28278 + Interview Questions in Maths in Class 12

1.	Simplify (20xx(-7))/(-35xx(-2))
Answer» ANSWER :`-2`

Discussion

2.	If p, q are true and r is a false statement, then which of the following is a true statement?
Answer» `(p ^^ Q) VV R ` is F `(p ^^ q) to r` IST `(p vv q) ^^ (p vv r) ` is T `(p to q) harr (p to r)` is T Answer :C

Discussion

3.	Let a=hatj-hatk and c=hati-hatj-hatk, the vector b satisfying axxb+c=vec0 and a.b=3, is
Answer» `-hati+hatj-2hatk` `2hati-hatj+2hatk` `hati-hatj-2hatk` `hati+hatj-2hati` Solution :Given , `a xx B+ c = 0` `RARR a xx (a xx b) + a xx c = 0` `rArr (a.b)a - (a.a) + a xx c = 0` `rArr 3a - 2B +a xx c = 0` `rArr 2b =3a+a xx c` `rArr 2b = 3hatj - 3hatk -2hati - hatj - hatk` `rArr 2b = - hati + 2hatj - 4hatk` `:. b= - hati + hatj - 2hatk`

Discussion

4.	Integrate the following intcosec(x+pi/4)cot(x+pi/4)dx (x=pi/4)
Answer» SOLUTION :`intcosec(x+pi/4)COT(x+pi/4)DX` put `(x+pi/4)=Z` then dx=dz `intcoseczcotzdz` -cosecz+C=`-COSEC(x+pi/4)+C`

Discussion

5.	Find a vector of magnitude 9 units and perpendicular to the vectors veca=4hati-hatj+hatk and vecb= -2hati+hatj-2hatk.
Answer» SOLUTION :N/A

Discussion

6.	The totalcost of daily output of x tons of coal is Rs. ((1)/(10) x^(3)-3x^(2) +50x). What is theMarginal cost funvtion .
Answer» SOLUTION :N/A

Discussion

7.	If int(dx)/(x^(2) + 2x+2) =f(x) +c, then f(x) is equal to
Answer» `TAN^(-1)(x+1)` `2TAN^(-1)(x+1)` `-tan^(-1)(x+1)` `3TAN^(-1)(x+1)` ANSWER :A

Discussion

8.	Find the value of x, y and z from the following equations: (i) [(4,3),(x,5)]=[(y,z),(1,5)] (ii)[(x+y, 2 ),(5+z, xy)]=[(6,2),(5,8)] (iii) [(x+y+z),(x+z), (y+z)]=[(9),(5),(7)]
Answer» ANSWER :(i) `x=1,y=4,z=3` (II) `x=4,y=2,z=0 or x=2, y=4, z=0` (III) `x=2,y=4,z=3`

Discussion

9.	We say an equation f(x)=g(x) is consistent, if the curves y=f(x) and y=g(x) touch or intersect at atleast one point. If the curves y=f(x) and y=g(x) do not intersect or touch, then the equation f(x)=g(x) is said to be inconsistent i.e. has no solution. The equation sinx=x^(2)+x+1 is
Answer» CONSISTENT and has infinite NUMBER of solutions consistent and has finite number of solutions inconsistent None of the above Answer :C

Discussion

10.	ABCD is a parallelogram and O is the point of intersection of its diagonals. If points P, Q, R, S are the mid-points of OA, PB, QC, RD respectively, then the points Q, O, S
Answer» FORMS a triangle are non-coplanar are collinear are non-collinear Answer :C

Discussion

11.	The plane containing lines(x+1)/(3)=(y+3)/(5)=(z+5)/(7)" and "(x-2)/(1)=(y-4)/(4)=(z-6)/(7) passes through
Answer» (0,0,0) (1,0,1) (1,-1,1) (-1,1,0) ANSWER :A

Discussion

12.	Find the value of the following integral int_(0)^((pi)/(2)) cos^(6) x dx
Answer» ANSWER :`(5PI)/(32)`

Discussion

13.	If f(x) = ax^(2) + bx + c is such that \|f(0)\| le 1, \|f(1)\| le 1 and \|f(-1)\| le 1, prove that \|f(x)\| le 5//4, AA x in [-1, 1]
Answer» Answer :`RARR""\|f(x)\| LE (5)/(4), AA x in [-1,1]`

