28278 + Interview Questions in Maths in Class 12 Page 112 InterviewSolution

5551.	(a) Show that for every nutural number n relatively prime to 10, there is another natural number m all of whose digits are 1 's such that n divides m. (b) Hence or otherwise show that every positive rational number can be expressed in the form (a)/(10^(b)(10^(c)-1)) for some natural a, b, c.
Answer» Solution :(a) Divide the n+1 number 1, 11, 111, ....,111,....1 (All having only 1 as digits ) by n. Among the n+1 remainders so obtained, two must be equal as the possibilities for remainders are 0, 1, 2,....., n-1 which are n in number. Thus there must be two number x=11.... and y=11.....1 having say j digits and k digits respectively which LEAVE the same remainders after DIVISION by n. We may take `j lt k`. Now we see that y-x is divisible by n. But y-x = 11....100 ... 0 where there are k - j number of 1's and remaining zeros. Since n is COPRIME to 10, we see that n divides m=11 ... 1, a number having only 1's as its digits. (b) If p/q is any rational number `(p gt 0, q gt0)`, then we may write `q=2^(r)5^(s)t`, where t is coprime to 10. Choose a number m having only 1's as its digits and is divisible by t. Consider 9m, Which has only 9 as its digits and is still divisible by t. Let k=9 m/t. We see that, `qk=9m2^(r)5^(s)=(10^(@)-1)2^(r)5^(s)`, where c is the number of digits in m. Hence we can find d such that `qd=10^(b)(10^(c)-1)` multiply by a suitable power of 2 if `s gt r` and by a suitable power of 5 if `r gt s`). Then `(p)/(q)=(pq)/(qd)=(a)/(a0^(b)(10^(c)-1))` where a=pd.

Discussion

5552.	Find the transpose of each of each of the following matrics: [[1,2],[-1,3]]
Answer» SOLUTION :`[[1,2], [-2,3]]`

Discussion

5553.	If I_(n) = int (log x)^(n) dx then I_(6)+ 6I_(5) =
Answer» `X(logx)^(5) + c` `- x(LOG x)^(5)+ c` `x (log x)^(6) + c` `- x(log x)^(6)+ c` ANSWER :C

Discussion

5554.	Vertex is (4, 3) and diretctrix is 3x+2y-7=0 then equation of latusrectum is
Answer» 3x+2y-18 =0 3x+2y-29 = 0 3x+2y-8 = 0 3x+2y-31 =0 Answer :B

Discussion

5555.	Let K is a positive Integer such that 36 +K , 300 + K , 596 + K are the squares of teree consecutive terms of an arithmetic progression. Find K.
Answer» ANSWER :925

Discussion

5556.	A species has an initial population 4^(10). At the end of first day, the population increases by 50%. At the end of second day, it decreases by the same percentage. Days for the population to reach 3^(10) is
Answer» 10 20 50 100 Answer :B

Discussion

5557.	Discuss the continuity of the function f, where f is defined by f(x)={{:(2x," if "x lt 0),(0," if "0 le x le 1),(4x," if "x gt 1):}.
Answer» ANSWER :x=1 is the only POINT of DISCONTINUITY.

Discussion

5558.	Let A={1,2,3} and Let R={(1,1),(2,2),(3,3),(1,3),(3,2),(1,2)} then R is
Answer» REFLEXIVE and SYMMETRIC but TRANSITIVE Reflexive and transitive but not symmetric symmetric and transitive but not reflexive An EQUIVALENCE relation Answer :B

Discussion

5559.	Consider the equation E_(1):vecr xx (2hati-hatj+3hatk)=3hati+hatk and E_(2): vecr xx (hati+2hatj-3hatk)=2hati-hatj, hten
Answer» `E_(1)` represents a line `E_(1)` represents two parallel LINES `E_(2)` represents a line `E_(2)` represents two parallelplanes Solution :`E_(1): vecr xx (2hati-HATJ+3hatk)=3hati+hatk` `rArr 3hati(3y+z)-hatj(3x-2z)+hatk(-x-2y)=3hati+hatk` `therefore 3y+z=3, 3x-2y=0, -x-2y=1` From first two EQUATIONS, `3x-2(3-3y)=0` `rArr 3x+6y=6 rArr x+2y=2` Now, `x+2y=-1, x+2y=2` are parallel planes. `E_(2): vecr xx (hati+2hatj-3hatk)=2hati-hatj` `rArr hati(-3y-2z)-hatj(-3x-z)+hatk(2x-y)=2hati-hatj` `therefore hati(-3y-2z)-hatj(-3x-z)+hatk(2x-y)=2hati-hatj` `therefore -3y-2z=2, 3x+z=-1, 2x-y=0` i.e., `-6x-2z=2, 3x+z=-1` `therefore` Straight line, `2x-y=0, 3x+z=-1`

