that sum of the numbers appearing on the top face of two dice is 12, if 6 appears on the top face of first dice is ……….
Answer» `(1)/(36)` `(1)/(6)` `(5)/(6)` `(5)/(36)` ANSWER :B

Discussion

5233.	Equation of the tangent line to the curve y= int_(0)^(x) cos theta d theta at x= pi/2 is
Answer» `x=0` `y=0` `x=1` `y=1` ANSWER :D

Discussion

5234.	Differentiate w.r.t.x the function. sin^(3)x+ cos^(6)x
Answer» ANSWER :`3 sin X COS x(sin x-2 cos^(4)x)`

Discussion

5235.	Ifalpha, beta, gammaare therootsofx^3 -px^2+qx -r=0andr ne 0thenfind(1)/( alpha^2) +(1)/( beta^2) +(1)/( gamma^2)in termsof p,q ,r
Answer» ANSWER :`(q^2 -2 RP^(-))/( r^2)`

Discussion

5236.	Entries of a 2xx2 matrix are chosen from the set {0,1}. The probability that the determinant has zero value is
Answer» `(1)/(4)` `(1)/(3)` `(1)/(6)` `(5)/(8)` ANSWER :D

Discussion

5237.	If the vertices of a diagonal of a square (-2, 4) and (-2, 2) then its other two vertices are
Answer» (1,-1) and (5, 1) (1, 1) and (5, 1) (1, 1) and (-5, 1) NONE of these Answer :D

Discussion

5238.	Let C_(1) :x^(2)+y ^(2) =a ^(2) be a circle. From a pointA(-a,0) chord AB is crawn, at point B tangent is drawn to the circle. On the tangent through B, at a distance 'r' from B is a point P. Find the locus of mid point of AP.
Answer» ANSWER :`=> (x+ a//2)^(2) + y^(2) = (a ^(2) + R ^(2))/(4)` is the locus of mid POINT of PA

Discussion

5239.	A line (x-3)/(1) = (y-6)/(5) = (z-4)/(4) is in the plane which passes through (3,2,0). The normal to the plane is .........
Answer» (1,1,1) (-1,1,1) (1,-1,1) (-1,-1,1) ANSWER :C

Discussion

5240.	Three persons A,B,C in order cut a pack of cards replacing them after each cut. The person who first cuts a spade shall win a prize. The probability that C wins the prize is
Answer» `(16)/(37)` `(9)/(37)` `(12)/(37)` `(1)/(37)` Answer :B

Discussion

5241.	Consider the following system of equations : x^2 + y^2 -x-y=10 x^2 + y^2 -5x + 3y=4 What is the value of 2x-2y ?
Answer» 6 5 4 3 Answer :D

Discussion

5242.	sec((pi)/(4) + theta ) . Sec ((pi)/(4)- theta ) isequalto
Answer» `SEC ^2(pi)/(4) - "COSEC" ^2THETA ` 1 0 `2 sec ^2 theta ` Answer :D

Discussion

5243.	Use product{:[( 1,1,2),( 0,2,3),( 3,2,4) ]:} {:[( 2,0,1),(9,2,3),(6,1,2) ]:}to solve the system of equations x-y+2z=1 xy-3z=1 3x-2y+4z =2
Answer» ANSWER :` {:(0,1,-2),(-2,9,-23),(-1,5,-13):},x=1,y=2,z=3`

Discussion

5244.	Express in the form((a+ib)^3)/(a-ib)-((a-ib)^3)/(a+ib)
Answer» Solution :`((a+ib)^3)/(a-ib)-((a-ib)^3)/(a+ib)` `=((a+ib)^4-(a-ib)^4)/((a-ib)(a+ib))` `OVERSET((a^4+4a^3ib+6a^2i^2b^2+4ai^3b^3+i^4b^4))underset(-(a^4-4a^3ib+6a^2i^2b^2-4ai^3b^3+i^4b^4))"/(a^2-i^2b^2)` `=(8a^3ib+8ai^3b^3)/(a^2+b^2)=(8a^3ib-8aib^3)/(a^2+b^2)` `(8abi(a^2-b^2))/(a^2=b^2)=0+(8ab(a^2-b^2)i)/(a^2+b^2)`