Discussion

14.	Find the value of tan [1/2 sin^(-1) ((2a)/(1+a^(2))) + 1/2 cos^(-1) ((1-a^(2))/(1+a^(2)))]
Answer» ANSWER :`(2A)/(1-a^(2))`

Discussion

15.	If a circle of area 16pihas two of its diamters along the line 2x-3y +5=0 and x+3y -11=0then the equation of the circle is
Answer» `X^(2) +y^(2) -4X +6Y -13=0` ` x^(2) +y^(2) -4x -6y -3=0 ` ` x^(2) + y^(2) -4x -6y -13=0 ` ` x^(2) +y^(2) -4x +6y -3=0 ` Answer :B

Discussion

16.	Find the equation of all possible curves such that length of intercept made by any tangent on x-axis is equal to the square of X-coordinate of the point of tangency. Given that the curve passes through (2,1)
Answer» ANSWER :POSSIBLE curve are `y=(X)/(2(x-1)) or y=(3X)/(2(1+x))`

Discussion

17.	If 5 fair coins are tossed, find the probability of getting heads in majority.
Answer» ANSWER :`(1)/(2)`

Discussion

18.	The probability of a missile hitting a target is 1/2 and two direct hits are required to destroy it. Find the least number of missles, so that the probability of the target destroyed is greater than 0.9.
Answer» ANSWER :7

Discussion

19.	If 2(cos ( alpha-beta)+cos(beta-gamma)+cos(gamma-alpha)+3=0, prove that (d alpha)/(sin ( beta+theta)sin(gamma+theta))+(d beta)/(sin(alpha+beta)sin(beta+theta))+(d gamma)/(sin(alpha+theta)sin(beta+theta))=0, where, 'theta' is any real angle such thatalpha+theta, beta+theta, gamma+theta are not the multiple of pi.
Answer» ANSWER :

Discussion

20.	If a line has the direction ratios '-18,(12) ,-4', then what are its directión cosines?
Answer» Answer :The d.c.'s are `(-18)/(SQRT(18^2+12^2+(-4)^2), (12)/(sqrt(18^2+12^2+(-4)^2), (-4)/(sqrt(18^2+12^2+(-14)^2)` If a, b, c are the direction ratios of a LINE then its d.c.'s are `(a)/(sqrt(a^2+b^2+c^2), (b)/(sqrt(a^2+b^2+c^2), (c)/(sqrt(a^2+b^2+c^2)` i.e., `(-18)/22, (12)/22, (-4)/22` i.e., `(-9)/11, (6)/11, (-2)/11`

Discussion

21.	If 2 dice are rolled then find the probability that the dice show different numbers or sum 10.
Answer» ANSWER :`(31)/(36)`

Discussion

22.	Compute the 1/(8!)+1/(9!)+1/(10!)
Answer» Solution :`1/(8!)+1/(9!)+1/(10!)` `=1/(8!)=1/(98!)+1/(1098!)` `=(109+10+1)/(1098!)=(101)/(3628800)`

Discussion

23.	Express with rational denominator(3+2sqrt(-1))/(2-5sqrt(-1))+(3-2sqrt(-1))/(2+5sqrt(-1))
Answer» SOLUTION :`(3+2sqrt(-1))/(2-5sqrt(-1))+(3-2sqrt(-1))/(2+5sqrt(-1))=(3+2i)/(2-5i)+(3-2i)/(2+5i)` `((3+2i)(2+5i)+(3-2i)(2-5i))/((2-5i)(2+5i))` `(6+15i+4i+10i^2+6-15i-4i+10i^2)/(4-15i^2)` `(12-20)/(4+25)=-8/(29)`

