28278 + Interview Questions in Maths in Class 12 Page 221 InterviewSolution

11001.	12 different toys are to be distributed to three children equally. In how many ways this can be done?
Answer» ANSWER :34650

Discussion

11002.	Check whether the relation R in R defined by R = {(a,b): a le b ^(3)} is reflexive, symmetric or transitive.
Answer» ANSWER :NEITHER REFLEXIVE nor symmetyric nor TRANSITIVE.

Discussion

11003.	If int(dx)/(sin2x-2xsinx)=C-(1)/(4)log\|f(x)\|+(1)/(8sin^(2)(x)/(2)) then f(x) is equal to
Answer» `TAN^(2)X` `2 tan (x)/(2)` `tan (x)/(2)` `SIN (x)/(2)` ANSWER :C

Discussion

11004.	Simplify (i) (1 + i)^(18) "" (ii) (-sqrt(3) + 3i)^(31)
Answer» Answer :`(2sqrt(3))^(31)(-(1)/(2)+i(sqrt(3))/(2))`

Discussion

11005.	Fill int the blanks choosing correct answer from the bracket. In triangle ABC if cosA/a = cosB/b = cosC/c then the triangle is _____.
Answer» equilateral isosceles scalene Answer :A

Discussion

11006.	Which of the following species exist as liquid at room temperature ?
Answer» `I_2` `AU` `AG` `Br_2`

Discussion

11007.	If theta is the angle between the curves xy = 2 and x^2 + 4y = 0 then tantheta is equal to
Answer» 1 `-1` 2 3 Answer :D

Discussion

11008.	Prove that .^(n)C_(1)- (1+1/2) .^(n)C_(2) + (1+1/2+1/3) .^(n)C_(3) + "…"+ (-1)^(n-1) (1+1/2+1/3 + "…." + 1/n) .^(n)C_(n) = 1/n
Answer» SOLUTION :LET `S = .^(n)C_(1) - (1+1/2) .^(n)C_(2) + (1+1/2 + 1/3) .^(n)C_(3) + "….."` `+(-1)^(n-1)(1+1/2+1/3+"…."+1/n) .^(n)C_(n)`. rth term ofthe series is `T(r ) = (-1)^(r-1) . C_(r ) (1+1/2+1/3+"……"+1/r)`, where `C_(r) = .^(n)C_(r)` Let us consider a series whose general term is `T_(1)(r ) = (-1)^(r-1). C_(r)(1+X+x^(2)+"...."+x^(r-1))` `= (-1)^(r-1). C_(r) ((1-x^(r))/(1-x))` ` = ((-1)^(r-1)C_(r))/(1-x) +((-1)^(r)x^(r)C_(r))/(1-x)` `rArr underset(r=1)overset(n)sum T_(1)(r ) = (1)/((x-1))underset(r=1)overset(n)sum (-1)^(r) C_(r ) + (1)/((1+x))underset(r=1)overset(n)sum(-1)^(r). C_(r).x^(r )` `rArrunderset(r=1)overset(n)sumT_(1)(r ) = (1)/((x-1)) (0-x) + (1)/((1-x)) ((1-x)^(n) - 1) = (1-x)^(n-1)` `= L` (say) Clearly `S= underset(0 )overset(1)intLdx = underset(0)overset(1)INT(1-x)^(n-1) dx = 1/n`

Discussion

11009.	A set A has 3 elements anda set B has 4 elements . The number of one one function defined from set A to B is .........
Answer» 144 12 24 64 Solution :N/A

Discussion

11010.	LetP(n ) =n ( n +1)isaneven number, thenwhichofthefollowingis true ?
Answer» <P>`p(3)` `p(100)` `p(50)` ALLOF these Answer :D

Discussion

11011.	Find the value of x,y and z. [{:(x+y+z),(x+y),(y+z):}]=[{:(7),(5),(3):}]
Answer» ANSWER :`x=4,y=1,z=2`

Discussion

11012.	Let (x, y) be any point on the parabola y^2=4x. Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1 : 3. Then, the locus of P is :
Answer» `x^2=y` `y^2=2x` `y^2=x` `x^2=2y` ANSWER :C

Discussion

11013.	Integrate the following functions: (sin^3x + cos^3x)/(sin^2x cos^2x)
Answer» SOLUTION :`(sin^3 x+cos^3 x)/(sin^2 xcos^2x) = sinx/cos^2x + cosx/sin^2x` = SECX tanx+cosecx COTX THEREFORE` int (sin^3x+cos^3x)/(sin^2x cos^2x) dx` =secx-cosecx+c

