28278 + Interview Questions in Maths in Class 12

1.	If ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of lines then prove that h^2geab,f^2gebc,g^2geac.
Answer» ANSWER :`g^2geac,f^2gebc`

Discussion

2.	Using elementary transformations, find the inverseof the matrices [(2,1),(4,2)]
Answer» ANSWER :`therefore[{:(2,1),(0,0):}]=[{:(1,0),(-2,1):}]A "" R_(2)toR_(2)-2R_(1)`

Discussion

3.	The mean and the median of 100 observation have been computed to be 60 and 70 respectively. Later it was discovred that three observations which have been recorded 18,28 and 98 are actually 80,26 and 38 respectively. If the mean and median are recalculated with equal observations, then
Answer» MEDIAN will CHANGE but MEAN will not change NEITHER mean nor median will change both mean and median will change mean will change but median will not change ANSWER :A

Discussion

4.	int(x^(3)-1)/(1+sinx)dx=
Answer» `x-logabs(x)+1/2logabs(x^(2)+1)+tan^(-1)x+c` `x-logabs(x)+logabs(sqrt(x^(2)+1))-tan^(-1)x+c` `x+logabs(x)+logabs(sqrt(x^(2)+1))+tan^(-1)x+c` NONE of these Answer :B

Discussion

5.	There are three kinds of fruits in the market. How many ways are there to purchase 25 fruits from among them if each kind has at least 25 of its fruit available?
Answer» ANSWER :351

Discussion

6.	Theroots of(1)/(x-1)_(1)/(x-2)=(1)/(x-3) are
Answer» `3+-sqrt(2)` ` 2 +- sqrt(3)` `6 +- sqrt(8)` `8 +- sqrt(6) ` Answer :A

Discussion

7.	A closed organ pipe of radiusr_(1) and an open organ pipe of radius r_(2) and having same length 'L' resonate when exited with a given tuning fork. Closed organ pipe and open organ pipe resonates in fundamental mode, then :
Answer» `1.2 (r_(2)-r_(1)) =L` `r_(2)-r_(1)=L` `r_(2)-2r_(1) = 2.5L` `2r_(2)-r_(1) = 2.5L` SOLUTION :With END correction for closed organ pipe `implies (lambda)/4 = L+e` and for open organ pipe `(lambda)/2 = L + 2e_(2)` SO `4(L+e_(1))=2(L+2e_(2))` Now, `e_(1) = 0.6 r_(1)` and `e_(2) = 0.6 r_(2)` `2L = 4(e_(2)-e_(1))` `L = 2(e_(2)-e_(1))` `=2 xx 0.6 (r_(2)-r_(1))` `L = 1.2 (r_(2)-r_(1))`.

Discussion

8.	Method of integration by parts : int (x tan^(-1)x)/((1+x^(2))^((3)/(2)))dx=.....
Answer» `(x+TAN^(-1)x)/(SQRT(1+x^(2)))+C` `(x-tan^(-1)x)/(sqrt(1+x^(2)))+c` `(tan^(-1)x-x)/(sqrt(1+x^(2)))+c` NONE of these Answer :B

Discussion

9.	If a, b, c, d be 3^(rd), 4^(th), 5^(th) and 6^(th) terms of the expansion of (p+q)^(n), where n is a positive integer prove that (b^(2)-ac)/(c^(2)-b)=(5a)/(3c).
Answer» SOLUTION :N/A

Discussion

10.	If A= [[1 ,-2, 2],[0, 2, -3],[3 ,-2, 4]], then A . adj A=
Answer» `{:[(5,1,1),(1,5,1),(1,1,5)]:}` `{:[(5,0,0),(0,5,0),(0,0,5)]:}` `{:[(8,0,0),(0,8,0),(0,0,8)]:}` `{:[(0,0,0),(0,0,0),(0,0,0)]:}` ANSWER :C

Discussion

11.	There are p copies each of n different subjects. Find the number of ways in which a nonempty selection can be made from them. Also find the number of ways in which at least one copy of each subject is selected.
Answer» Solution :Number of WAYS of selection of zero or more copies of any subject =1+1+1+..+1 ((p+1) times) =p+1 So, total number of ways of selection of zero or more copies from all N subjects =(p+1)(p+1)..(p+1)(n times) `=(p+1)^(n)` But this INCLUDES one CASE when no book is selected. So, number of nonempty selections `=(p+1)^(n)-1` Now number of ways of selection of at least one copy of any subject =1+1+1+..+1(p times )=p So, number of ways in which at least one copy of each subject is selected `=pxxpxxpxx.xxp`(n times) `=p^(n)`.

