28278 + Interview Questions in Maths in Class 12

1.	int(1)/(x^(4)sqrt(x^(2)+4))dx
Answer» ANSWER :`-(1)/(48)(1+(4)/(x^(2)))^(3//2)+(1)/(16)(1+(4)/(x^(2)))^(1/2)+C`

Discussion

2.	If a=a_(1)i+a_(2)j+a_(3)k, b=b_(1)i+b_(2)j+b_(3)k, c=c_(1)i+c_(2)j+c_(3)k, d=d_(1)i+d_(2)j+d_(3)k and k(a times b) times (c times d)=\|{:(-a, -b, c, d), (a_(1), b_(1), c_(1), d_(1)), (a_(2), b_(2), c_(2), d_(2)), (a_(3), b_(3), c_(3), d_(3)):}\| (formal expression) then
Answer» K = 16 k = 2 k = 4 none of these Answer :B

Discussion

3.	If ax^(2) + 2hxy + by^(2) + 2gx + 2f y + c = 0, then show that (dy)/(dx).(dx)/(dy)=1
Answer» ANSWER :1

Discussion

4.	For the triangle whose sides are x+y-6=0, 7x+y-6=0 and x-7y=6, the co-ordinates of the incentre are:
Answer» `((12)/(5), (6)/(5))` `((3)/(4), -(1)/(7))` `(-1, 5)` None of these ANSWER :A

Discussion

5.	If A={a,b,c,d} mention the type of relations on A given below, which of them are equivalence relations? {(a,a),b,b),(c,c),(d,d),(a,d),(a,c),(d,a),(c,a),(c,d),(d,c)}
Answer» SOLUTION :Reflexive, SYMMETRIC and transitive . Hence it is an equivalence RELATION.

Discussion

6.	Classify 20 m/s towards north measures as scalar and vector.
Answer» SOLUTION :Velocity-vector

Discussion

7.	The sum of the 9 AM's between 2 & 24 is
Answer» 99 1289 117 143 Answer :C

Discussion

8.	Find values of k if area of triangle is 4 sq. units and vertices are ( i) (k,0),(4,0) ,( 0,2) "" ( -2,0),( 0,4),( 0,k )
Answer» ANSWER :`K = 0,8`

Discussion

9.	If f(x)=3x^2 +2x-5, then find f(0)
Answer»

Discussion

10.	The vector in the direction of the vector vec(a)=bar(i)-2bar(j)+2bar(k) that has magnitude 9 is ……..
Answer» `bar(i)-2BAR(J)+2bar(k)` `(bar(i)-2bar(j)+2bar(k))/(3)` `3(bar(i)-2bar(j)+2bar(k))` `9(bar(i)-2bar(j)+2bar(k))` Answer :C

Discussion

11.	If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume
Answer» ANSWER :`3.92 PIM^(3)`

Discussion

12.	For the binomial distribution X with parameters n=12,p=(1)/(2), compute i) P(10leXle12)""ii) P(3 lt X lt 6)
Answer» ANSWER :(i) `(79)/(2^(12))`, (II) `(1287)/(2^(12))`

Discussion

13.	Which of the following volume or capacity of lungs can't be measured directly by the spirometer ?
Answer» RESIDUAL VOLUME Total LUNG capacity Functional residual volume All of the above Answer :A

Discussion

14.	Write the following function in the simplest form : "tan"^(-1)1/(sqrt(x^(2)-1)),\|x\|gt1
Answer» ANSWER :`(PI)/2-sec^(-1)X`

Discussion

15.	Two parabolas with a common vertex and with axes along x-axis and y-axis respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is:
Answer» `4(x+y)+3=0` `8(2x+y)+3=0` `3(x+y)+4=0` `x+2y+3=0` ANSWER :A

Discussion

16.	Solve (dy)/(dx) = (xy-2y^(2))/(x^(2)-3xy)
Answer» ANSWER :`y^(3) = CX^(2) E^(-x/y)`

Discussion

17.	LetA=[[1,-1,1],[2,1,-3],[1,1,1]] Using A^-1 solve the system of equations x-y+z=4 2x+y-3z=0 x+y+z=2
Answer» Solution :[[1,-1,1],[2,1,-3],[1,1,1]][(x),(y),(z)]=[(4),(0),(2)] AX =B `\|A\|=10!=0` `X+A^(-1)B` `A^(-1)=1/10 [[4,2,2],[-5,0,5],[1,-2,3]]` `X=A^(-1)B` x=2,y=-1,z=1

