28278 + Interview Questions in Maths in Class 12

1.	If z = x + iy and if the point P in the argand plane represents z , then the locus of P satisfying the equation z(z + 2) = 3
Answer» ANSWER :B::C

Discussion

2.	I. The varianceof first 5 natural number is 2 . II :Thestandarddeviationof first3 positiveintergers is 2/3.
Answer» only I is TURE only IIis ture both I andII are TRUE NEITHER I nor II true Answer :C

Discussion

3.	If (1 + x) (1 + x + x^(2)) (1 + x + x^(2) + x^(3))...(1 + x + x^(2) + . . . + x^(n)) = a_(0) + a_(1)x + a_(2)x_(2) + ... +a_(m)x^(m), then value of a_(1) is
Answer» m+1 n+1 n m Answer :C

Discussion

4.	If \|a\|=10, \|b\|=2 and a.b=12, then value of \|a xx b\| is
Answer» 5 10 14 16 Solution :Given, `\|a\|=10, \|b\|=2` and `a.b =12` `:' a.b =\|a\|\|b\| cos THETA` `implies 12=10xx2.cos theta` `implies cos theta=3/5` `:' axxb=\|a\|\|b\| sin theta.HAT(N)` `implies \|axxb\|=\|a\|\|b\|\|sin theta\|.\|hat(n)\|""[ :' \|hat(n)\|=1]` `implies \|axxb\|=10.2.\|sqrt(1-cos^(2) theta)\|.1` `=20.\|sqrt(1-9//25)\|` `=20xxsqrt(\|16/25\|)=20xx4/5` `implies \|axxb\|=16`

Discussion

5.	Given vecA=3 hati+hatj and vecB=6hati+8hatj. Which of the following satements is incorrect ?
Answer» `VECA.VECB=50` `(\|vecA\|)/(\|vecB\|)=1/2` `\|vecA\|=5` `vecA.vecB=48` SOLUTION :`(A) vecA.vecB=18+52=50` `(B)\|A\|=5,\|B\|=10]`

Discussion

6.	Area of the parallelogram on the vectors a + 3b and 3a + b if abs(a)=abs(b)=1 and the angle between a and b is pi//6 is
Answer» 2 4 8 16 Answer :B

Discussion

7.	A publisher sells a hard cover edition of a text book for Rs. 72 and a paperback edition of the same text for Rs. 40. Costs to the publisher are Rs. 56 and Rs. 28 per book respectively in addition to weekly costs of Rs. 9600. Both types require 5 minutes of priniting time, although hard cover requires 10 minutes binding time and the paper back requires only 2 minutes. Both the printing and binding operations have 4800 minutes available each week. How many of each types of book should be produced in order to maximise profit ?
Answer» ANSWER :360 hard COVER textbook, 600 paper BACK textbook.

Discussion

8.	How many valuesofthetabetween 0^(@)and360^(@)satisfytantheta=kne0, where k is a given number ?
Answer» 1 2 4 Many Solution :GIVEN, equation is `tantheta=k,kne0` `rArrtheta=tan^(-1)k` Now , we know , If`tan^(-1)x=theta`then`-ooltxltooand(-pi)/(2)ltthetalt(pi)/(2)` Thus, `theta`will have 2 values between `0^(@)and360^(@)`. orThe equation`tantheta=k,-ooltkltoo`for any real values of k there are two values of the form `alphaand pi+alpha`,in the INTERVAL`0lethetale2pi`,which SATISFIES the given equation.

Discussion

9.	If z = x + iy and if the point P in the argand plane represents z , then the locus of P satisfying the equation \|z\| = 2
Answer» ANSWER :B::D

Discussion

10.	If f(x) = int(3x+2)/(x^(4)-x^(3)+x^(2)-1)dx then f(x) has
Answer» ONE CRITICAL point two critical POINTS three critical points no critical points Answer :C

Discussion

11.	Let alpha represent an imaginary cube root of unity Then the value of (2+alpha^(13)+alpha^(29))^(99)+(1+alpha^(19)-alpha^(35))^(96)-(1-3alpha^(25)+alpha^(38))^(48) is
Answer» `1//2` `-1//2` `-1` 1 Answer :D

Discussion

12.	If S_(n)=81+54+36+24+.. upto n terms, then value of x=(S_(n)-4S_(n-1)+6S_(n-2)-4S_(n-3)+S_(n-4))/(S_(n-1)-4S_(n-2)+6S_(n-3)-4S_(n-4)+S_(n-5)) is equal
Answer» `(2)/(3)` `(3)/(2)` `(1)/(2)` 2 Answer :A