Discussion

12.	How many 9 digited numbers can be formed using 0, 1, 2 so that 0, 1, 2 must occur atleast once in each 9 digited number.
Answer» ANSWER :`2(3^8-2^9+1)`

Discussion

13.	An iron ball having 10 cm radius is covered equally with Ice. Ice is melted at the rate of 50 cm^(3)/min. when the thickness of ice is 5 cm, rate of decrease in radius is ………….. cm/min.
Answer» `(1)/(36 pi)` `(1)/(18pi)` `(1)/(54 pi)` `(5)/(6PI)` Answer :B

Discussion

14.	Let l_(n)=int_(0)^(1)l_(n)=2^(n)int_(0)^(1)(1+x^(4))^(n)dx. If (k+1)l_(n)=2k(1+l_(n-1)) then the value of n is (k,ninN) ______
Answer» ANSWER :2

Discussion

15.	Equation of the tangent to the hyperbola 4x^(2)-9y^(2)=1 with eccentric angle pi//6 is
Answer» `4x+3y=sqrt3` `4x-3y=sqrt3` `3x-4y=sqrt3` `3x-4y=sqrt5` ANSWER :B

Discussion

16.	If A,B,C,D are angles of a cyclic quadrilateral, then cos A +cos B +cos C +cos D is equal to
Answer» 0 1 `-1` 4 Answer :A

Discussion

17.	f: R rarr (-1, 1) , f(x) = (10^(x)-10^(x))/(10^(x)+10^(-x)).If inverse of f^(-1) exists then find it .
Answer» SOLUTION :N/A

Discussion

18.	Which of the the solution is (x-5)/(x+3) lt -1 ?
Answer» X LT -3 or x GT 5 x lt -3 or x gt 1 `-3` lt x lt 5 `-3` lt x lt 1 Answer :D

Discussion

19.	A sample of 2 itmes is selected at random from a bag containing 5 items of which 2 are defective. Then mean of number of defective items is
Answer» `(4)/(5)` `(1)/(5)` `(2)/(5)` `(3)/(5)` ANSWER :A

Discussion

20.	A: int (1)/(3+4cosx)dx=(1)/(sqrt(7))log\|(sqrt(7)+tan(x//2))/(sqrt(7)-tan(x//2))\|+c R : If a lt b then int(dx)/(a+b cosx)= (1)/(sqrt(b^(2)-a^(2)))log\|(sqrt(b+a)+sqrt(b-a)tan(x//2))/(sqrt(b+a)-sqrt(b-a)tan(x//2))\|+c
Answer» Both A and R are TRUE and R is the CORRECT EXPLANATION of A Both A and R are true and R is not correct explanation of A A is true R is false A is false but R is true. Answer :1

Discussion

21.	Let a,b,c epsilonR and alpha, beta,are the real roots of the equation ax^(2)+bx+c=0 and in a+b+clt0,a-b+clt0 andcgt0 then [alpha]+[beta] is equal to (where[.]denotes the greatest integer function).
Answer» 0 1 -1 None of these Solution :`(ax-b)^(2)+(bx-c)^(2)+(cx-d)^(2)lt0` `b/a=c/b=d/c=x""b^(2)=ac""2 LOG 6=LOGA+logc` `\|(33,14,loga),(65,27,lobg),(97,40,logc)\|to` apply `R_(1)toR_(1)+R_(3)-2R_(2)` `=0`

Discussion

22.	On Z, a relation R is defined as follows: a,b in Z, aRb if 7 divides a -b The equivalence class containing -17 is
Answer» {...,-17,-10,-3,4,11,...} {...,-17,-9,-2,3, 10, ...} {...,-17,-13,-10,7,13,...} NONE of these Answer :A

Discussion

23.	The sidesAB,BC,CA of a DeltaABChave3,4and 5interiorpointsrespectivelyon them. Thenumberof triangles thatcan besonstructedusingthesepointsas verticesis
Answer» 205 210 315 216 Answer :A

Discussion

24.	Let x, p in R, x + 1 gt 0, p ne 0, 1. Then
Answer» <P>`(1 + X)^(p) gt 1 px "for" p gt 0` `(1 + x)^(p) gt 1 + px "for" p in (-oo, 0) UU (1, oo)` `(1 + x)^(p) gt 1 + px "for" 0 lt p lt 1` `(1 + x)^(p) lt 1 + px "for" p lt 1` Answer :B