Discussion

5560.	If a 679b is a five digit number that is divisible by 72, then a+b is equal to
Answer» ANSWER :C

Discussion

5561.	There are 5 copies each of 4 different books. Find the number of ways of arranging these books in a shelf.
Answer» ANSWER :`(LFLOOR20)/((lfloor5)^4)`

Discussion

5562.	Let A and B be two sub-sets of R x R, defined as follows: A = {(a,b) : a,b in R " and " tan^(-1)a + cot^(-1)b = pi/2} and B={(a,b) : a,b in R " and " sin^(2) a + cos^(2)b =1}, then
Answer» `A CAP B = {{a,a) : a in R}` `A cap B = phi` `A CUP B = R xx R` `A cup B = {(a,a), a in R}` ANSWER :A

Discussion

5563.	If for a Binomial distribution, mu=10 and sigma^(2)=5, then find P(X gt 6).
Answer» Answer :`(1)/(20^(20))sum_(r = 7)^(20)""^(20)C_(r)`

Discussion

5564.	S and S^(1) foci of an ellipse. B is one end of the minor axis. If I.SBS^(1) is a right angled isoscles triangle, then e =
Answer» PARALLELGRAM RHOMBUS square rectangle Answer :C

Discussion

5565.	The partial fractions of (x^(2)+1)/(x(x^(2)-1)) are
Answer» `(1)/(X)-(1)/(x+1)+(1)/(x-1)` `-(1)/(x)+(1)/(x+1)+(1)/(x-1)` `1/x - (1)/(x+1)+(1)/(x-1)` `1/x + (1)/(x+1)-(1)/(x-1)` ANSWER :B

Discussion

5566.	Find the static moment of the upper portion of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2))=1 about the x-axis.
Answer» ANSWER :1

Discussion

5567.	MatricesA and B are givenbelow.FindA+B,B+A,A-BandB -A Verify that A+B=B+A and B-A=-(A-B).A=[{:(7),(1):}]B=[{:(-6),(9):}]
Answer» SOLUTION :`A+B =[[1],[10]],B+A=[[1],[10]]` `A-B=[[13],[-8]],B-A=[[-13],[8]]` `:. A+B=B+A "and" B-A =-(A-B)`

Discussion

5568.	n is a natural number. It is given that (n +20) + (n +21) + ......+ (n + 100) is a perfect square. Then the least value of n is "___________"
Answer» ANSWER :4

Discussion

5569.	Find the eccentricity, foci, length of latusrectum and the equations to thedirectrices of the hyperbola(x^(2))/(16)-(y^(2))/(9) = 1
Answer» Answer :`E=(sqrt(7))/(4)` foci, `(+- 2,sqrt(3))`,length of LATUS RECTUM =9 EQUATION of directrix `x sqrt(7)+32=0`

Discussion

5570.	Find the eccentricity, co ordinates of foci-length of latus rectum and equation of directrices of the folloeing ellipses. 9x^2+16y^2-36x+32y-92=0
Answer» Answer :`e=(SQRT(7))/(4)` foci `(2+- sqrt(7)-1)`, Length of latus RECTUM =9/2. , Equation to DIRECTION `sqrt(7)=2 sqrt(7)+-16`

Discussion

5571.	If Lim_(xto oo) "sin"((pi(1-cos^(m)x))/(x^(n))) exists and non-zero where m,n in N then
Answer» m=1 , n=1 m=1 , n=2 m=2 , n=2 m=3 , n=2 Solution :When m=1, n=1 `UNDERSET(NTO oo)Lim"SIN"((pi(1-cosx))/(x))=sin0=0` When m=1 , n=2 `underset(nto oo)Lim"sin"((pi(1-cosx))/(x^(2)))=sin(pi//2)=1` When m=n=2 `underset(nto oo)Lim"sin"((pi(1-cos^(2)x))/(x^(2)))=underset(nto oo)Lim"sin"((pi(1-cosx)(1+cosx))/(x^(2)))=sin(pi)=0` When m=3 , n=2 `underset(nto oo)Lim"sin"((pi(1-cos^(3)x))/(x^(2)))=underset(nto oo)Lim"sin"((pi(1-cosx)(1+cos^(2)x+cosx))/(x^(2)))=sin((3PI)/(2))=-1`