Discussion

5245.	Construct 2 xx 2matrix A=[aij] whose elements are given by: a_(ij) = 1/2\|-3i + j\|
Answer» ANSWER :`[{:(1,1/2),(5/2,2):}]`

Discussion

5246.	The maximum possible number of real roots of the equation x^(5)-6x^(2)-4x+5=0, is
Answer» 0 3 4 5 Answer :B

Discussion

5247.	If m_(1) and m_(2) are the roots of the equation x^(2) + (sqrt3 + 2) x + (sqrt3 - 1) = 0then the area of the triangle formed by the lines x = m_(1) x , y = m_(2) x and y = c , is
Answer» `((sqrt(33) - sqrt(11))/(4))C^(2)` `((sqrt(33) + sqrt(11))/(4)) c^(2)` `((sqrt(11) - sqrt(33))/(2))c^(2)` `(sqrt(33))/(2) c^(2)` Answer :B

Discussion

5248.	Let M_n =[m_g] denotes a square matrix of order n with entries as follows for1 le 1le n,m_n = 10 : for 1 le 1 le n-1 m_n +1,=m_(li+1) =3 and all other entries in M_n are zero , Let D_n be the determinant of matrix M_(nr)then find the value of (D_3 9D_2)
Answer» 0 1 2 none of these ANSWER :B

Discussion

5249.	Observe the following statements : Statement-1 : The probabilities of the events A,B and C are respectively (2)/(3), (1)/(4) and (1)/(6) then A,B,C are exhaustive Statement-2 : If the probability for A to fail in an examination is 0.2 and that for B is 0.3 then the probability that either A or B fails is 0.5 Statement-3 : If A and B are two independent events then P(AnnbarB)+P(A)P(B)=P(A) Which of the above are false
Answer» `S_(1),S_(2)` `S_(2),S_(3)` `S_(1),S_(3)` all the above Answer :A

Discussion

5250.	Which of the following set is pair of isoster species.
Answer» `PO_4^(3-), ClO_3^-` `BO_3^(3-),B_3N_3H_6` `CO_2,CO_3^(2-)` `NO^(o+),CO`

Discussion

Explore topic-wise InterviewSolutions in .

Obtain the following integrals : int (sinx+cosx)/(sqrt(1+sin (2x)))dx

int(cotx cot(x + alpha) +1)dx=

Find the values of x and y, if 2{:[(1,3),(0,x)]+{:[(y,0),(1,2)]={:[(5,6),(1,8)]:}

Construct a 3xx4 matrix , whose elements are given by : (i)a_(ij)=(1)/(2)|3i+j| (ii)a_(ij)=2i-j

Let f(x)=2 tan^(-1)((1-x)/(1+x))

H_(2)S gas is not evolved when SO_(3)^(2-) ion reacts with following reagents.

Coffiecient of x^3 in the expansion of e^(-bx)

If the standard deviation of 0,1,2,3,4,5,6,7,8,9 is K, then the standard deviation of 10,11,12,…,19 is

Differentiate w.r.t.x the function in Exercises 1 to 11. sin^(3)x+ cos^(6)x

If alpha, beta, gamma are roots of x^(3) +4x+1=0, then (alpha+beta)^(-1) +(beta+gamma)^(-1) +(gamma+alpha)^(-1) equals

Arrange the following according to their values in ascending order A) int_(0)^(1) sqrt(1-x^(2))dx B) int_(0)^(1) (1)/(sqrt(1-x^(2)))dx C) int_(0)^(1//sqrt(3))(1)/(1+x^(2))dx

thetangent andnormaltothetangentto theellipse(x^(2))/(a^(2))+(y^(2))/(b^(2))=1at thepoint(3,(-9)/(2)),thenthe area( in sq units ) oftheDeltaPQRIs

Integration by partial fraction : int(x-1)/((x-3)(x-2))dx=....

Solve the inequation (sqrt(6+x-x^(2)))/(2x+5) ge (sqrt(6+x-x^(2)))/(x+4).