Discussion

25.	Find the particular solution of the differential equations (dy)/(dx)+ycotx=4cosec x xcancel=0 given that y=0 when x=pi/2
Answer» ANSWER :`y sin X = 2x^(2) - (pi^(2))/(2)(sin x NE 0)`

Discussion

26.	How many moles of P_(4) can be produced by reaction of 0.10 moles Ca_(5)(PO_4)_(3) F, 0.36 moles SiO_(2) and 0.90 moles C according to the following reaction? 4Ca_(5)(PO_4)_(3)F + 18SiO_(2) + 30 Cto 3P_(4) + 2CaF_(2) + 18CaSiO_(3)+30CO.
Answer» <P>`0.060` `0.030` `0.045` `0.075` SOLUTION :`SiO_(2)` = Limiting REACTANT `18 SiO_(2) overset("give")(rarr) 3P_(4)` `0.36 mol SiO_(2) to 3/18 xx 0.36 = 0.06 mol P_(4)`.

Discussion

27.	The centre of the circle touching the y-axis at (0,3) and making an intercept 2 unit on positive x-axis is
Answer» `(SQRT(10),3)` `(3,sqrt(10))` `(-sqrt(10),3)` `(sqrt(10),-3)` ANSWER :A

Discussion

28.	The number of common tangents to the circle x^(2)+y^(2)-4x-6y-12=0 and x^(2)y^(2)+6x+18y+26=0 is
Answer» ANSWER :` 212=0 `

Discussion

29.	the value of thedeterminant \|{:(.^(n)C_(r-1),,.^(n)C_(r),,(r+1)^(n+2)C_(r+1)),(.^(n)C_(r),,.^(n)C_(r+1),,(r+2)^(n+2)C_(r+2)),(.^(n)C_(r+1),,.^(n)C_(r+2),,(r+3)^(n+2)C_(r+3)):}\| is
Answer» `n^(2)+n-1)` `0` `.^(n+3)C_(r+3)` `.^(n)C_(r-1)+^(n)C_(r)+^(n)C_(r+1)` Solution :`DELTA = \|{:(.^(n)C_(r-1),,.^(n)C_(r),,(r+1)^(n+2)C_(r+1)),(.^(n)C_(r),,.^(n)C_(r+1),,(n+2)^(n+1)C_(r+1)),(.^(n)C_(r+1),,.^(n)C_(r+2),,(r+3)^(n+2)C_(r+3)):}\|` Applying `C_(1) to C_(1)+C_(2) " and USING " .^(n)C_(r)=(n)/(r )^(n-1) C_(r+1) " in " C_(3)` we get ` Delta =\|{:(.^(n+1)C_(r),,.^(n)C_(r),,(n+2)^(n+1)C_(r)),(.^(n+1)C_(r+1),,.^(n)C_(r+1),,(n+2)^(n+1)C_(r+1)),(.^(n+1)C_(r+2),,.^(n)C_(r+2),,(n+2)^(n+1)C_(r+2)):}\|` `=(n+2) \|{:(.^(n+1)C_(r),,.^(n)C_(r),,.^(n+1)C_(r)),(.^(n+1)C_(r+1),,.^(n)C_(r+1),,.^(n+1)C_(r+1)),(.^(n+1)C_(r+2),,.^(n)C_(r+2),,.^(n+1)C_(r+2)):}\|` ( as `C_(1) " and " C_(3)`are identical )

Discussion

30.	The tangent at (3,4), (4,-3) to the circle x^(2)+y^(2)=25" are"
Answer» coincident parallel perpendicular at an ANGLE of `45^(@)` ANSWER :C

Discussion

31.	Prove that sin^2(18)^@ + cos^2(36)^@ = 3/4
Answer» SOLUTION :`sin^2 18^@+cos^236^@=`((sqrt5-1)/4)^2+((sqrt5+1)/4)^2=((sqrt5-1)^2+(sqrt5+1))/16=3/4`

Discussion

32.	Integrationof rationalfunctions int(dx)/((x+1)(x+2)^(2)(x-3)^(3))
Answer» Answer :`(9x^(2)+50x+68)/(4(x+2)(x+3)^(2))+(1)/(8) In\|((x+1)(x+2)^(16))/((x+3)^(17))\|+C.`

Discussion

33.	State with reason, "All citizens of india earning more than Rs.10,000/- per month " is set or not ?
Answer» SOLUTION :It is a SET, as it is WELL DEFINED.

