28278 + Interview Questions in Maths in Class 12

1.	Method of integration by parts : If int log(x^(2)+x)dx=x log(x^(2)+x)+A then A=.....
Answer» `2x+ln(x+1)+` CONSTANT `2x-ln(x+1)+` constant constant None of these Answer :D

Discussion

2.	If A and B are two events such that P(AuuB)=(5)/(6), P(AnnB)=(1)/(3) and P(A)=(2)/(3) then A and B are
Answer» DEPENDENT events INDEPENDENT events mutually EXCLUSIVE events mutually exclusive and independent events Answer :B

Discussion

3.	If A and B are two events such that P(A uu B)=3//4, P(A nn B)=1//4 , P(A')=2//3 , then P(A' uu B) is
Answer» `5/12` `3/8` `5/8` `1/4` ANSWER :A

Discussion

4.	From a ship at sea it is observed that the angle subtended by feet A and B of two light houses, at the ship is 30^(@). The ship sails 4 km towards A and this angle is then 48^(@), the distance of B from the ship at the second observation is
Answer» 6.460 KM 6.472 km 6.476 km 6.478 km ANSWER :B

Discussion

5.	Evaluate: int_(0)^(1.5)[x^(2)]dx, where [x] is the greatest integor funtion.
Answer» ANSWER :`2-sqrt2`.

Discussion

6.	If A is non-singular matrix of order 3 and \|A\|=4 then \|Adj. (Adj. A)\| =
Answer» 16 4 256 64 Answer :C

Discussion

7.	if f(x)={{:( (a cos x+bx sin x+ce^(x)-2x)/(x^(2)), xne 0),(0, x=0):} is differentiable at x=0, then
Answer» `a+B+C=2` `a+b=-4` `F'(0)=1//3` `a-c=4` ANSWER :B::C

Discussion

8.	Find the principal value of "cosec"^-1(-sqrt2).
Answer» ANSWER :`-pi/4or -45^@`

Discussion

9.	The equation of the normal to the curve x^2=4y at (2,1) is
Answer» (4,4) (1,2) (9,6) (4,5) ANSWER :B

Discussion

10.	Evaluate int(1)/(x^(4)+x^(2)+1)dx
Answer» ANSWER :`I_(11)=(1)/(2)(I_(2)-I_(5))`

Discussion

11.	Evaluate int(1)/(x^(4)-x^(2)+1)dx
Answer» ANSWER :`I_(12)=(1)/(2)(I_(2)-I_(5))`

Discussion

12.	Let A and b be events with P(A) = 1/3, P(A cup B)= 3/4andP(A cap B)= 1/4, Find P(A cap B^c)
Answer» <P> ANSWER :`P(A)=1/3, P(A CUP B)=3/4` and P ` (A CAP B)=1/4` `P(A cup B^c)` `P(A-B)=P(A)-P(A cap B)` `1/3-1/4=(4-3)/12=1/12`

Discussion

13.	N is a five digit number. 1 is written after the 5 digit of N to make it a six digit number, which is three times the same number with 1 written before N. (If N = 23456 it means 234561 and 123456). Then the middle digit of the number N is
Answer» ANSWER :8

Discussion

14.	intP(x)e^(kx)dx=Q(x)e^(4x)+C , where P(x) is polynomial of degree n and Q(x) is: polynomial of degree 7. Then the value of n+7+k+lim_(xrarrinfty)(P(x))/(Q(x)) is :
Answer» ANSWER :22

Discussion

15.	Form the polynomial equation with rational coefficients whose roots are -sqrt(3)+isqrt(2)
Answer» ANSWER :`x^4 -2x^2 +25 =0`