Discussion

24.	Twofunctions are defined as f(x)={:{(x+1,"if" x le1),(2x+1,"if" lt x le 2):} g(x)={:{(x^(2),"if" -1 le x lt 2),(x+2,"if" 2 le x le 3):}
Answer» `{:{(X+1,"if" \|x\| le1),(2X^(2)+1,"if" lt x le SQRT(2)):}` `{:{(x+1,"if" \|x\| le1),(2x^(2)+1,"if" lt x lt sqrt(2)):}` `{:{(x+1,"if" \|x\| le1),(2x^(2)+1,"if" lt x ge sqrt(2)):}` noneof these Answer :A

Discussion

25.	Let f(x) be a differentiable and g(x) be a twice differentiable function such that \|f(x)-1\|le1 and f^(')(x)=g(x). If f^(2)(3)+g^(2)(3)=20 then number of value(s) of cepsilon(0,4) such that g(c)g^('')(c)gt0 is/are _________
Answer» Solution :`:' 0 LE f(x)le2` and `g(3) epsilon [-2sqrt(5), -4]uu[4,2sqrt(5]` Also `int_(0)^(4)g(x)dx=int_(0)^(4)f^(')(x)dx(f(4)-f(0) in(-2,2))` Case I: Let `g(x) gt0` and `g^('')(x)gt0` Clearly `int_(0)^(4)g(x)dx le` Area (MDKS)`=4` Which is a contradiction THUS, there is no such `C` Similarly case II: Let `g(x)LT0` and `g^('')(x)lt0`

Discussion

26.	Evaluate int sin ^(4) x dx.
Answer» `(sin^(3)"xcosx")/(4) - (3)/(8) "SINX cosx" - (3)/(8) x + c` `(1)/(4) sin^(3)"xcosx "+ (3)/(8) x + c ` `- (1)/(4) sin^(3)"xcosx" - (3)/(8) "sinx cosx" + (3)/(8) x + c` `- (1)/(4)" sin"^(3) " xcosx" - (3)/(8) x + c` Answer :C

Discussion

27.	Let A = { a,b,c }, absB = {1,2} Of all the relations from A to B identify which relations are many one, one many and one-one and represent these diagramatically.
Answer» SOLUTION :Some MANY onerelations are {(a,1), (b.1),(c,1),(b,2)(c,2)} {(a,2),(b,2),(c,2)}

Discussion

28.	If (7+4sqrt3)^n=I+F where I and n are +ve integers and F is +ve proper fraction, then (I+F)(1-F)=
Answer» only I is true only II is true both I and II are true neither I nor II true Answer :A

Discussion

29.	Find the asymptotes of the hyperbolaxy - 3y - 2x = 0
Answer» ANSWER :X - 3 = 0 and y - 2 = 0

Discussion

30.	If N = 6 m (where m is obtained in question number 35) then :
Answer» TOTAL number of divisors of N is 36 total number of divisors of N in form of `(2n+1)` is `12 (n in "Natural")` The number of ways in which N can be resolved as product of TWO factors is 18 The number of ways in which N can be resolved as product of two coprime factore is 8. Answer :A

Discussion

31.	The order of the differential equation of the family of curves y=(a)/(c ) sin (bx)+3^(dx) where a, b, c, d are arbitrary constants is
Answer» 4 3 2 1 Answer :B

Discussion

32.	d/dx{tan^-1(e^x)} is equal to :
Answer» e^xtan^(-1)e^x (e^x)/(1+e^(2X) 0 e^x SEC^(-1)x Answer :B

Discussion

33.	A circle C whose radius is 1 unit, thuches the x-axis at point A. The centre Q of C lies in first quadrant. The tangent from origin O to the circle touches it at T and a point P lies on it such that Delta OAP is a right angled triangle at A and its perimeter is 8 units. If tangent OT cuts the two parallel tangents (one of them is OA) at O and R, then equation of circle circumscribing the Delta ORQ is
Answer» `X ^(2) +y ^(2) - sqrt3 x - y=0` `x ^(2) +y ^(2) - sqrt3 x - 2y =0` `x ^(2) +y ^(2) -2 sqrt3 x - 2y =0` NONE of these Answer :D