Discussion

5572.	Find the equation of the circle with centre C and redius r where. C = (a,-b),r=a+b
Answer» ANSWER :`X ^(2) + y^(2) -2ax +2by-2ab =0 `

Discussion

5573.	Letf (x)=[x]andg (x )=\|x\| ,AAxin Rthen valueofgof (( - 5 ) /(3))+fog((- 5)/(3))isequal to:( wheref _0 g (x)=f (g (x))).
Answer» ` 1 ` ` - 1 ` ` - 2 ` ` 3 ` SOLUTION :`f(X) = [x], g (x) = \|X\|` `g(f(x)) + f(g(x))` `= \|[x]\| + \|[x]\|` `= \|[(-5)/(3)]\| + [\|(-5)/(3)\|]` ` = \|-2\| + [(5)/(3)] = 2 + 1 = 3`

Discussion

5574.	An equilateral triangle is of side 10 units. In measuring the side, an error of 0.05 units is made. Then the percentage error in the area of the triangle is
Answer» 5 4 1 0.5 Answer :C

Discussion

5575.	Sum of solution of the equation \|{:(1,2,x),(2,3,x^2),(3,5,2):}\|=10is :
Answer» 1 `-1` 2 4 Answer :B

Discussion

5576.	If f(x) =[\|x\|]where[.]denotesthegreatestintergerfunction , then whichof thefollowingis not true?
Answer» f(X)is continuous`AA x in R` f(x)is continuousfromrightand discontinuousfromleft `AA s in N` f(x) is conttinuousfromrightleftanddiscontinuous from RIGHT`AA x in I` f(X)is continuousat x=0 Answer :B::D

Discussion

5577.	Choose the correct answer. Let veca"and"vecb be two unit vectors and theta be the angle between them.Thenveca+vecb is a unit vector,if:a)theta=pi/4b)theta=pi/3c)theta=pi/2d)theta=(2pi)/3
Answer» `THETA=pi/4` `theta=pi/3` `theta=pi/2` `theta=(2PI)/3` ANSWER :D

Discussion

5578.	If f(x)=\|cosx-sinx\|," then "f^(1)(pi/6) is equal to
Answer» 1)`-1/2(1+sqrt3)` 2)`1/2(1+sqrt3)` 3)`-1/2(1-sqrt3)` 4)`1/2(1-sqrt3)` ANSWER :A

Discussion

5579.	By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(2log sin x - log sin 2x)dx
Answer» ANSWER :`pi/2log1/2`

Discussion

5580.	If order of matrix A is 2X3 and order of matrix B is 3X5 then order of matrix B'A' is :
Answer» 5X2 2X5 5X3 3X2 Answer :A

Discussion

5581.	Find the values of a,b if ax^(2) + bxy+ 3y^(2) -5x +2y -3 = 0represents a circle . Also find the radius and centre of the circle .
Answer» Answer :a=3,b =0 radius = ` (SQRT(65))/( 6), ( ( 5)/(6), (-1)/(3)) `

Discussion

5582.	Find the sum of the infinite series (7)/(5)(1+(1)/(10^(2))+(1.3)/(1.2).(1)/(10^(4))+(1.3.5)/(1.2.3).(1)/(10^(6))+....)
Answer» SOLUTION :N/A

Discussion

5583.	Which of the following statement(s) is//are correct
Answer» Mass of one ca atom is `6.64xx10^(-23) g` Volume of 18 g `H_(2)O` at 1 atm pressure and 273 K temperature is 22.4 L Number of oxygen atoms in `C_(4)H_(6)O_(2)` sample is 2, if this sample has 6 g atom hydrogen ANSWER :A

Discussion

5584.	If the points with position vectors 10hati+3hatj, 12hati-5hatj and ahati+11hatj are collinear, find the value of a.
Answer» SOLUTION :LET the points are A,B and C. As A,B and C are co-llinear. We have `VEC(AB)` = `vec(AC)` `vec(AB)` = `lambdavec(AC)` `IMPLIES (12i-5j)-(10i+3) = `lambda[(ai+11j)-(10i+3j)]` `implies` 2i-8j = `(a-10)lambdai+8lambdaj` Comparing the components we have `8lambda`= -8 `implies lambda` = -1(a-10)(-1) = 2 `implies` -a+10 = 2 `implies` a= 8.