Discussion

13.	If z = x + iy and if the point P in the argand plane represents z , then the locus of P satisfying the equation \|z + i\|^(2) - \|z - i\|^(2) =2
Answer» ANSWER :A::B

Discussion

14.	If 2x+3y le 12, 3x+y le 12, x ge 0, y ge 0 then the maximum value of f=5x+7y is
Answer» 6 12 36 204/7 Answer :D

Discussion

15.	A pair of fair dice is rolled together till a sum of 7 or 11 is obtained. Let p denote the probability that 7 comes before 11, then the of p is equal to _____
Answer» ANSWER :`0.75`

Discussion

16.	Find the coordinates of the point of in- tersection of tangents at the points where x + 4y - 14 = 0meets the circle x^(2) + y^(2) - 2 x + 2y - 5 = 0
Answer» <P> Answer :`THEREFORE` CO- ordinates of p are `(109/76, 938)`

Discussion

17.	Evaluate : int_(0)^(1)(tan^(-1)x)/(1+x^(2))dx
Answer» ANSWER :`(PI^(2))/(32)`

Discussion

18.	If D, E, F are the midpoints of sides BC, CA, AB of triangle ABC and G is the centroid then match the following {:(I,AD + BE + CF,(a),CB),(II,GA + GB,(b),3 OG),(III.,AB + CA,(c),O),(IV.,OD + OE + OF,(d),-(2)/(3)(AD + BE)),(,,(e),"3 OE"):}
Answer» C, d, a, B d, b, a, c c, d, E, a b, c, e, a Answer :A

Discussion

19.	The triangle of maximum area inscribed in a circle is :
Answer» equilateral isosceles right-angled none of these Solution :The area of the triangle is maximum, when vertex C is at maximum distance from the base AB, or C is a point on diameter perpendicular to AO, OC = OB = a. `THEREFORE Delta ABC` is isosceles triangle. Area of `Delta ABC` is `Z=(1)/(2)xx AB xx CD` `= a^(2)sin 2theta(1+cos 2theta)` `therefore (dz)/(d THETA)=2a^(2)(cos 4theta + cos 2theta)=0` `rArr 2 cos 3theta cos theta = 0` `rArr theta = (pi)/(2)` or `theta = (pi)/(6)` `therefore theta = (pi)/(2)` is impossible, `therefore` at `theta = (pi)/(6)` area of triangle is maximum.

Discussion

20.	If f(x)=1-x-x^(3), .............
Answer» SOLUTION :`f(X)=1-x-x^(3)` `f(f(x))=1-f(x)-f^(3) (x)` `f'(x)=-1-3x^(2)` (decreasing FUNCTION) `:. f(x) lt 1-5X` `1-x-x^(3) lt 1 -5x` `x^(3)-4x gt 0` `x(x^(2)-4) gt 0`

Discussion

21.	Evalute the following integrals int (1)/((1 -x)(x^(2)+4)) dx
Answer» ANSWER :`- (1)/(5) LOG \|1 - X\|+ (1)/(10) log (x^(2) + 4) + (1)/(10) tan^(-1) ((x)/(2)) ` + c

Discussion

22.	From the figure, which of the following must be true? (I) x + y = 90 (II) x is 35 units greater than y (III) x is 35 units less than y
Answer» I only II only III only I and II only ANSWER :B

Discussion

23.	Let alpha and beta be two real roots of the equation 5cot^2x-3cotx-1=0 , then cot^2 (alpha+beta) =
Answer» 2 3 4 5 Solution :`cot ALPHA + cot BETA =3/5 cot alpha .cot beta = -1/5` `cot(alpha+beta)=(cot alpha cot beta-1)/(cot alpha+cot beta)=(-1/5-1)/(3/5)` `=-6/3 =-2 rArr cot^2 (alpha+beta)=4`

Discussion

24.	IfB. B^(1)are the ends of minor axis ,F_(1) , F_(2) arefociof the ellispex^(2)/8+ y^(2)/4=1 then area ofF_(1) BF_(2) B^(1) is
Answer» 16 8 `16sqrt2` `32sqrt2` ANSWER :B

Discussion

25.	Evaluation of definite integrals by subsitiution and properties of its : int_(theta)^(pi/2)\|sin(x-(pi)/(4))\|dx=.........
Answer» `2+sqrt2` `2-sqrt2` `-2+sqrt2` 0 Answer :B