Discussion

34.	A circle C whose radius is 1 unit, thuches the x-axis at point A. The centre Q of C lies in first quadrant. The tangent from origin O to the circle touches it at T and a point P lies on it such that Delta OAP is a right angled triangle at A and its perimeter is 8 units. Equation of the larger circle which touches the tangents drawn from origin to the circle C and the circle C extermally is
Answer» `{x -2 (2 - sqrt3)} ^(2) + (y-2) ^(2) =4` `{x-2 (2+ sqrt3) }^(2) + {y-2(7 +2SQRT3)} ^(2) = 4(7 +2 sqrt3) ^(2)` `{x -3(2 -sqrt3)}^(2) + (y-3)^(2) =9` none of these Answer :D

Discussion

35.	A right circular cone has height 9 cm and radius of the base 5 cm. it is inverted and water is poured into it. If an any instant the water level rises at the rate of(pi/A) cm /sec, where A is the area of the water surface at the instant , show that the vessel will be full in 75 seconds
Answer» Solution :LET r be the radius of the water surface and h be the HEIGHT of the water at time t. area of the water surface `A = pir^(2)` sqcm. Since height of the right cicrular cone is 9 cm and radius of the base is 5 cm. ` r/h = 5/9therefore r = 5/9 h` area of water surface i.e., A` = pi (5/9 h)^2` ` A = (25 pih^(2))/(81)` The water level, i.,e, the RATE of change of h is `(DH)/(dt) ` RISES at the rate of `(pi/2)` cm/sec. ` (dh)/(dt) = pi/A = ( pi xx 81)/( 25 pih^(2))` ` (dh)/(dt) = 81/ (25h^(2))"" therefore h^(2)dh = (81)/25 dt` On integrating we get ` int h^(2) dh = (81)/25 int dt +c"" therefore h^(3)/3 81/25 .t +c` Initially ,i.e. when t = 0 , h=0 ` therefore0=0+ctherefore c=0` ` h^(3)/3 = 81/25 t` when the vessel will be full h = 9` therefore ((9)^(3))/3= 81/25 xx t` ` t = (81 xx 9 xx 25)/(3 xx 81) =75` Hence, the vessel will be full in 75 seconds `(NVT_21_MAT_XII_C16_SLV_043_S01)`

Discussion

36.	Find the locus of the point of intersection of tangents to the ellipseat the points the sum of a b whose ordinates are constant.
Answer» ANSWER :`(2U)/(LAMBDA)`

Discussion

37.	If ""^nC_2+2(""^nC_3)+"^nC_3gt^((n+2))C_3 then find n.
Answer» ANSWER :`ngt5`

Discussion

38.	There are five boggarts placed in a maze on blocks A,B,C,D and E. Every student starts on Block X, and can control the movement of other blocks. The objective is to take their wands from the centre of the maze and use it to shoot the boggarts As the maze is enchanted, there are restrictions on the movement of the blocks. Each block can be made to travel horizontally or vertically, but only directly towards another block -- as far as it can go until hitting it edge to edge. One set of move is a continuous sequence of such movements made by the same block. Each move is indicated by the block’s letter followed by the directions traveled: up (U), Down (D), left (L), and right (R). For Example, X- RUL is one move, which states that Block X first moved Right, then Up, then Left. How many times does each of the blocks,student move? (A, B, C, D, E, X) and total set of moves?
Answer» 1,3,2,0,2,4 and 6 1,3,2,0,2,4 and 5 0,3,1,3,0,5 and 7 1,3,1,0,2,4 and 5 Solution :The STEPS are as FOLLOWS D-D, C-D, D-L, X-UL, B-LDR, D-U, X-LUR

Discussion

39.	Consider the functions, f(x) = \|x -2 \| + \|x - 5 \|, x in RStatement-1 : f'(4) = 0 Statement-2 : f is continuous in [2, 5], differentiable in (2, 5) and F(2) =F(5)
Answer» Statement 1 is true , statement 2 is true, statement 2 is not a CORRECT EXPLANATION for statement 1 statement 1 is true, statement 2 is false statement 1 is false, statement 2 is true statement 1 is true , statement 2 is true, statement 2 is a correct explanation for statement 1 ANSWER :A