Discussion

11014.	If a and b are two non-zero, non-collinear vectors, then 2[abhati]hati+2[abhatj]hatj+2[abhatk]hatk+[abc] is equal to
Answer» `2(axxb)` `axxb` `a+b` None of these Solution :Let `a=a_(1)hat(i)+a_(2)hat(j)+a_(3)hat(K) and b=b_(1)hat(i)+b_(2)hat(j)+b_(3)hat(k)` Now , `[abhat(i)]=\|{:(a_1,a_2,a_3),(b_1,b_2,b_3),(1,0,0):}\|` `=a_(1)(0-0)-a_2(0-b_3)+a_(3)(0-b_2)=a_2b_3-a_3b_2` `therefore 2[ab hat(i)]hat(i)=2(a_2b_3-a_3b_2)hat(i)` Similarly, `2[a b hat(j)]hat(j)=2(a_1b_2-a_1b_3)hat(j)` and `2[a BHAT(k)]hat(k)=2(a_2b_2-a_2b_1)hat(k)` `therefore 2[ab hat(i)]hat(i)+2[abhat(j)]hat(j)+2[abhat(k)]hat(k)+[aba]` `=2[(a_2b_3-a_(3)b_2)hat(i)+(a_3b_1-a_1b_3)hat(j)+0+(a_1b_2-a_2b_1)hat(k)]` `=2(axxb)` .

Discussion

11015.	A company has three plants at which it produces a certain item. 30% are produced at plant A, 50% at plant B and 20% at plant C. Suppose that 1%, 4% and 3% of the items produced at plants A, B and C respectively are defective. If an item is selected at random from all those produced, what is the probability that the item is defective ?
Answer» ANSWER :0.029

Discussion

11016.	For the differential equations, find a particular solution satisfying given condition;(x^(3) + x^(2) + x+ 1)(dy)/(dx) = 2x^(2) + x, y = 1 when x = 0.
Answer» ANSWER :`y = (1)/(4) log [ (x + 1)^(2)(x^(2) + 1)^(3)]- (1)/(2) TAN^(-1) x+ 1`

Discussion

11017.	If for a continuous function f(x), int_(-pi)^(t) (f(x)+ x) dx= pi^(2) -t^(2), for all t ge - pi, then f(-(pi)/( 3) ) is equal to:
Answer» `PI` `(pi)/(2)` `pi/3` `pi/6` ANSWER :A

Discussion

11018.	""^10C_1 . ""^9C_5 + ""^10C_2. ""^9C_4 + ""^10C_3. ""^9C_3 + ""^10C_4. ""^9C_2 + ""^10C_5. ""^9C_1 + ""^10C_6 = ""^19C_6 + xthen x =
Answer» `-84` 84 81 `-81` ANSWER :A

Discussion

11019.	Differentiate the functions with respect to x in sin(ax+b)
Answer» ANSWER :`a.cos (AX + B)`

Discussion

11020.	Find the value of y if the following equations has at least one solution. (i) 5sinx + 12cosx = y^(2)-4y+17 (ii) 4"cosec "^(2)pi(y+x)+y^(2)-4y=0
Answer» Solution :(i) `-13 le 5sinx + 12 cosx le 13`…………(i) Also, `y^(2)-4y+17=(y-2)^(2)+13 ge 13`……….(ii) By (i) and (ii) we observe that SOLUTIONS is obtained at `5 sinx + 12 cosx = (y-2)^(2) + 13=13` `RARR y=2`. (ii) `4 " cosec "pi(y+x)=-y^(2)+4y-4+4=4-(y-2)^(2)` As we KNOW that `4" cosec "^(2)pi(y+x) ge 4` and `4-(y-2)^(2) le 4` Hence, solution is obtained at `4" cosec " ^(2)pi(y+x)=4-(y-2)^(2)=4 rArr y=2`

Discussion

11021.	i. Show that the lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent. ii.Show that the joins of the midpoints of the opposite edges of a tetrahedron intersect and bisect each other.
Answer» Solution :i. `G_(1)`, the centroid of `DeltaBCD`, is `(vecb+vecc+vecd)/(3) and A` is `VECA`. The position vector of point G which divides `AG_(1)` in the ratio 3 : 1 is `""(3(vecb+vecc+vecd)/(3)+1veca)/(3+1)=(veca+vecb+vecc+vecd)/(4)` The symmetry of the result shows that this point will also lie on `BG_(2)`, `CG_(3) and DG_(4)` (where `G_(2), G_(3), G_(4)` are centroids of faces ACD, ABD and ABC, respectively). Hence, these FOUR lines are concurrent at point `(veca+vecb+vecc+vecd)/(4)` , which is called the centroid of the tetrahedron. ii. The midpoint of `DA` is `(veca+vecd)/(2)`and the of `BC` is `(vecb+vecc)/(2)` and the midpoint of these midpoint is `(veca+vecb+vecc+vecd)/(4)` and symmetry of the result proves the fact.