Discussion

5585.	Find the equation of all lines having slope 2 which are tangents to the curve y=(1)/(x-3) , x ne 3 .
Answer» ANSWER :No TANGENT to the CURVE which has SLOPE 2.

Discussion

5586.	The value of int_(0)^(1) (xdx)/( (x^(2) +1)^(2) ) is
Answer» `1/2` `1` `1/3` `1/4` ANSWER :D

Discussion

5587.	Let f(x)=\|{:(,1//x,logx,x^(n)),(,1,-1//n,(-1)^(n)),(,1,a,a^(2)):}\| where ("where"f^(n)(x) "donotes "n^(th)derivative of f(x).
Answer» `F^(N)(1)"is indepent of a"` `f^(n)(1)"is indepent of n"` `f^(n)(1)"is indepent a of n"` `y=a(x-f^(n)(1))` represent a straight LINE through the origin Answer :A::B::D

Discussion

5588.	The number of ways that 3 English, 3 Hindi & 3 Telugu books can be chosen from a shelf containing 5 English, 4 Hindi and 3 Telugu books is
Answer» 10 20 40 60 Answer :C

Discussion

5589.	Two this slabs ................
Answer» SOLUTION : From the given vectors for the direction of LIGHT RAYS we can use For the first medium `SIN theta_(1)=a/SQRT(a^(2)+b^(2))` and for the second medium `sin theta_(2)= c/sqrt(c^(2)+d^(2))` By snell's law, we have `mu_(1) sin theta_(1) = mu_(2) sin theta_(2)` `implies (mu_(1) a)/sqrt(a^(2)+b^(2))=(mu_(2) c)/sqrt(c^(2)+d^(2))`.

Discussion

5590.	Letf(x): R to Rb " and "g (x)=x-7, x in R". Find"(f o g) (7)
Answer» SOLUTION :(fog )(7) =f{G(7)}=f(7-7) =f(0) =(0+7)=7

Discussion

5591.	vec(u),vec(v) and vec(w) are not co-planar vectors and p and q are real numbers. If [3vec(u),p vec(v),p vec(w)]-[p vec(v),vec(w),q vec(u)]-[2vec(w),q vec(v),q vec(u)]=0 then ……………
Answer» (p, q) has only TWO VALUES. (p, q) has more than two values. But not all the values. (p . q) has all the values. `(p.q)` has only ONE VALUE. ANSWER :B

Discussion

5592.	The maximum value of \|3z + 9 - 7i\| if \|z + 2- i\| = 5 is
Answer» 10 15 20 5 Answer :C

Discussion

5593.	x^2+y^2+2lambdax+5=0 and x^2+y^2+2lambday+5=0 are two circles. P is a point on the line x-y=0. If PA and PB are the lengths of the tangents from P to the two cricles and PA=3, thenPB=
Answer» 1 3 8 5 Answer :B

Discussion

5594.	Let f (x) be a function which satisfy the equatio f (xy) = f9x) + f(y) for all x gt 0, y gt 0 such that f '(1) =2. Let A be the area of the region bounded by the curves y =f (x), y = \|x ^(3) -6x ^(2)+11 x-6\| and x=0, then find value of(28)/(17)A.
Answer» ANSWER :7

Discussion

5595.	The locus of z satisfying the \|(x+2i)/(2z+i)\| lt 1, inequality where z=x+iy, is
Answer» `x^(2)+y^(2) LT 1` `x^(2)-y^(2) lt 1` `x^(2)+y^(2) GT 1` `2X^(2)+3Y^(2) lt 1`