Discussion

40.	There are 12 points in a plane of which no three points are collinearand 5 points are concyclic . The number of differentcircles that can be drawn throughatleast3 pointsof these points is
Answer» 120 220 211 144 Answer :C

Discussion

41.	The quadratic equations x^(2)-6x+a=0" and "x^(2)-cx+6=0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is
Answer» `2` `1` `4` `3` ANSWER :A

Discussion

42.	Let L:y = mx +c C_(1) :x^(2) = 4y C_(2):y^(2) = 4ax, a ne 0 be three curves in xy plane. If L is normal to C_(1) and tangent to C_(2) then the possible value of a^(2) can be
Answer» 1 4 6 16 Solution :Equation of NORMAL to `x^(2) =4y` is `x=-yt + t^(3) + 2t`…….(1) If the line TOUCHES `t in R y^(2) = 4ax`, then `t^(2) + at + 2=0` As `t in R, D ge 0` `a^(2) ge 8`

Discussion

43.	Show that the equation ax+by+d=0 represents a plane parallel to the z-axis. Hence findthe equation of plane parallel to the z-axis and passing through the points (-4,7,6) and(2,-3,1). Also convert to vector form.
Answer» SOLUTION :N/A

Discussion

44.	IfP -= ((1)/(x_(p)), p ), Q = ((1)/(x_(q)),q), R = ((1)/(x_(r)), r) wherex _(k) ne 0 ,denotes thek^(th)terms of a H.P. fork in N , then :
Answer» ar. `( Delta PQR)= (p^(2)Q^(2)R^(2))/(2) sqrt((p-q)^(2) + (q-r)^(2) + (r-p)^(2))` ` Delta PQR` is a RIGHT angled triangle the POINTS P,Q, R are collinear None of these Answer :C

Discussion

45.	In the matrixA=[{:(a,1,x),(2,sqrt(3),x^(2)-y),(0,5,-(2)/(5)):}] , write : (i) The order of the matrix A (ii) The number of elements (iii)Write elements a_(23),a_(31),a_(12)
Answer» ANSWER :(i) `n=3xx3`. (II) `=9` (III) `=1`

Discussion

46.	The sum of the series S= overset(n)underset(r=1)Sigma log ((a^(r+1))/(b^(r-1))) is
Answer» `(n)/(2)LOG((a^(n-1))/(b^(n)))` `(n)/(2)log((a^(n+3))/(b^(n-1)))` `(n)/(2)log((a^(n-+2))/(b^(n-1)))` none of these Answer :B

Discussion

47.	A person standing on the bank of a river observes that the angle of the top of a tree on the opposite hank of the river is 60^(@) and when he retires 40 metres away from the tree the angle of elevation becomes 30^(@). The breadth of the river is:
Answer» 20 m 30 m 40 m 60 m. ANSWER :A

Discussion

48.	Urn A contains 1 white, 2 blackand 3 red balls, urn B contains 2 white, 1 black and 1 red balls, and urn C contains 4 white , 5 blackand 3 red balls. One urn is chosen at random and two balls are drawn. These happen to be one white and one red. What is the probability that they come from urn A?
Answer» SOLUTION :Let `E_1,E_2,E_3` be the EVENTS that the balls are drawn from urn A, urn B and urn C respectively, and let E be the event that the balls drawn are one WHITE and one RED. Then, `P(E_1)=P(E_2)=P(E_3)=1/3`. `P(E//E_1)`= probability that the balls drawn are one white and one red, giventhat the balls are from urn A `=(.^1C_1xx.^3 C_1)/(.^6C_2)=3/15=1/5`. `P(E//E_2)`= probability that the drawn are one white and one red,given that the balls are from urn B `=(.^2C_1xx.^1C_1)/(.^4C_2)=2/6=1/3` `P(E//E_3)`= probability that the balls drawn are one white and one red, given that the balls are from urn C `=(.^4C_1xx.^3C_1)/(.^12C_2)=12/66=2/11` Probability that the balls drawn are from urn A, it being given that the balls drawn are one white and one red `=P(E-1//E)` `(P(E//E_1).P(E_1))/(P(E//E_1).P(E_1)+P(E//E_2).P(E_2)+P(E//E_3).P(E_3))`[by Bayes's theorem] `((1/5xx1/3))/((1/5xx1/3)+(1/3xx1/3)+(2/11xx1/3))` `=(1/15xx495/118)=33/118`. Hence, the required probability is `33/118`.