Discussion

26.	Solve the equation sqrt(-x^92)+6x-5 gt 8-2x.
Answer» ANSWER :`{X: 3lt x LE 5}`

Discussion

27.	Let A is set of all real values of a for which equation x^(2)-ax+1=0 has no real roots and B is set of al real values of b for which f(x)=bx^(2)+bx+0.5gt0AAxepsilonR then AcapB=
Answer» `{X:0ltxlt2}` `{x:0lexlt2}` `{x:0lexle2}` `{x:-2ltxlt2}` SOLUTION :`x^(2)-ax+1=0` has REAL root ` `becauseDlt0impliesa^(2)-4lt0` `impliesaepsilon(-2,2)` `because A={x:-2ltxlt2}` `f(x)=bx^(2)+bx+0.5gt0AAxepsilonR`, if `bgt0` `because Dlt0impliesb^(2)-4b.(1)/(2)lt0` `impliesb^(2)-2blt0impliesbepsilon(0,2)` ALSO `b=0` then `f(x)gt0AAxepsilonRbecausebepsilon[0,2]` `becauseB={x:0lexlt2}` `becauseAcapB={x:0lexlt2}`

Discussion

28.	If A=[{:(" 1",1," 1"),(" 2", 1," -3"),(-1,2," 3"):}] , then co-factor of 3^(rd) row are
Answer» `4, -5, 1` `-4, 5, -1` `-4, 5, 1` `4, 5 , -1` ANSWER :B

Discussion

29.	If the line y = x + 3 meets the circle x ^(2) + y ^(2) =a ^(2) at A and B, then equation of the circle on AB as diameter is
Answer» `X ^(2) + y ^(2) + 3X - 3Y -a ^(2) + 9=0` `x ^(2) + y ^(2) - 3x + 3y -a ^(2) - 9=0` `x ^(2) + y ^(2) + 3x + 3y +a ^(2) - 9=0` `x ^(2) +y ^(2) - 3x + 3y -a ^(2) + 9=0` ANSWER :A

Discussion

30.	Find the 2xx2 mtrix X if[[x_1,x_2], [y_1,y_2]]-[[2,0],[0,2]]=[[3,5],[1,2]] determine x_1,x_2,y_1,y_2.
Answer» SOLUTION : `[[x_1,x_2], [y_1,y_2]]-[[2,0],[0,2]]=[[3,5],[1,2]]` ` `[[x_1,x_2], [y_1,y_2]]=[[2,3],[0,1]]+[[3,5],[1,2]]=[[5,8],[1,3]]` `:. x_1=5,x_2=8,y_1=1,y_2=3`

Discussion

31.	I) For x in (2, 4) the sign of x^(2)-6x+5 is negative II) Forx in (-oo, 2)uu(4, oo) the sign of x^(2)-6x+5 is positive then Which of the above statement (s) is /are true
Answer» only I only II both I and II neither I nor II Answer :A

Discussion

32.	A coin is biased such that the probability of getting head is thrice to that of getting a tail. If such coin is tossed twice find the probability of getting one head exactly.
Answer» ANSWER :`3//8`

Discussion

33.	A particle moves along the curve 6y = x^(3) +2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.
Answer» ANSWER :(4,11) and `(-4 , (-31)/(3))`

Discussion

34.	Evaluate int_(0)^(pi)(xdx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)
Answer» ANSWER :`(PI^(2))/(2AB)`

Discussion

35.	Another name for the mean of a probability distribution is expected value.
Answer» ANSWER :1

Discussion

36.	If y =2 Tan ^(-1) ((x sqrt2)/( 1 - x ^(2))) + log ((1+ x sqrt2 + x ^(2))/(1 - x sqrt2 + x ^(2)))then (dy)/(dx) =
Answer» `(1)/(1 + x ^(4))` `(2)/(1 + x ^(4))` `(2SQRT2)/(1 + x ^(4))` `(4sqrt2)/(1 + x ^(4))` Answer :D

Discussion

37.	Using properties of determinants in Exercise 11 to 15 prove that \|{:(1,1+p,1+p+q),(2,3+2p,4+3p+2q),(3,6+3p,10+6p+3q):}\|=1
Answer» ANSWER :1

Discussion

38.	Find the ratio of the areas in which the curve y=[(x^3)/(100)+x/35] divides the circle x^(2)+Y^(2)-4x+2y+1=0. (where, [.] denotes the greated integer function).
Answer» ANSWER :`(4pi-3sqrt(3))/(8pi+3sqrt(3))`

Discussion

39.	Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(oo)f(x+(1)/(x))(logx)/(x)dx=...........
Answer» 0 1 `(1)/(2)` can not DECIDE ANSWER :A

Discussion

40.	Let a kind of bacteria grow in such a way that at time t sec, there aret^(3//2) bacteria. Find tha rate of growth at time t = 4 hours.
Answer» ANSWER :180 bacteria/sec