Discussion

11022.	If Ram secure 100 marks in Maths, then he will get a mobile. The converse is
Answer» If RAM gets a MOBILE, then he will not SECURE 100 marks in Maths. If Ram does not GET a mobile, then he will secure 100 marks in Maths. If Ram will get a mobile, then he secure 100 marks in maths. none of these Answer :C

Discussion

11023.	Select the Correct Optiond/dx {log(logx)}=
Answer» 1/logx 1/(XLOGX) 1/x xlogx Answer :D

Discussion

11024.	Prove the A uu B = A for all A implies B =phi
Answer» Solution :As `A UU B` = A for all A we have `B sub A` for all A `:. B sub A` EVEN for `A =phi` Thus `B =phi`

Discussion

11025.	Some standard forms of integration : intsqrt(3-x^(2))dx=...............+c (where \|x\|ltsqrt3 )
Answer» `(X)/(2)sqrt(3-x^(2))+(3)/(2)SIN^(-1)((x)/(SQRT3))` `(x)/(2)sqrt(3-x^(2))+(3)/(2)log(x+sqrt(3-x^(2)))` `(x)/(2)sqrt(3-x^(2))-(3)/(2)log(sqrt((3)/(x)))` `(x)/(2)sqrt(3-x^(2))+(3)/(2)log(sqrt(x)/(3))` ANSWER :A

Discussion

11026.	If y = lamda x -3, y = mu x + , y = x +4 are three nomals drawn from a fixed point P to the parabola whose axis is along x-axis then 2 lamda - 3mu is equal to
Answer» 5 `5/2` `-5/2` NONE of these ANSWER :C

Discussion

11027.	underset(theta to pi//2)lim ([1-tan(x//2)][1-sin x])/([1+tan(x//2)][pi-2x]^(3))=
Answer» `1//8` 0 `1//32` `OO` ANSWER :C

Discussion

11028.	The value of ((100),(0))((200),(150))+((100),(1))((200),(151))+......+((100),(50))((200),(200)) equals (where ((n),(r ))="^(n)C_(r))
Answer» `((300),(50))` `((100),(50))((200),(150))` `((100),(50))^(2)` `((300),(50))^(2)` Solution :`(a)` Writing `((200),(r ))=((200),(200-r))`, we have `((100),(0))((200),(50))+((100),(1))((200),(49))+((100),(2))((200),(48))+......+((100),(50))((200),(0))` `=` Coefficient of `X^(50)` in the expansion of `(1+x)^(100)(x+1)^(200)` `=` Coefficient of `x^(50)` in the binomial expansion of `(1+x)^(300)` `=((300),(50))`

Discussion

11029.	If a,b,c are all different and \|(a,a^(3),a^(4)-1),(b,b^(3),b^(4)-1),(c,c^(3),c^(4)-1)\|=0 then abc (ab+bc+ca)=
Answer» 0 1 -1 `a+b+c` ANSWER :D

Discussion

11030.	If p,q are two statements, then
Answer» `not(p^^q)=notp^^notq` `not(PVVQ)=notpvvnotq` `not(PTOQ)=p^^q` `not(ptoq)=p^^notq` ANSWER :D

Discussion

11031.	ABCD is a square, vertices being taken in the anticlockwise sense. If A represents the complex number z and the intersection of the diagonals is the origin then
Answer» B REPRESENTS the COMPLEX number IZ D represents the complex number `ibar(z)` B represents the complex number `i_bar(z )` D represents the complex number – iz Answer :A,D

Discussion

11032.	If f'(x)=sqrt(2x^2-1) and y=f(x^2) then what is dy/dx at x = 1 ?
Answer» SOLUTION :`y=f(X^2)rArrdy/dx=f(x^2)2x=2xsqrt(2x^4-1)(thereforef(x)=SQRT(2x^2-1))thereforedy/dx]_(x=1)=2sqrt(2-1)=2