Discussion

34.	If OA = 2hati + 2hatj+ hatk, OB = 2hati + 4hatj + 4hatkand the length of the internal bisector ofangle BOAof triangle AOB is k, then 9k^(2) =
Answer» A225 B136 C712 D20 Answer :B

Discussion

35.	Which of the following are True? (where [.] denotes greatest integer funstion)
Answer» if `f(x)=[x],g(x)=\|x-1\|` then the VALUE of fog `(-7)/(4)+gof(-7)/(4)` is equal to 5 The number of solution of equation `\|[x]-1\|=x^(2)` is 2. if `f^(2)(x)=x^(2)` then number of DIFFERENT POSSIBLE continuous FUNCTIONS `f(x)` is 4 if a polynomial function is invertible, then its inverse function is always differentiable. Solution : (A) fog `((-7)/(4))=f((11)/(4))=2` `gof((-7)/(4))=g(-2)=\|-2-1\|=3` (B) only ONE solution (C). `\|f(x)\|=\|x\|` `becausef(x)=x,\|x\|,-\|x\|` (D). `f(x)=x^(3)` `f^(-1)(x)=x^((1)/(3))` which is not differentiable at `x=0`

Discussion

36.	If \|[[x,2],[18,x]]\|=\|[[6,2],[18,6]]\|, then x is equal to:
Answer» 6 `+-6` -6 6,6 Answer :B

Discussion

37.	A pair of dice is thrown and the random variable X is defined as the sum of numbers that appear on the two dice. Find the mean or expectation of X.
Answer» ANSWER :7

Discussion

38.	Find the area enclosed between the curves y= \|x\| and y= x^(2)-2
Answer» ANSWER :`((20)/(3))`

Discussion

39.	An equatin of the family of circles passing through a given pair of points (x_(1), y _(1))and (x _(2), y _(2)) can be taken ad (x - x _(1)) (x -x _(2))+ (y - y_(1)) (y-y_(2))+ k \|{:(x,y,1),(x_(1), y _(1), 1),(x_(2), y_(2), 1):}\|=0, k being a real parameter. If a member of this family satisfies some other condition then that enables us to determine k and hence the number. Consider the set S of all possible circles that pass through (4,-3) and (-3,4) and thouch the line x +y -5 sqrt2=0. Then which of the following statements is correct ?
Answer» S CONSISTS of exactly one circle, having radius 5 S consists of exactly one circle, having radius 10 S consists of exactly two CIRCLES, the ratio of radi being `1:2` S consists of exactly two circles, the ratio of RADII being `2:3` Answer :A

Discussion

40.	Find the coordinates of the focus, the axis, the equation of the directrix and the lengths of the latus rectum of the following parabolas i. x^2 = 6y "" ii. x^2 + 16y = 0 iii. y^2 = 10x "" iv. y^2 = -8x.
Answer» Answer :(i) 4a = 6 , (ii) 4a = 16 , (iii) 4a = 10 , (IV) 4a = 8.

Discussion

41.	An equatin of the family of circles passing through a given pair of points (x_(1), y _(1))and (x _(2), y _(2)) can be taken ad (x - x _(1)) (x -x _(2))+ (y - y_(1)) (y-y_(2))+ k \|{:(x,y,1),(x_(1), y _(1), 1),(x_(2), y_(2), 1):}\|=0, k being a real parameter. If a member of this family satisfies some other condition then that enables us to determine k and hence the number. The number of values of lamda in R for which there exists exactly one circle passing through the point (2, -3) and (lamda, 2 lamda -1) and touching the line 16x-2y + 27=0, is
Answer» 0 1 2 infinitely MANY ANSWER :C

Discussion

42.	Construct a 2xx2 matrix, A=[a_(ij)], whose elements are given by: (i) a_(ij)=((i+j)^(2))/(2) (ii) a_(ij)=(i)/(j) (iii) a_(ij)=((i+2j)^(2))/(2)
Answer» Answer :`(i)[(2,(9)/(2)),((9)/(2),8)] (II) [(1,(1)/(2)),(2,1)] (iii) [((9)/(2),(25)/(2)),(8,18)]`

Discussion

43.	hati *(hatj xx hatk) +hatj(hatk xx hati) +hatk (hati xx hatj) is :
Answer» -3 0 1 3 Solution :N/A

Discussion

44.	Differentiate the functions with respect to x in Exerecises 1 to 8. cos x^(3). Sin^(2) (x^5).
Answer» Answer :`10X^(4)SIN x^(5) cosx^(5) cox^(3) -3X^(2) sinx^(3)sin^(2)x^(5)`.