If A is square matrix of order 2 and A^2+A+2I=0 then

Number of words consisting of two vowels and two consonants which can be made out of the letters of word "DEVASTATION" is

Name the square matrix A=[a_(ij)] in which a_(ij)=0, i!=j.

int_(0)^(1)x(1-x)^(10)dx=

int (a + b sin x )/((b+ a sin x )^(2))dx =

Find the co-ordinates of the point where the line (x+1)/(2)=(y+2)/(3)=(z+3)/(4) cross the planel x + y + 4z = 6.

Express with rational denominator(a+xsqrt(-1))/(a-xsqrt(-1))-(a-xsqrt(-1))/(a+xsqrt(-1))

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

There are two perpendicular lines, one touches to the circle x^(2) + y^(2) = r_(1)^(2) and other touches to the circle x^(2) + y^(2) = r_(2)^(2) if the locus of the point of intersection of these tangents is x^(2) + y^(2) = 9, then the value of r_(1)^(2) + r_(2)^(2) is.

If (1 div 3p)/(3), (1-p)/(4), (1-2p)/(2) are the probabilities of 3 mutually exclusive events then find the set of all values of p.

The total numberof relation fromtheset{p,q} to the set{e,f} is-

A random veriable X takes the values 0,1 and 2. If P(X =1) = P(X=2) and P(X =0) = 0.4 , then the mean of random veriable X is

A plane passes through the points (1, 1, 1). If b, c, a are the direction ratios of a normal to the plane where a, b, c (a lt b lt c) are the prime factors of 2001, then the equation of the plane is:

The solution of (dy)/(dx) = (x log x^(2) + x)/(sin y + y cos y) is

Two unbiased dice are thrown. The probability that sum of the numbers appearing on the top face of two dice is 12, if 6 appears on the top face of first dice is ……….

Equation of the tangent line to the curve y= int_(0)^(x) cos theta d theta at x= pi/2 is

Differentiate w.r.t.x the function. sin^(3)x+ cos^(6)x

Ifalpha, beta, gammaare therootsofx^3 -px^2+qx -r=0andr ne 0thenfind(1)/( alpha^2) +(1)/( beta^2) +(1)/( gamma^2)in termsof p,q ,r

Entries of a 2xx2 matrix are chosen from the set {0,1}. The probability that the determinant has zero value is

If the vertices of a diagonal of a square﻿ (-2, 4) and (-2, 2) then its other two﻿ vertices are﻿

Let C_(1) :x^(2)+y ^(2) =a ^(2) be a circle. From a pointA(-a,0) chord AB is crawn, at point B tangent is drawn to the circle. On the tangent through B, at a distance 'r' from B is a point P. Find the locus of mid point of AP.

A line (x-3)/(1) = (y-6)/(5) = (z-4)/(4) is in the plane which passes through (3,2,0). The normal to the plane is .........

Three persons A,B,C in order cut a pack of cards replacing them after each cut. The person who first cuts a spade shall win a prize. The probability that C wins the prize is

Consider the following system of equations : x^2 + y^2 -x-y=10 x^2 + y^2 -5x + 3y=4 What is the value of 2x-2y ?

sec((pi)/(4) + theta ) . Sec ((pi)/(4)- theta ) isequalto

Use product{:[( 1,1,2),( 0,2,3),( 3,2,4) ]:} {:[( 2,0,1),(9,2,3),(6,1,2) ]:}to solve the system of equations x-y+2z=1 xy-3z=1 3x-2y+4z =2

Express in the form((a+ib)^3)/(a-ib)-((a-ib)^3)/(a+ib)

Construct 2 xx 2matrix A=[aij] whose elements are given by: a_(ij) = 1/2|-3i + j|

The maximum possible number of real roots of the equation x^(5)-6x^(2)-4x+5=0, is

If m_(1) and m_(2) are the roots of the equation x^(2) + (sqrt3 + 2) x + (sqrt3 - 1) = 0then the area of the triangle formed by the lines x = m_(1) x , y = m_(2) x and y = c , is

Let M_n =[m_g] denotes a square matrix of order n with entries as follows for1 le 1le n,m_n = 10 : for 1 le 1 le n-1 m_n +1,=m_(li+1) =3 and all other entries in M_n are zero , Let D_n be the determinant of matrix M_(nr)then find the value of (D_3 9D_2)

Which of the following set is pair of isoster species.

If the vertices of a diagonal of a square (-2, 4) and (-2, 2) then its other two vertices are