Discussion

11033.	If matrix A_lambda=[{:(lambda+1,lambda-2),(lambda-1,lambda):}], lambda in N then the value of \|A_1\|+\|A_2\|+\|A_3\|+..... + \|A_300\| is :-
Answer» `(299)^2` `(300)^2` `2(300)^2` `(301)^2` Solution :`\|A_lambda\|=lambda(lambda+1)-(lambda-1)(lambda-2)=4lambda-2` `\|A_1\|+\|A_2\|+\|A_3\|` + …. + `\|A_300\|` `RARR` 4{1+2+3+….+300} -600 `rArr 4.(300.301)/2 -600=2(300)^2`

Discussion

11034.	If two events A and B are such that P(barA)=0.3, P(B)=0.4and P(AnnbarB)=0.5 then P((B)/(AuubarB))=
Answer» `1//3` `1//4` `1//2` `1//5` ANSWER :B

Discussion

11035.	If each of the three matrices of the same order are symmetric , then their sum is a symmetric matrix.
Answer» ANSWER :TRUE

Discussion

11036.	If (bar(a)xx bar(b))xx(bar(b)xx bar( c ))=bar(b), where bar(a),bar(b),bar( c ) are non zero vectors, then …………..
Answer» `BAR(a),bar(b),bar( C )` are COPLANAR VECTORS. `bar(a),bar(b),bar( c )` may be coplanar vectors. `bar(a),bar(b),bar( c )` are not coplanar vectors. can not say ANYTHING. Answer :C

Discussion

11037.	In the parallelogram ABCD, overline(AD)^(2) - overline(AB)^(2) =
Answer» `4 overline(AB)`. (orthogonal PROJECTION of `overline(AD)` on `overline(AB)`) `2 overline(AB)`. (orthogonal projection of `overline(AD)` on `overline(AB)`) ` overline(AC)`. (orthogonal projection of `overline(BD)` on `overline(AC)`) `2 overline(AC)`. (orthogonal projection of `overline(BD)` on `overline(AC)`) Answer :C

Discussion

11038.	If y= x^(x^(x)) then find (dy)/(dx)
Answer» ANSWER :`X^(x^(x)).LOG x^((x^(x))) [1 + log x + (1)/(x log x)]`

Discussion

11039.	Evalute the following integrals int (1)/((x+ 1)^(2)(x^(2) + 1)) dx
Answer» ANSWER :`(1)/(2) LOG \| X+1\|-(1)/(4) log (x^(2) + 1) - (1)/(2(x + 1)) + c `

Discussion

11040.	For the same laon, what is the loan balance after 3 years assuming no payments on the loan, and ul("annual") compounding?
Answer» ANSWER :`$17,778.53`

Discussion

11041.	Coefficient of a^8b^6c^4 in (a+b+c)^18 is
Answer» `(18!)/(4!10!5!)` `(18!)/(3!8!8!)` `(18!)/(2!7!9!)` `(18!)/(8!6!4!)` Answer :D

Discussion

11042.	The median from the following data is{:("Mid-value","Frequency"),(115,6),(125,25),(135,48),(145,72),(155,116),(165,60),(175,38),(185,22),(195,3):}
Answer» `153.79` `153.91` `165.18` `165.93` ANSWER :A

Discussion

11043.	Which of the following is NOT equivalent to ~ p wedge q ?
Answer» <P>`~(Q to p)` `~p WEDGE (~p to q)` `~ (p VV ~q)` `~p to ~ q` ANSWER :D

Discussion

11044.	Let R be a relation defined on the set of real numbers by aRb iff 1+ab gt 0 then R is
Answer» REFLEXIVE & SYMMETRIC transitive anti symmetric EQUIVALENCE ANSWER :A

Discussion

11045.	Solve system of linear equations ,using matrix method2x+ y +z=1 x- 2y -z= (3)/(2)3y-5z =9
Answer» ANSWER :`x=1,y=(1)/(2) ,Z=(-3)/(2) `