Discussion

45.	Find the eccentricity of the ellipse (i) (x^(2))/(16)+(y^(2))/(9)=1 (ii) (x^(2))/(64)+(y^(2))/(36)=1 (iii)25x^(2)+4y^(2)=100
Answer» ANSWER :`sqrt21/4`

Discussion

46.	Differentiate x^(sinx)+(sinx)^(cosx) w.r.t x.
Answer» ANSWER :`x^(sin x)[(SINX)/(x)+cosxlogx]+(sinx)^(cos x)[cos xcot x-sin x LOG sin x]`

Discussion

47.	Let P be a point on the parabola, x^2=4y. If the distance of P from the centre of the circle, x^2+y^2+6x+8=0 is minimum, then the equation of the tangent to the parabola at P, is:
Answer» `x+4y-2=0` `x+y+1=0` `x-y+3=0` `x+2y=0` ANSWER :B

Discussion

48.	If the straightline2x+3y-1=0, x+2y-1=0 and ax+by-1=0 form a triangle with origin as orthocentre, then (a,b) is equal to
Answer» (6,4) (-3,3) (-8,8) (0,7) ANSWER :C

Discussion

49.	If z+1/z=1 and z be any complex number,then the value of z^(99)+(1)/(z^(99)) is
Answer» 1 -1 2 -2 Answer :D

Discussion

50.	Which of the following is not a negation of the statement p:sqrt(5) is rational ?
Answer» It is not the CASE that `sqrt(5)` is rational `sqrt(5)` is not rational `sqrt(5)` is an IRRATIONAL number `- sqrt(5)` is rational. ANSWER :D

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of lines then prove that h^2geab,f^2gebc,g^2geac.

Using elementary transformations, find the inverseof the matrices [(2,1),(4,2)]

The mean and the median of 100 observation have been computed to be 60 and 70 respectively. Later it was discovred that three observations which have been recorded 18,28 and 98 are actually 80,26 and 38 respectively. If the mean and median are recalculated with equal observations, then

int(x^(3)-1)/(1+sinx)dx=

There are three kinds of fruits in the market. How many ways are there to purchase 25 fruits from among them if each kind has at least 25 of its fruit available?

Theroots of(1)/(x-1)_(1)/(x-2)=(1)/(x-3) are

A closed organ pipe of radiusr_(1) and an open organ pipe of radius r_(2) and having same length 'L' resonate when exited with a given tuning fork. Closed organ pipe and open organ pipe resonates in fundamental mode, then :

Method of integration by parts : int (x tan^(-1)x)/((1+x^(2))^((3)/(2)))dx=.....

If a, b, c, d be 3^(rd), 4^(th), 5^(th) and 6^(th) terms of the expansion of (p+q)^(n), where n is a positive integer prove that (b^(2)-ac)/(c^(2)-b)=(5a)/(3c).

If A= [[1 ,-2, 2],[0, 2, -3],[3 ,-2, 4]], then A . adj A=

There are p copies each of n different subjects. Find the number of ways in which a nonempty selection can be made from them. Also find the number of ways in which at least one copy of each subject is selected.

How many 9 digited numbers can be formed using 0, 1, 2 so that 0, 1, 2 must occur atleast once in each 9 digited number.

An iron ball having 10 cm radius is covered equally with Ice. Ice is melted at the rate of 50 cm^(3)/min. when the thickness of ice is 5 cm, rate of decrease in radius is ………….. cm/min.

Let l_(n)=int_(0)^(1)l_(n)=2^(n)int_(0)^(1)(1+x^(4))^(n)dx. If (k+1)l_(n)=2k(1+l_(n-1)) then the value of n is (k,ninN) ______

Equation of the tangent to the hyperbola 4x^(2)-9y^(2)=1 with eccentric angle pi//6 is

If A,B,C,D are angles of a cyclic quadrilateral, then cos A +cos B +cos C +cos D is equal to

f: R rarr (-1, 1) , f(x) = (10^(x)-10^(x))/(10^(x)+10^(-x)).If inverse of f^(-1) exists then find it .

Which of the the solution is (x-5)/(x+3) lt -1 ?