Discussion

5596.	f(x) and g(x)are polynomicalof degree 2 such that \|int_(a_(1))^(a_(2))(f(x) - 1)dx\|=\|int_(b_(1))^(b_(2))(g(x)-1)dx\| where a_(1), a_(2)(a_(2) gt a_(1)) are rootsof equation f(x) = 1 and b_(1), b_(2)(b_(2) gt b_(1)) are roots of equation g(x) = 1. If f"(x) and g"(x) are positive constant and \|int_(a_(1))^(a_(2))f((x))dx\|=(a_(2)-a_(1))-\|int_(b_(1))^(b_(2))(f(x)-1)dx\| but \|int_(b_(1))^(b_(2))(g(x))dx\|ne(b_(2) -b_(1))-\|int_(b_(1))^(b_(2))(g(x)-1)dx\|then
Answer» `\|f"(X)\|lt \|G"(x)\|` `\|f"(x)\|gt\|g"(x)\|` `a_(2)-a_(1)gt b_(2) - b_(1)` `a_(2) - a_(1) gt b_(2) - b_(1)` Solution :N//A

Discussion

5597.	Suppose A and B are events with P(A)=0.5, P(B)=0.4 and P(AcapB)=0.3. Find the probability that i) A does not occur, ii) neither A nor B occurs.
Answer» ANSWER :0.5 ; 0.4

Discussion

5598.	Let f and g be increasing and decreasing functions respectively from [0,oo) to [0, oo), Let h(x)=f(g(x)). If h(0)=0, then h(x)-h(1) is :
Answer» LESS than - H(1) ALWAYS +ve always -ve STRICTLY increasing. Answer :A

Discussion

5599.	f:NxxNrarrN , f("(m,n)")=m+n . If f one one and onto ?
Answer» SOLUTION :N/A

Discussion

5600.	Each of graph drawn has same initial and final of velocity over same time interval :- Which of the following statements is TRUE ?
Answer» Average VELOCITY is same for all the particle Average ACCELERATION is same for all the particles Displacement is same for all particles DISTANCE travelled is same for all particles

Discussion

Explore topic-wise InterviewSolutions in .

(a) Show that for every nutural number n relatively prime to 10, there is another natural number m all of whose digits are 1 's such that n divides m. (b) Hence or otherwise show that every positive rational number can be expressed in the form (a)/(10^(b)(10^(c)-1)) for some natural a, b, c.

Find the transpose of each of each of the following matrics: [[1,2],[-1,3]]

If I_(n) = int (log x)^(n) dx then I_(6)+ 6I_(5) =

Vertex is (4, 3) and diretctrix is 3x+2y-7=0 then equation of latusrectum is

Let K is a positive Integer such that 36 +K , 300 + K , 596 + K are the squares of teree consecutive terms of an arithmetic progression. Find K.

A species has an initial population 4^(10). At the end of first day, the population increases by 50%. At the end of second day, it decreases by the same percentage. Days for the population to reach 3^(10) is

Discuss the continuity of the function f, where f is defined by f(x)={{:(2x," if "x lt 0),(0," if "0 le x le 1),(4x," if "x gt 1):}.

Let A={1,2,3} and Let R={(1,1),(2,2),(3,3),(1,3),(3,2),(1,2)} then R is

Consider the equation E_(1):vecr xx (2hati-hatj+3hatk)=3hati+hatk and E_(2): vecr xx (hati+2hatj-3hatk)=2hati-hatj, hten

If a 679b is a five digit number that is divisible by 72, then a+b is equal to

There are 5 copies each of 4 different books. Find the number of ways of arranging these books in a shelf.

Let A and B be two sub-sets of R x R, defined as follows: A = {(a,b) : a,b in R " and " tan^(-1)a + cot^(-1)b = pi/2} and B={(a,b) : a,b in R " and " sin^(2) a + cos^(2)b =1}, then

If for a Binomial distribution, mu=10 and sigma^(2)=5, then find P(X gt 6).

S and S^(1) foci of an ellipse. B is one end of the minor axis. If I.SBS^(1) is a right angled isoscles triangle, then e =

The partial fractions of (x^(2)+1)/(x(x^(2)-1)) are

Find the static moment of the upper portion of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2))=1 about the x-axis.