Discussion

49.	If vec(a)=2hati+hatj+3hatk,vec(b)=-hati+2hatj+hatk and vec( c )=3hati+hatj+2hatk then find vec(a).(vec(b)xx vec( c )).
Answer» ANSWER :`-10`

Discussion

50.	A gardener is digging a plot of land. As he gets tired, he works more slowly. After 't' minutes he is digging at a rate of (2)/(sqrt(t)) square metres per minutes. How long will it take him to dig an area of 40 square meters ?
Answer» 100 minutes 10 minutes 30 minutes 40 minutes Answer :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Simplify (20xx(-7))/(-35xx(-2))

If p, q are true and r is a false statement, then which of the following is a true statement?

Let a=hatj-hatk and c=hati-hatj-hatk, the vector b satisfying axxb+c=vec0 and a.b=3, is

Integrate the following intcosec(x+pi/4)cot(x+pi/4)dx (x=pi/4)

Find a vector of magnitude 9 units and perpendicular to the vectors veca=4hati-hatj+hatk and vecb= -2hati+hatj-2hatk.

The totalcost of daily output of x tons of coal is Rs. ((1)/(10) x^(3)-3x^(2) +50x). What is theMarginal cost funvtion .

If int(dx)/(x^(2) + 2x+2) =f(x) +c, then f(x) is equal to

Find the value of x, y and z from the following equations: (i) [(4,3),(x,5)]=[(y,z),(1,5)] (ii)[(x+y, 2 ),(5+z, xy)]=[(6,2),(5,8)] (iii) [(x+y+z),(x+z), (y+z)]=[(9),(5),(7)]

We say an equation f(x)=g(x) is consistent, if the curves y=f(x) and y=g(x) touch or intersect at atleast one point. If the curves y=f(x) and y=g(x) do not intersect or touch, then the equation f(x)=g(x) is said to be inconsistent i.e. has no solution. The equation sinx=x^(2)+x+1 is

ABCD is a parallelogram and O is the point of intersection of its diagonals. If points P, Q, R, S are the mid-points of OA, PB, QC, RD respectively, then the points Q, O, S

The plane containing lines(x+1)/(3)=(y+3)/(5)=(z+5)/(7)" and "(x-2)/(1)=(y-4)/(4)=(z-6)/(7) passes through

Find the value of the following integral int_(0)^((pi)/(2)) cos^(6) x dx

If f(x) = ax^(2) + bx + c is such that |f(0)| le 1, |f(1)| le 1 and |f(-1)| le 1, prove that |f(x)| le 5//4, AA x in [-1, 1]

Find the value of tan [1/2 sin^(-1) ((2a)/(1+a^(2))) + 1/2 cos^(-1) ((1-a^(2))/(1+a^(2)))]

If a circle of area 16pihas two of its diamters along the line 2x-3y +5=0 and x+3y -11=0then the equation of the circle is

Find the equation of all possible curves such that length of intercept made by any tangent on x-axis is equal to the square of X-coordinate of the point of tangency. Given that the curve passes through (2,1)

If 5 fair coins are tossed, find the probability of getting heads in majority.

The probability of a missile hitting a target is 1/2 and two direct hits are required to destroy it. Find the least number of missles, so that the probability of the target destroyed is greater than 0.9.

If a line has the direction ratios '-18,(12) ,-4', then what are its directión cosines?

If 2 dice are rolled then find the probability that the dice show different numbers or sum 10.

Compute the 1/(8!)+1/(9!)+1/(10!)