A sample of 2 itmes is selected at random from a bag containing 5 items of which 2 are defective. Then mean of number of defective items is

A: int (1)/(3+4cosx)dx=(1)/(sqrt(7))log|(sqrt(7)+tan(x//2))/(sqrt(7)-tan(x//2))|+c R : If a lt b then int(dx)/(a+b cosx)= (1)/(sqrt(b^(2)-a^(2)))log|(sqrt(b+a)+sqrt(b-a)tan(x//2))/(sqrt(b+a)-sqrt(b-a)tan(x//2))|+c

Let a,b,c epsilonR and alpha, beta,are the real roots of the equation ax^(2)+bx+c=0 and in a+b+clt0,a-b+clt0 andcgt0 then [alpha]+[beta] is equal to (where[.]denotes the greatest integer function).

On Z, a relation R is defined as follows: a,b in Z, aRb if 7 divides a -b The equivalence class containing -17 is

The sidesAB,BC,CA of a DeltaABChave3,4and 5interiorpointsrespectivelyon them. Thenumberof triangles thatcan besonstructedusingthesepointsas verticesis

Let x, p in R, x + 1 gt 0, p ne 0, 1. Then

Find the particular solution of the differential equations (dy)/(dx)+ycotx=4cosec x xcancel=0 given that y=0 when x=pi/2

How many moles of P_(4) can be produced by reaction of 0.10 moles Ca_(5)(PO_4)_(3) F, 0.36 moles SiO_(2) and 0.90 moles C according to the following reaction? 4Ca_(5)(PO_4)_(3)F + 18SiO_(2) + 30 Cto 3P_(4) + 2CaF_(2) + 18CaSiO_(3)+30CO.

The centre of the circle touching the y-axis at (0,3) and making an intercept 2 unit on positive x-axis is

The number of common tangents to the circle x^(2)+y^(2)-4x-6y-12=0 and x^(2)y^(2)+6x+18y+26=0 is

the value of thedeterminant |{:(.^(n)C_(r-1),,.^(n)C_(r),,(r+1)^(n+2)C_(r+1)),(.^(n)C_(r),,.^(n)C_(r+1),,(r+2)^(n+2)C_(r+2)),(.^(n)C_(r+1),,.^(n)C_(r+2),,(r+3)^(n+2)C_(r+3)):}| is

The tangent at (3,4), (4,-3) to the circle x^(2)+y^(2)=25" are"

Prove that sin^2(18)^@ + cos^2(36)^@ = 3/4

Integrationof rationalfunctions int(dx)/((x+1)(x+2)^(2)(x-3)^(3))

State with reason, "All citizens of india earning more than Rs.10,000/- per month " is set or not ?

If OA = 2hati + 2hatj+ hatk, OB = 2hati + 4hatj + 4hatkand the length of the internal bisector ofangle BOAof triangle AOB is k, then 9k^(2) =

Which of the following are True? (where [.] denotes greatest integer funstion)

If |[[x,2],[18,x]]|=|[[6,2],[18,6]]|, then x is equal to:

A pair of dice is thrown and the random variable X is defined as the sum of numbers that appear on the two dice. Find the mean or expectation of X.

Find the area enclosed between the curves y= |x| and y= x^(2)-2

Find the coordinates of the focus, the axis, the equation of the directrix and the lengths of the latus rectum of the following parabolas i. x^2 = 6y "" ii. x^2 + 16y = 0 iii. y^2 = 10x "" iv. y^2 = -8x.

Construct a 2xx2 matrix, A=[a_(ij)], whose elements are given by: (i) a_(ij)=((i+j)^(2))/(2) (ii) a_(ij)=(i)/(j) (iii) a_(ij)=((i+2j)^(2))/(2)

hati *(hatj xx hatk) +hatj(hatk xx hati) +hatk (hati xx hatj) is :

Differentiate the functions with respect to x in Exerecises 1 to 8. cos x^(3). Sin^(2) (x^5).

Find the eccentricity of the ellipse (i) (x^(2))/(16)+(y^(2))/(9)=1 (ii) (x^(2))/(64)+(y^(2))/(36)=1 (iii)25x^(2)+4y^(2)=100

Differentiate x^(sinx)+(sinx)^(cosx) w.r.t x.

Let P be a point on the parabola, x^2=4y. If the distance of P from the centre of the circle, x^2+y^2+6x+8=0 is minimum, then the equation of the tangent to the parabola at P, is:

If the straightline2x+3y-1=0, x+2y-1=0 and ax+by-1=0 form a triangle with origin as orthocentre, then (a,b) is equal to

If z+1/z=1 and z be any complex number,then the value of z^(99)+(1)/(z^(99)) is

Which of the following is not a negation of the statement p:sqrt(5) is rational ?