Discussion

41.	Area of the triangle in the Argand diagram formed by the complex numbers z, iz, z+iz, where z=x+iy is
Answer» `\|Z\|` `\|z\|^2` `2\|z\|^2` `(1/2)\|z\|^2` ANSWER :D

Discussion

42.	L A = NxxN and ** be the binary operation on A defined by (a,b) "" (c,d) = (a+c,b+d)Show that * is commutative and associative . Find the identity element for ** on A , if any.
Answer» SOLUTION :N/A

Discussion

43.	Draw the graph of the following function. f(x-1)
Answer» ANSWER :`F(x-1)` is SHOWN as `(##ARH_AMA_DIF_CAL_C04_E02_003_A01##)`

Discussion

44.	Draw the graph of the following function. f(x+1)
Answer» ANSWER :`F(x+1)` is SHOWN as `(##ARH_AMA_DIF_CAL_C04_E02_002_A01##)`

Discussion

45.	If x^(2) + y^(2) + 2gx + 2fy = 0 represents a circle with cerntre (-4, -3) then find g, f and the radius of the circle.
Answer» ANSWER :` G= 4 , f= 3 ` RADIUS =5

Discussion

46.	If z_(1),z_(2),z_(3) are collinear and z_(3)-z_(1)/(z_(2)-z_(1)) is purely real, then arg(z_(3)-z_(1)/(z_(2)-z_(1)))
Answer» 0 1 2 3 Answer :A

Discussion

47.	Match the following :
Answer» SOLUTION :N/A

Discussion

48.	Match the following :
Answer» <P>`{:(P,Q,R,S),(2,4,3,1):}` `{:(P,Q,R,S),(4,3,1,2):}` `{:(P,Q,R,S),(3,1,2,4):}` `{:(P,Q,R,S),(2,4,1,3):}` SOLUTION :N/A

Discussion

49.	intdx/(x(x^4+1))
Answer» SOLUTION :`I=intdx/(X(x^4+1))=intdx/(x^5(1+1/x^4))` LET `1+1/x^4=t` `-4/x^5dx=dt` `THEREFORE I=-1/4intdt/t` =`-1/4Inabst+c` =`-1/4Inabs(1+1/x^4)+c`

Discussion

50.	If f(x)=\|(1-x, -1,0),(2,3-x, 1),(4,-2,5-x)\| , numberof realroots of f(x)=0 is ____
Answer» 1 0 2 3 Answer :A

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If z = x + iy and if the point P in the argand plane represents z , then the locus of P satisfying the equation z(z + 2) = 3

I. The varianceof first 5 natural number is 2 . II :Thestandarddeviationof first3 positiveintergers is 2/3.

If (1 + x) (1 + x + x^(2)) (1 + x + x^(2) + x^(3))...(1 + x + x^(2) + . . . + x^(n)) = a_(0) + a_(1)x + a_(2)x_(2) + ... +a_(m)x^(m), then value of a_(1) is

If |a|=10, |b|=2 and a.b=12, then value of |a xx b| is

Given vecA=3 hati+hatj and vecB=6hati+8hatj. Which of the following satements is incorrect ?

Area of the parallelogram on the vectors a + 3b and 3a + b if abs(a)=abs(b)=1 and the angle between a and b is pi//6 is

How many valuesofthetabetween 0^(@)and360^(@)satisfytantheta=kne0, where k is a given number ?

If z = x + iy and if the point P in the argand plane represents z , then the locus of P satisfying the equation |z| = 2

If f(x) = int(3x+2)/(x^(4)-x^(3)+x^(2)-1)dx then f(x) has

Let alpha represent an imaginary cube root of unity Then the value of (2+alpha^(13)+alpha^(29))^(99)+(1+alpha^(19)-alpha^(35))^(96)-(1-3alpha^(25)+alpha^(38))^(48) is

If S_(n)=81+54+36+24+.. upto n terms, then value of x=(S_(n)-4S_(n-1)+6S_(n-2)-4S_(n-3)+S_(n-4))/(S_(n-1)-4S_(n-2)+6S_(n-3)-4S_(n-4)+S_(n-5)) is equal

If z = x + iy and if the point P in the argand plane represents z , then the locus of P satisfying the equation |z + i|^(2) - |z - i|^(2) =2

If 2x+3y le 12, 3x+y le 12, x ge 0, y ge 0 then the maximum value of f=5x+7y is

A pair of fair dice is rolled together till a sum of 7 or 11 is obtained. Let p denote the probability that 7 comes before 11, then the of p is equal to _____