Discussion

11046.	n different things are arrnaged around a circle. In how many ways can 3 objects be selected when no two of the selected objects are consecutive?
Answer» Solution :Let the object be denoted by `a_(1),a_(2),a_(3), . .,a_(n)` arranged in a circle, we have to select 3 objects so that no TWO of them are consecutive. For this, we first find the number of ways in which 2 or 3 objects are consecutive. Now, number of ways in which 2 or 3 objects are consecutive, is obtained as follows with `a_(1)`. the number of such triples is `a_(1)a_(2)a_(3),a_(1)a_(2)a_(4),a_(1)a_(2)a_(5), . . .,a_(1)a_(2)a_(n-1)`. [Since, we have excluded `a_(1)a_(2)a_(n),` so it will be repeated again. if we start with `a_(n)`, then we shall GET triples: `a_(n)a_(1)a_(2),a_(n)a_(1)a_(3)`] so, number of such triples when we start with `a_(1)`, is (n-3). similarly, with `a_(2),a_(3),a_(4), K, . . .,` we shall get the numbers of triples that is (n-3). but total number of triples is `.^(n)C_(3)`. Hence, REQUIRED number of ways `=.^(n)C_(3)-n(n-3)` `=(n(n-1)(n-2))/(123)-n(n-3)=(n)/(6)[n^(2)-3n+2-6n+18]` `=(n)/(6)(n^(2)-9n+20)=(n)/(6)(n-4)(n-5)`.

Discussion

11047.	Let vec(a)=2hat(i)+hat(j)+hat(k),vec(b)=hat(i)+2hat(j)-hat(k) and a unit vector vec(c) be coplanar. If vec(c)" is perpendicular to "vec(a)," then "vec(c)=
Answer» `(-hat(J)+hat(k))/(SQRT(2))` `(-hat(i)-hat(j)-hat(k))/(sqrt(3))` `(hat(i)-2hat(j))/(sqrt(5))` `(hat(i)-hat(j)-hat(k))/(sqrt(3))` ANSWER :A

Discussion

11048.	inttan^-1sqrt((1-cos2x)/(1+cos2x))dx
Answer» SOLUTION :`I=inttan^-1sqrt((1-cos2x)/(1+cos2x))DX` =`inttan^-1(sinx/cosx)dx` =`inttan^-1(TANX)dx` =`intxdx=x^2/2+c`

Discussion

11049.	If X+Y=[(5,2),(0,9)] and X-Y=[(3, 6), (0,-1)] and X=[(k,k),(0,k)], then k =
Answer» 8 2 4 1 Solution :N/A

Discussion

11050.	A compound (X) on decomposition gives a colourless gas. The residue is dissolved in water to obtain (Y). Excess CO_(2) is bubbled through aqueoussolution of (Y) and (Z) is formed. (Z) are gentle heating gives back (X) . The (X) is
Answer» `CaCO_(3)` `Ca(HCO_(3))_(2)` `NaHCO_(3)` `Na_(2)CO_(3)` SOLUTION :

Discussion

Explore topic-wise InterviewSolutions in .

12 different toys are to be distributed to three children equally. In how many ways this can be done?

Check whether the relation R in R defined by R = {(a,b): a le b ^(3)} is reflexive, symmetric or transitive.

If int(dx)/(sin2x-2xsinx)=C-(1)/(4)log|f(x)|+(1)/(8sin^(2)(x)/(2)) then f(x) is equal to

Simplify (i) (1 + i)^(18) "" (ii) (-sqrt(3) + 3i)^(31)

Fill int the blanks choosing correct answer from the bracket. In triangle ABC if cosA/a = cosB/b = cosC/c then the triangle is _____.

Which of the following species exist as liquid at room temperature ?

If theta is the angle between the curves xy = 2 and x^2 + 4y = 0 then tantheta is equal to

Prove that .^(n)C_(1)- (1+1/2) .^(n)C_(2) + (1+1/2+1/3) .^(n)C_(3) + "…"+ (-1)^(n-1) (1+1/2+1/3 + "…." + 1/n) .^(n)C_(n) = 1/n

A set A has 3 elements anda set B has 4 elements . The number of one one function defined from set A to B is .........

LetP(n ) =n ( n +1)isaneven number, thenwhichofthefollowingis true ?

Find the value of x,y and z. [{:(x+y+z),(x+y),(y+z):}]=[{:(7),(5),(3):}]

Let (x, y) be any point on the parabola y^2=4x. Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1 : 3. Then, the locus of P is :

Integrate the following functions: (sin^3x + cos^3x)/(sin^2x cos^2x)

If a and b are two non-zero, non-collinear vectors, then 2[abhati]hati+2[abhatj]hatj+2[abhatk]hatk+[abc] is equal to

For the differential equations, find a particular solution satisfying given condition;(x^(3) + x^(2) + x+ 1)(dy)/(dx) = 2x^(2) + x, y = 1 when x = 0.