Discussion

16.	A number is chosen at random from the set {1,2,3,4,....,n} . Let E_(1) be the event that the number drawn is divisible by 2 and E_(2) be the event that the number drawn is divisible by 3, then
Answer» `E_(1)` and `E_(2)` are ALWAYS independent `E_(1)` and `E_(2)` are independent if `n=6k(KIN N)` `E_(1)` and `E_(2)` are independent if `n=6k+2(k in N)` `E_(1)` and `E_(2)` are dependent if n = 10 Solution :S = {1, 2, 3, , ...n} `E_(1)=` No. is DIVISIBLEBY 2. `E_(2) ` = No. is divisible by3. If n = 6ksay n = 6 S={ 1, 2, 3, 4, 5, 6 } `P(E_(1))=(3)/(6)=(1)/(2), P(E_(2))=(2)/(6)=(1)/(3)` `P(E_(1) NN E_(2))=(1)/(6)=P(E_(1)).P(E_(2))rArr` (B) is correct. If n = 6k say n = 8 S = { 1, 2, 3, 4, 5, 6, 7, 8 } `P(E_(1))=(4)/(8)=(1)/(2), P(E_(2))=(2)/(8)=(1)/(4)` Here, `P(E_(1) nnE_(2))=(1)/(8)=P(E_(1))P(E_(2))rArr ` (C) is correct. Note that : `P(E_(1)nnE_(2))=(1)/(10)!=P(E_(1)).P(E_(2))` `rArr` Not independent `rArr`dependent.

Discussion

17.	If y=3x is a tangent to a circle with centre (1,1) then the other tangent drawn through (0,0) to the circle is
Answer» `3y=x` `y=-3x` `y=2x` `3y=-2x` ANSWER :A

Discussion

18.	f(x) =([x]+1)/({x}+1) "for"f:[0,(5)/(2)) to ((1)/(2) , 3],where[.]repesents the greatest integerfunction and {.}representsthefractionalpart ofx thenwhichof thefollowingis true ?
Answer» F(X)isinjectivediscontinuousfuntion f(x)f(x) issurjectivenon -differntiable function . ` min( lim_( x to 1^(-))f(x), lim_(x to 1^(+)) f(x))= f(1).` MAX( x valuesof pointofdiscontinuity function . ANSWER :A::B::D

Discussion

19.	3log 2 +(1)/(4) -(1)/(2)((1)/(4))^(2)+(1)/(3)((1)/(4))^(3)-….. =
Answer» log3 log5 LOG 10 log 2 ANSWER :C

Discussion

20.	Definea functions. Whatdo you meanby thedomainand rangeof afunction ? Giveexamples.
Answer»

Discussion

21.	Find the equation of the line through the points (-1, -2, 1) and (1, 2, 5).
Answer» ANSWER :The direction ratios of the TWO lines are 2-4, 3-7, 4-8 i.e., -2, -4, -4 and 1+1, 2+2, 5-1 i.e., 2, 4, 4 respectively. Two lines are PARALLEL if their direction ratios are proportional Since `(-2)/2-(-4)/4=(-4)/4`, the two linesa are parallel.

Discussion

22.	If the angle between the planes barr.(xhati+hatj-hatk)=4" and "barr.(hati+xhatj+hatk)= -1 is (pi)/(3), then the value of x is
Answer» 2 0 -2 4 Answer :A

Discussion

23.	A ,B ,C are there routes from the house to the office. On any day, the route slected by the officier is independent of the climate. On a rainy day, the probabilities of reaching the office late. Thorugh these routes are , 1/125 , 1/10 , 1/4 respectively . If a rainy day, the officer is late to the office then the probability that the routes to be B is
Answer» `5//6` `7//40` 29/40 `10//39` ANSWER :D

Discussion

24.	If sum of the series (1)/(x+1)+(1)/(x(x+2))+(1)/(x(x+1)(x+3))+...+(1)/(x(x+1)...(x+99)(x+100))+(1)/(x(x+1)(x+2)...(x+100)(x+101)) is (2)/(3), then x is equal to
Answer» ANSWER :1.5

Discussion

25.	Consider a hyperbola xy = 4 and a line y = 2x = 4. O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B. Let the given line intersects the x-axis at R. if a line through R. intersect the hyperbolas at S and T, then minimum value of RS xx RT is
Answer» 2 4 6 8 Solution :Let `(2t,2//t)` be a point on the hyperbola. Equation of the tangent at this point `x + YT^(2) = 4t`. `:. A = (4t,0),B = (0,4//t)` Locus of circumcentre of triangle is `xy = 16` Its eccentricity is `sqrt(2)` SHORTEST distance exist along the common NORMAL. `:. t^(2) = 1//2` or `t = 1//sqrt(2)` `:.` Foot of the perpendicular is `C (sqrt(2),2sqrt(2))` `:.` Shortest distance is distance of C from the given line which is `(4(sqrt(2)-1))/(sqrt(5))` Given line intersect the x-axis at `R(2,0)` Any point on this line at distance 'r' from R is `(2+r cos theta, r SIN theta)` If this point lies on hyperbola, then we have `(2+r cos theta) (r sin theta) =4` Product of roots of above quadratie in 'r' is `r_(1)r_(2) = 8//\|sin 2 theta\|`, which has minimum value 8 `:.` Minimum value of `RS xx RT` is 8