MatricesA and B are givenbelow.FindA+B,B+A,A-BandB -A Verify that A+B=B+A and B-A=-(A-B).A=[{:(7),(1):}]B=[{:(-6),(9):}]

n is a natural number. It is given that (n +20) + (n +21) + ......+ (n + 100) is a perfect square. Then the least value of n is "___________"

Find the eccentricity, foci, length of latusrectum and the equations to thedirectrices of the hyperbola(x^(2))/(16)-(y^(2))/(9) = 1

Find the eccentricity, co ordinates of foci-length of latus rectum and equation of directrices of the folloeing ellipses. 9x^2+16y^2-36x+32y-92=0

If Lim_(xto oo) "sin"((pi(1-cos^(m)x))/(x^(n))) exists and non-zero where m,n in N then

Find the equation of the circle with centre C and redius r where. C = (a,-b),r=a+b

Letf (x)=[x]andg (x )=|x| ,AAxin Rthen valueofgof (( - 5 ) /(3))+fog((- 5)/(3))isequal to:( wheref _0 g (x)=f (g (x))).

An equilateral triangle is of side 10 units. In measuring the side, an error of 0.05 units is made. Then the percentage error in the area of the triangle is

Sum of solution of the equation |{:(1,2,x),(2,3,x^2),(3,5,2):}|=10is :

If f(x) =[|x|]where[.]denotesthegreatestintergerfunction , then whichof thefollowingis not true?

Choose the correct answer. Let veca"and"vecb be two unit vectors and theta be the angle between them.Thenveca+vecb is a unit vector,if:a)theta=pi/4b)theta=pi/3c)theta=pi/2d)theta=(2pi)/3

If f(x)=|cosx-sinx|," then "f^(1)(pi/6) is equal to

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(2log sin x - log sin 2x)dx

If order of matrix A is 2X3 and order of matrix B is 3X5 then order of matrix B'A' is :

Find the values of a,b if ax^(2) + bxy+ 3y^(2) -5x +2y -3 = 0represents a circle . Also find the radius and centre of the circle .

Find the sum of the infinite series (7)/(5)(1+(1)/(10^(2))+(1.3)/(1.2).(1)/(10^(4))+(1.3.5)/(1.2.3).(1)/(10^(6))+....)

Which of the following statement(s) is//are correct

If the points with position vectors 10hati+3hatj, 12hati-5hatj and ahati+11hatj are collinear, find the value of a.

Find the equation of all lines having slope 2 which are tangents to the curve y=(1)/(x-3) , x ne 3 .

The value of int_(0)^(1) (xdx)/( (x^(2) +1)^(2) ) is

Let f(x)=|{:(,1//x,logx,x^(n)),(,1,-1//n,(-1)^(n)),(,1,a,a^(2)):}| where ("where"f^(n)(x) "donotes "n^(th)derivative of f(x).

The number of ways that 3 English, 3 Hindi & 3 Telugu books can be chosen from a shelf containing 5 English, 4 Hindi and 3 Telugu books is

Two this slabs ................

Letf(x): R to Rb " and "g (x)=x-7, x in R". Find"(f o g) (7)

vec(u),vec(v) and vec(w) are not co-planar vectors and p and q are real numbers. If [3vec(u),p vec(v),p vec(w)]-[p vec(v),vec(w),q vec(u)]-[2vec(w),q vec(v),q vec(u)]=0 then ……………

The maximum value of |3z + 9 - 7i| if |z + 2- i| = 5 is

x^2+y^2+2lambdax+5=0 and x^2+y^2+2lambday+5=0 are two circles. P is a point on the line x-y=0. If PA and PB are the lengths of the tangents from P to the two cricles and PA=3, thenPB=

Let f (x) be a function which satisfy the equatio f (xy) = f9x) + f(y) for all x gt 0, y gt 0 such that f '(1) =2. Let A be the area of the region bounded by the curves y =f (x), y = |x ^(3) -6x ^(2)+11 x-6| and x=0, then find value of(28)/(17)A.

The locus of z satisfying the |(x+2i)/(2z+i)| lt 1, inequality where z=x+iy, is

Suppose A and B are events with P(A)=0.5, P(B)=0.4 and P(AcapB)=0.3. Find the probability that i) A does not occur, ii) neither A nor B occurs.

Let f and g be increasing and decreasing functions respectively from [0,oo) to [0, oo), Let h(x)=f(g(x)). If h(0)=0, then h(x)-h(1) is :

f:NxxNrarrN , f("(m,n)")=m+n . If f one one and onto ?

Each of graph drawn has same initial and final of velocity over same time interval :- Which of the following statements is TRUE ?