If for a continuous function f(x), int_(-pi)^(t) (f(x)+ x) dx= pi^(2) -t^(2), for all t ge - pi, then f(-(pi)/( 3) ) is equal to:

""^10C_1 . ""^9C_5 + ""^10C_2. ""^9C_4 + ""^10C_3. ""^9C_3 + ""^10C_4. ""^9C_2 + ""^10C_5. ""^9C_1 + ""^10C_6 = ""^19C_6 + xthen x =

Differentiate the functions with respect to x in sin(ax+b)

Find the value of y if the following equations has at least one solution. (i) 5sinx + 12cosx = y^(2)-4y+17 (ii) 4"cosec "^(2)pi(y+x)+y^(2)-4y=0

i. Show that the lines joining the vertices of a tetrahedron to the centroids of opposite faces are concurrent. ii.Show that the joins of the midpoints of the opposite edges of a tetrahedron intersect and bisect each other.

If Ram secure 100 marks in Maths, then he will get a mobile. The converse is

Select the Correct Optiond/dx {log(logx)}=

Prove the A uu B = A for all A implies B =phi

Some standard forms of integration : intsqrt(3-x^(2))dx=...............+c (where |x|ltsqrt3 )

If y = lamda x -3, y = mu x + , y = x +4 are three nomals drawn from a fixed point P to the parabola whose axis is along x-axis then 2 lamda - 3mu is equal to

underset(theta to pi//2)lim ([1-tan(x//2)][1-sin x])/([1+tan(x//2)][pi-2x]^(3))=

The value of ((100),(0))((200),(150))+((100),(1))((200),(151))+......+((100),(50))((200),(200)) equals (where ((n),(r ))="^(n)C_(r))

If a,b,c are all different and |(a,a^(3),a^(4)-1),(b,b^(3),b^(4)-1),(c,c^(3),c^(4)-1)|=0 then abc (ab+bc+ca)=

If p,q are two statements, then

ABCD is a square, vertices being taken in the anticlockwise sense. If A represents the complex number z and the intersection of the diagonals is the origin then

If f'(x)=sqrt(2x^2-1) and y=f(x^2) then what is dy/dx at x = 1 ?

If matrix A_lambda=[{:(lambda+1,lambda-2),(lambda-1,lambda):}], lambda in N then the value of |A_1|+|A_2|+|A_3|+..... + |A_300| is :-

If two events A and B are such that P(barA)=0.3, P(B)=0.4and P(AnnbarB)=0.5 then P((B)/(AuubarB))=

If each of the three matrices of the same order are symmetric , then their sum is a symmetric matrix.

If (bar(a)xx bar(b))xx(bar(b)xx bar( c ))=bar(b), where bar(a),bar(b),bar( c ) are non zero vectors, then …………..

In the parallelogram ABCD, overline(AD)^(2) - overline(AB)^(2) =

If y= x^(x^(x)) then find (dy)/(dx)

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

For the same laon, what is the loan balance after 3 years assuming no payments on the loan, and ul("annual") compounding?

Coefficient of a^8b^6c^4 in (a+b+c)^18 is

The median from the following data is{:("Mid-value","Frequency"),(115,6),(125,25),(135,48),(145,72),(155,116),(165,60),(175,38),(185,22),(195,3):}

Which of the following is NOT equivalent to ~ p wedge q ?

Let R be a relation defined on the set of real numbers by aRb iff 1+ab gt 0 then R is

Solve system of linear equations ,using matrix method2x+ y +z=1 x- 2y -z= (3)/(2)3y-5z =9

n different things are arrnaged around a circle. In how many ways can 3 objects be selected when no two of the selected objects are consecutive?

Let vec(a)=2hat(i)+hat(j)+hat(k),vec(b)=hat(i)+2hat(j)-hat(k) and a unit vector vec(c) be coplanar. If vec(c)" is perpendicular to "vec(a)," then "vec(c)=

inttan^-1sqrt((1-cos2x)/(1+cos2x))dx

If X+Y=[(5,2),(0,9)] and X-Y=[(3, 6), (0,-1)] and X=[(k,k),(0,k)], then k =

A compound (X) on decomposition gives a colourless gas. The residue is dissolved in water to obtain (Y). Excess CO_(2) is bubbled through aqueoussolution of (Y) and (Z) is formed. (Z) are gentle heating gives back (X) . The (X) is