Discussion

26.	Consider a hyperbola xy = 4 and a line y = 2x = 4. O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B. Shortest distance between the line and hyperbola is
Answer» `(8sqrt(2))/(sqrt(5))` `(4(sqrt(2)-1))/(sqrt(5))` `(2sqrt(2))/(sqrt(5))` `(4(sqrt(2)-1))/(sqrt(5))` SOLUTION :Let `(2t,2//t)` be a point on the hyperbola. Equation of the TANGENT at this point `x + yt^(2) = 4T`. `:. A = (4t,0),B = (0,4//t)` Locus of circumcentre of TRIANGLE is `xy = 16` Its eccentricity is `sqrt(2)` Shortest distance exist along the common normal. `:. t^(2) = 1//2` or `t = 1//sqrt(2)` `:.` Foot of the perpendicular is `C (sqrt(2),2sqrt(2))` `:.` Shortest distance is distance of C from the given line which is `(4(sqrt(2)-1))/(sqrt(5))` Given line intersect the x-axis at `R(2,0)` Any point on this line at distance 'r' from R is `(2+r cos theta, r sin theta)` If this point lies on hyperbola, then we have `(2+r cos theta) (r sin theta) =4` Product of roots of above quadratie in 'r' is `r_(1)r_(2) = 8//\|sin 2 theta\|`, which has minimum value 8 `:.` Minimum value of `RS xx RT` is 8

Discussion

27.	Consider a chessboard of size 8 units xx8 units (i.e., each small square on the board has a side length of 1 unit). Let S be the set of all the 81 vertices of all the squares on the board. What is number of line segments whose vertices are in S_(1) and whose length is a positive integer? (The segments need not be parallel to the sides of the board).
Answer» ANSWER :780

Discussion

28.	Consider a hyperbola xy = 4 and a line y = 2x = 4. O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B. Locus of circumcentre of triangle OAB is
Answer» an ELLIPSE with eccentricity `(1)/(sqrt(2))` an ellipse with eccentricity `(1)/(sqrt(3))` a hyperbola with eccnetricity `sqrt(2)` a circle Solution :Let `(2t,2//t)` be a point on the hyperbola. Equation of the tangent at this point `x + yt^(2) = 4t`. `:. A = (4t,0),B = (0,4//t)` Locus of circumcentre of triangle is `xy = 16` Its eccentricity is `sqrt(2)` Shortest distance exist along the common normal. `:. t^(2) = 1//2` or `t = 1//sqrt(2)` `:.` Foot of the perpendicular is `C (sqrt(2),2sqrt(2))` `:.` Shortest distance is distance of C from the given LINE which is `(4(sqrt(2)-1))/(sqrt(5))` Given line intersect the x-axis at `R(2,0)` Any point on this line at distance 'r' from R is `(2+r cos theta, r sin theta)` If this point LIES on hyperbola, then we have `(2+r cos theta) (r sin theta) =4` Product of roots of above quadratie in 'r' is `r_(1)r_(2) = 8//\|sin 2 theta\|`, which has minimum value 8 `:.` Minimum value of `RS XX RT` is 8

Discussion

29.	You are given n ( ge 3)circles having different radical axes and radical centres. The value of 'n' for which the number of radical axes is equal to the number of radical centres is
Answer» 3 4 5 8 Answer :C

Discussion

30.	i) Find the two consecutive positive even integers, the sum of whose square is 340. ii) Prove that there is a unique pair of consecutive odd positive integers such that sum of their squares is 290 find them. iii) Find all the numbers which exceeds their square root by 12. iv) Find the quadratic equation for which sum of the roots is 1 and sum of the squares of the roots is 13.
Answer» Answer :i) 12, 14 ii) 11, 13 III) 16 IV) `x^(2)-x-6=0`