Find the coordinates of the point of in- tersection of tangents at the points where x + 4y - 14 = 0meets the circle x^(2) + y^(2) - 2 x + 2y - 5 = 0

Evaluate : int_(0)^(1)(tan^(-1)x)/(1+x^(2))dx

If D, E, F are the midpoints of sides BC, CA, AB of triangle ABC and G is the centroid then match the following {:(I,AD + BE + CF,(a),CB),(II,GA + GB,(b),3 OG),(III.,AB + CA,(c),O),(IV.,OD + OE + OF,(d),-(2)/(3)(AD + BE)),(,,(e),"3 OE"):}

The triangle of maximum area inscribed in a circle is :

If f(x)=1-x-x^(3), .............

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

From the figure, which of the following must be true? (I) x + y = 90 (II) x is 35 units greater than y (III) x is 35 units less than y

Let alpha and beta be two real roots of the equation 5cot^2x-3cotx-1=0 , then cot^2 (alpha+beta) =

IfB. B^(1)are the ends of minor axis ,F_(1) , F_(2) arefociof the ellispex^(2)/8+ y^(2)/4=1 then area ofF_(1) BF_(2) B^(1) is

Evaluation of definite integrals by subsitiution and properties of its : int_(theta)^(pi/2)|sin(x-(pi)/(4))|dx=.........

Solve the equation sqrt(-x^92)+6x-5 gt 8-2x.

Let A is set of all real values of a for which equation x^(2)-ax+1=0 has no real roots and B is set of al real values of b for which f(x)=bx^(2)+bx+0.5gt0AAxepsilonR then AcapB=

If A=[{:(" 1",1," 1"),(" 2", 1," -3"),(-1,2," 3"):}] , then co-factor of 3^(rd) row are

If the line y = x + 3 meets the circle x ^(2) + y ^(2) =a ^(2) at A and B, then equation of the circle on AB as diameter is

Find the 2xx2 mtrix X if[[x_1,x_2], [y_1,y_2]]-[[2,0],[0,2]]=[[3,5],[1,2]] determine x_1,x_2,y_1,y_2.

I) For x in (2, 4) the sign of x^(2)-6x+5 is negative II) Forx in (-oo, 2)uu(4, oo) the sign of x^(2)-6x+5 is positive then Which of the above statement (s) is /are true

A coin is biased such that the probability of getting head is thrice to that of getting a tail. If such coin is tossed twice find the probability of getting one head exactly.

A particle moves along the curve 6y = x^(3) +2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.

Evaluate int_(0)^(pi)(xdx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)

Another name for the mean of a probability distribution is expected value.

If y =2 Tan ^(-1) ((x sqrt2)/( 1 - x ^(2))) + log ((1+ x sqrt2 + x ^(2))/(1 - x sqrt2 + x ^(2)))then (dy)/(dx) =

Using properties of determinants in Exercise 11 to 15 prove that |{:(1,1+p,1+p+q),(2,3+2p,4+3p+2q),(3,6+3p,10+6p+3q):}|=1

Find the ratio of the areas in which the curve y=[(x^3)/(100)+x/35] divides the circle x^(2)+Y^(2)-4x+2y+1=0. (where, [.] denotes the greated integer function).

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(oo)f(x+(1)/(x))(logx)/(x)dx=...........

Let a kind of bacteria grow in such a way that at time t sec, there aret^(3//2) bacteria. Find tha rate of growth at time t = 4 hours.

Area of the triangle in the Argand diagram formed by the complex numbers z, iz, z+iz, where z=x+iy is

L A = NxxN and ** be the binary operation on A defined by (a,b) "*" (c,d) = (a+c,b+d)Show that ** is commutative and associative . Find the identity element for ** on A , if any.

Draw the graph of the following function. f(x-1)

Draw the graph of the following function. f(x+1)

If x^(2) + y^(2) + 2gx + 2fy = 0 represents a circle with cerntre (-4, -3) then find g, f and the radius of the circle.

If z_(1),z_(2),z_(3) are collinear and z_(3)-z_(1)/(z_(2)-z_(1)) is purely real, then arg(z_(3)-z_(1)/(z_(2)-z_(1)))

Match the following :

Match the following :

intdx/(x(x^4+1))

If f(x)=|(1-x, -1,0),(2,3-x, 1),(4,-2,5-x)| , numberof realroots of f(x)=0 is ____

L A = NxxN and ** be the binary operation on A defined by (a,b) "*" (c,d) = (a+c,b+d)Show that is commutative and associative . Find the identity element for on A , if any.