Express with rational denominator(3+2sqrt(-1))/(2-5sqrt(-1))+(3-2sqrt(-1))/(2+5sqrt(-1))

Twofunctions are defined as f(x)={:{(x+1,"if" x le1),(2x+1,"if" lt x le 2):} g(x)={:{(x^(2),"if" -1 le x lt 2),(x+2,"if" 2 le x le 3):}

Let f(x) be a differentiable and g(x) be a twice differentiable function such that |f(x)-1|le1 and f^(')(x)=g(x). If f^(2)(3)+g^(2)(3)=20 then number of value(s) of cepsilon(0,4) such that g(c)g^('')(c)gt0 is/are _________

Evaluate int sin ^(4) x dx.

Let A = { a,b,c }, absB = {1,2} Of all the relations from A to B identify which relations are many one, one many and one-one and represent these diagramatically.

If (7+4sqrt3)^n=I+F where I and n are +ve integers and F is +ve proper fraction, then (I+F)(1-F)=

Find the asymptotes of the hyperbolaxy - 3y - 2x = 0

If N = 6 m (where m is obtained in question number 35) then :

The order of the differential equation of the family of curves y=(a)/(c ) sin (bx)+3^(dx) where a, b, c, d are arbitrary constants is

d/dx{tan^-1(e^x)} is equal to :

A right circular cone has height 9 cm and radius of the base 5 cm. it is inverted and water is poured into it. If an any instant the water level rises at the rate of(pi/A) cm /sec, where A is the area of the water surface at the instant , show that the vessel will be full in 75 seconds

Find the locus of the point of intersection of tangents to the ellipseat the points the sum of a b whose ordinates are constant.

If ""^nC_2+2(""^nC_3)+"^nC_3gt^((n+2))C_3 then find n.

Consider the functions, f(x) = |x -2 | + |x - 5 |, x in RStatement-1 : f'(4) = 0 Statement-2 : f is continuous in [2, 5], differ­entiable in (2, 5) and F(2) =F(5)

There are 12 points in a plane of which no three points are collinearand 5 points are concyclic . The number of differentcircles that can be drawn throughatleast3 pointsof these points is

The quadratic equations x^(2)-6x+a=0" and "x^(2)-cx+6=0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

Let L:y = mx +c C_(1) :x^(2) = 4y C_(2):y^(2) = 4ax, a ne 0 be three curves in xy plane. If L is normal to C_(1) and tangent to C_(2) then the possible value of a^(2) can be

Show that the equation ax+by+d=0 represents a plane parallel to the z-axis. Hence findthe equation of plane parallel to the z-axis and passing through the points (-4,7,6) and(2,-3,1). Also convert to vector form.

IfP -= ((1)/(x_(p)), p ), Q = ((1)/(x_(q)),q), R = ((1)/(x_(r)), r) wherex _(k) ne 0 ,denotes thek^(th)terms of a H.P. fork in N , then :

In the matrixA=[{:(a,1,x),(2,sqrt(3),x^(2)-y),(0,5,-(2)/(5)):}] , write : (i) The order of the matrix A (ii) The number of elements (iii)Write elements a_(23),a_(31),a_(12)

The sum of the series S= overset(n)underset(r=1)Sigma log ((a^(r+1))/(b^(r-1))) is

A person standing on the bank of a river observes that the angle of the top of a tree on the opposite hank of the river is 60^(@) and when he retires 40 metres away from the tree the angle of elevation becomes 30^(@). The breadth of the river is:

Urn A contains 1 white, 2 blackand 3 red balls, urn B contains 2 white, 1 black and 1 red balls, and urn C contains 4 white , 5 blackand 3 red balls. One urn is chosen at random and two balls are drawn. These happen to be one white and one red. What is the probability that they come from urn A?

If vec(a)=2hati+hatj+3hatk,vec(b)=-hati+2hatj+hatk and vec( c )=3hati+hatj+2hatk then find vec(a).(vec(b)xx vec( c )).

A gardener is digging a plot of land. As he gets tired, he works more slowly. After 't' minutes he is digging at a rate of (2)/(sqrt(t)) square metres per minutes. How long will it take him to dig an area of 40 square meters ?

Consider the functions, f(x) = |x -2 | + |x - 5 |, x in RStatement-1 : f'(4) = 0 Statement-2 : f is continuous in [2, 5], differentiable in (2, 5) and F(2) =F(5)