Discussion

31.	iff(x)={{:( x-1, xlt 0),( x^(2)- 2x , x ge 0):} , then
Answer» F(\|X\|) is discontinuousat x=0 f(x) \| isdiffererntiavbleatx=0 \|f(x)\| is NON- differentiableat=0,2 \|f(x)\| iscomtinuous at x=0 ANSWER :C

Discussion

32.	A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain atleast 8 units of vitamin A and 10 units of vitamin C. Food I' contains 2 units/kg of vitamin A and I unit/kg of vitamin C. Food 'Il' contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs Rs 50 per kg to purchase food T and Rs 70 per kg to purchase food I'. Formulate this problem as a linear programming problem to minimise the cost of such a mixture.
Answer» ANSWER :RS. 380

Discussion

33.	A letter is known to have come either from 'TATANAGAR' or 'CALCUTTA'. On the envelope just two consecutive letters 'TA' are visible. Find the probability that letter has come from CALCUTTA.
Answer» ANSWER :`(4)/(11)`

Discussion

34.	The number of ways in which an examiner can assign 30 marks to 8 question, giving no less than 2 marks to any questions is
Answer» `""^(21)C_(7)` `""^(21)C_(8)` `""^(21)C_(7)` `""^(30)C_(8)` ANSWER :C

Discussion

35.	Let f(x) = sin(ln x) AA x gt 0. Suppose f(e^(kpix)) = f(x) AA x gt 0, then least value of k =……………….
Answer» ANSWER :2

Discussion

36.	Let S= overset(oo)underset(r=1)Sigma (r )/(r^(4)+4), then 2S=
Answer» ANSWER :0.75

Discussion

37.	If int cos xcdot cos 2 x cdot cos 5 x dx =A sin 2 x + B sin 4 x + C sin 6x + D sin 8 x + k (where k is the arbitrary constant of integration), then 1/B + 1/C =
Answer» `1/A - 1/D` `1/A+1/D` 1 0 Answer :B

Discussion

38.	Let two circles S_1=0 and S_2=0 intersect at point A and B . L_1=0 is the line joining A and B where S_1=x^2+y^2+2ax+2by-5=0 and S_2=x^2+y^2+2x+4y-4=0 Let AB subtend and angle theta at (0,0) and angle subtended by S_1=0 and S_2=0at P(3,4) is alpha and beta respectively. If alpha=60^@,then (a,b) lies on a circle whose radius is
Answer» `sqrt10/3` `(4sqrt10)/3` `(2sqrt10)/3` NONE of these ANSWER :C

Discussion

39.	Area of a rectangle having vertices A(-hat(i)+(1)/(2)hat(j)+4hat(k)), B(hat(i)+(1)/(2)hat(j)+4hat(k)), C(hat(i)-(1)/(2)hat(j)+4hat(k)), and D(-hat(i)-(1)/(2)hat(j)+4hat(k)) is
Answer» `(1)/(2)` 1 2 4 Answer :C

Discussion

40.	Area bounded by the curve y=x^(3), the x-axis and the ordinates x = -2 and x = 1 is
Answer» -9 `-15/4` `15/4` `17/4` ANSWER :D

Discussion

41.	A faircoin is tossed until one of the 2 sides occurs twice is row. Probability that even number of tosses required is.
Answer» <P>`1/3` `2/3` `1/2` `3/4` SOLUTION :A={HH, HTHH, HTHTHH,…} B={TT, THTT, THTHTT,…} P(A) = P(B) = `1/4 + 1/16 + …………. " to" propto =1/3` `P(A cup B) = 1/3 + 1/3 = 2/3`

Discussion

42.	(i) Determine whether f(x)=(2x+3)/4 for f:RtoR is invertible or notIf so find it. (ii) Let f(x)=x^(2)+2x,xge-1 . Draw graph of f^(-1)(x) also find the number of solutions of the equation f(x)=f^(-1)(x) (iii) If y=f(x)=x^(2)-3x+2,xle1.Find the value of g'(2) where g is inverse of f
Answer» Solution :(i) GIVEN functionsis one -one and otno, therefore it is INVERTIBLE, `y=(2x+3)/4impliesx+(4y-3)/2:.f^(-1)(x)=(4x-3)/2` (ii) `f(x)=f^(-1)(x)` is equivalent to `f(x)=ximpliesx^(2)+2x=ximpliesx(x+1)=0impliesx=0,-1` HENCE two solution for `f(x)=f^(-1)(x)` (iii) `f(x)=x^(2)-3x+2,xle1` `FG(x)=g(x)^(2)-3g(x)+2` `implies2=g(2)^(2)-3g(2)+2` `impliesg(2)=0,3le1` so `g(2)=0` `f'(x)=2x-3` `fg(x)=ximpliesf'(g(x)).g'(x)=1impliesg'(2)=1/(f'(g(2)))=1/(f'(0))=-1/3`

Discussion

43.	Findthetransformedequationwhose roots arethe negativesof therootsof theequation x^4 +5x^3 +11 x+3=0
Answer» ANSWER :`x^4-5x^3-11x +3=0`

Discussion

44.	Evalute the following integrals int (x^(2))/(x^(4) -x^(2) + 1) dx
Answer» Answer :`I_(9) = (1)/(2) (I_(3) + I_(6))`

Discussion

45.	Evalute the following integrals int (x^(2))/(x^(4)+ x^(2) + 1) dx
Answer» ANSWER :`I_(8) = (1)/(2) (I_(2) + I_(5)) `

Discussion

46.	If A =({:(1,-1,1),(2,-1,0),(1,0,0):}) find A^(3), Hence find A^(-1)Use it to solve the following system of linear equation x-y +z=1 ,2x -y=0 , x-4 =0
Answer» ANSWER :` A^(3)= [{:( 1,0,0),(0,1,0),(0,0,1):}],A^(-1)= [(0,0,1),(0,-1,2),(1,-1,1):}]`

Discussion

47.	Column II : Contains gereral solution. Column III : Number of solution [0, pi] Whichof the following optionis the onlyCORRECT combination
Answer» (III)(II)(P) (IV)(ii)(P ) (II)(iv)(R ) (I)(iii)(R ) ANSWER :b

Discussion

48.	Column II : Contains gereral solution. Column III : Number of solution [0, pi] Whichof the followingoptions is the only CORRECT combination
Answer» <P>(II) (ii)(P) (II)(i)(P) (I)(i)(R ) (I)(III)(S) ANSWER :d

Discussion

49.	Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(pi/2)\|sinx-cosx\|dx=.........
Answer» 0 `2sqrt2-1` `sqrt2-1` `2(sqrt2+1)` ANSWER :B

Discussion

50.	Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x^(2)+y^(2)=32.
Answer» ANSWER :8

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Method of integration by parts : If int log(x^(2)+x)dx=x log(x^(2)+x)+A then A=.....

If A and B are two events such that P(AuuB)=(5)/(6), P(AnnB)=(1)/(3) and P(A)=(2)/(3) then A and B are

If A and B are two events such that P(A uu B)=3//4, P(A nn B)=1//4 , P(A')=2//3 , then P(A' uu B) is

From a ship at sea it is observed that the angle subtended by feet A and B of two light houses, at the ship is 30^(@). The ship sails 4 km towards A and this angle is then 48^(@), the distance of B from the ship at the second observation is

Evaluate: int_(0)^(1.5)[x^(2)]dx, where [x] is the greatest integor funtion.

If A is non-singular matrix of order 3 and |A|=4 then |Adj. (Adj. A)| =

if f(x)={{:( (a cos x+bx sin x+ce^(x)-2x)/(x^(2)), xne 0),(0, x=0):} is differentiable at x=0, then

Find the principal value of "cosec"^-1(-sqrt2).

The equation of the normal to the curve x^2=4y at (2,1) is

Evaluate int(1)/(x^(4)+x^(2)+1)dx

Evaluate int(1)/(x^(4)-x^(2)+1)dx

Let A and b be events with P(A) = 1/3, P(A cup B)= 3/4andP(A cap B)= 1/4, Find P(A cap B^c)

N is a five digit number. 1 is written after the 5 digit of N to make it a six digit number, which is three times the same number with 1 written before N. (If N = 23456 it means 234561 and 123456). Then the middle digit of the number N is

intP(x)e^(kx)dx=Q(x)e^(4x)+C , where P(x) is polynomial of degree n and Q(x) is: polynomial of degree 7. Then the value of n+7+k+lim_(xrarrinfty)(P(x))/(Q(x)) is :

Form the polynomial equation with rational coefficients whose roots are -sqrt(3)+isqrt(2)

A number is chosen at random from the set {1,2,3,4,....,n} . Let E_(1) be the event that the number drawn is divisible by 2 and E_(2) be the event that the number drawn is divisible by 3, then

If y=3x is a tangent to a circle with centre (1,1) then the other tangent drawn through (0,0) to the circle is

f(x) =([x]+1)/({x}+1) "for"f:[0,(5)/(2)) to ((1)/(2) , 3],where[.]repesents the greatest integerfunction and {.}representsthefractionalpart ofx thenwhichof thefollowingis true ?

3log 2 +(1)/(4) -(1)/(2)((1)/(4))^(2)+(1)/(3)((1)/(4))^(3)-….. =

Definea functions. Whatdo you meanby thedomainand rangeof afunction ? Giveexamples.

Find the equation of the line through the points (-1, -2, 1) and (1, 2, 5).

If the angle between the planes barr.(xhati+hatj-hatk)=4" and "barr.(hati+xhatj+hatk)= -1 is (pi)/(3), then the value of x is

If sum of the series (1)/(x+1)+(1)/(x(x+2))+(1)/(x(x+1)(x+3))+...+(1)/(x(x+1)...(x+99)(x+100))+(1)/(x(x+1)(x+2)...(x+100)(x+101)) is (2)/(3), then x is equal to

Consider a hyperbola xy = 4 and a line y = 2x = 4. O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B. Let the given line intersects the x-axis at R. if a line through R. intersect the hyperbolas at S and T, then minimum value of RS xx RT is

Consider a hyperbola xy = 4 and a line y = 2x = 4. O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B. Shortest distance between the line and hyperbola is

Consider a hyperbola xy = 4 and a line y = 2x = 4. O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B. Locus of circumcentre of triangle OAB is

You are given n ( ge 3)circles having different radical axes and radical centres. The value of 'n' for which the number of radical axes is equal to the number of radical centres is

iff(x)={{:( x-1, xlt 0),( x^(2)- 2x , x ge 0):} , then

A letter is known to have come either from 'TATANAGAR' or 'CALCUTTA'. On the envelope just two consecutive letters 'TA' are visible. Find the probability that letter has come from CALCUTTA.

The number of ways in which an examiner can assign 30 marks to 8 question, giving no less than 2 marks to any questions is

Let f(x) = sin(ln x) AA x gt 0. Suppose f(e^(kpix)) = f(x) AA x gt 0, then least value of k =……………….

Let S= overset(oo)underset(r=1)Sigma (r )/(r^(4)+4), then 2S=

If int cos xcdot cos 2 x cdot cos 5 x dx =A sin 2 x + B sin 4 x + C sin 6x + D sin 8 x + k (where k is the arbitrary constant of integration), then 1/B + 1/C =

Area of a rectangle having vertices A(-hat(i)+(1)/(2)hat(j)+4hat(k)), B(hat(i)+(1)/(2)hat(j)+4hat(k)), C(hat(i)-(1)/(2)hat(j)+4hat(k)), and D(-hat(i)-(1)/(2)hat(j)+4hat(k)) is

Area bounded by the curve y=x^(3), the x-axis and the ordinates x = -2 and x = 1 is

A faircoin is tossed until one of the 2 sides occurs twice is row. Probability that even number of tosses required is.

(i) Determine whether f(x)=(2x+3)/4 for f:RtoR is invertible or notIf so find it. (ii) Let f(x)=x^(2)+2x,xge-1 . Draw graph of f^(-1)(x) also find the number of solutions of the equation f(x)=f^(-1)(x) (iii) If y=f(x)=x^(2)-3x+2,xle1.Find the value of g'(2) where g is inverse of f

Findthetransformedequationwhose roots arethe negativesof therootsof theequation x^4 +5x^3 +11 x+3=0

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

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

If A =({:(1,-1,1),(2,-1,0),(1,0,0):}) find A^(3), Hence find A^(-1)Use it to solve the following system of linear equation x-y +z=1 ,2x -y=0 , x-4 =0

Column II : Contains gereral solution. Column III : Number of solution [0, pi] Whichof the following optionis the onlyCORRECT combination

Column II : Contains gereral solution. Column III : Number of solution [0, pi] Whichof the followingoptions is the only CORRECT combination

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(pi/2)|sinx-cosx|dx=.........

Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x^(2)+y^(2)=32.