Discussion

18.	A bag contains 4 white and 3 black balls. Another bag contains 5 white and 2 black balls. A pair of dice is rolled. If the sum on the dice is 10,1^(st) bag is selected. Otherwise 2^(nd) bag is selected. Find the probability of drawing white ball if one ball is drawn from the selected bag at random.
Answer» ANSWER :`(59)/(84)`

Discussion

19.	Find the middle term (s) in the expansion of (4x^2 + 5x^3)^17
Answer» ANSWER :`T_9 = ""^17C_8.4^9.5^8x^42`

Discussion

20.	For the differential equation xy(dy)/(dx) = (x + 2)( y + 2), find the solution curve passing through the point (1, -1).
Answer» ANSWER :`y - X + 2 = LOG (x^(2)(y + 2)^(2))`

Discussion

21.	A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg food is given below : {:("Food","Vitamin A","Vitamin B", "Vitamin C"),(X,1,2,3),(Y,2,2,1):} One kg of food X costs Rs. 16 and one kg of food Y costs Rs. 20. Find the least cost of the mixture which will produce the required diet ?
Answer» Answer :The least cost of mixture is RS. 112. It contains 2 KG of food X and 4 kg of food y.

Discussion

22.	If x in [0, pi/2]" and " 1 + log_(2) sin x + log_(2) sin 3x gt 0 then x does not belongs to
Answer» `(0, pi/6)` `(pi/6, pi/4)` `[pi/4, pi/3]` `[pi/3, pi/2]` ANSWER :A,C,D

Discussion

23.	If \|{:(1,2,x),(1,1,1),(2,1,-1):}\|=0 then find x.
Answer» ANSWER :4

Discussion

24.	if 2x+y=16 , x+2z=14 , and 2y+z=12 find the arithmetic mean of x, y and z.
Answer» `8/3` `11/3` `13/3` `14/3` ANSWER :D

Discussion

25.	Minimize and Maximizez=5x+2y subject to constrains -2x-3yle-6,x-2yle 2,3x+2yle 12,-3x+2yle3 and x,yge0
Answer» ANSWER :A::B::C::D

Discussion

26.	If f(x)={(2x+3,x,le1),(k,,x>):} is continuous at x=1 then k=
Answer» 2 5 3 1 Answer :B

Discussion

27.	Arrange the folloiwng in the ascendingorder Maximum value of 3 sin^(2) x+ 4 cos^(2) x(B) Maximum value of2 sin^(2) x - cos 2x (C) Maximum value of cos^(4) x- sin^(4) x(D) Maximum value ofcos^4 x- sin^(4) x
Answer» D,C,B,A A,C,B,D `C,B,D,A` B,A,D,C Answer :D

Discussion

28.	For continuous function f,f'(log_(e)(x)) ={{:(1 ,0lt x le1),(x",",x gt1):}. then f(x)=.....
Answer» `f'(x)={{:(1 ",",x LE 0),(E^(1)-1",",x GT1):}` `f(x)={{:(1 ",",x le 0),(e^(1)-1",",x gt1):}` `f(x)={{:(x ",",x lt 0),(e^(x)",",x gt1):}` `f(x)={{:(x ",",x lt 0),(e^(x)-1",",x gt1):}` ANSWER :D

Discussion

29.	If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)), then the value of (sumsum)_(0leiltjlen) (i/(""^(n)C_(i))+j/(""^(n)C_(j)))
Answer» `an^(2)` `(a^(2)n)/(2)` `a^(2)n` `(n^(2)a)/(2)` Solution :`S = UNDERSET(0leiltjlen)(sumsum)((i)/(.^(n)C_(i))+(j)/(.^(n)C_(j)))` `= underset(0leiltjlen)(sumsum)((n-i)/(.^(n)C_(n-i))+(n-j)/(.^(n)C_(n-j)))` `= n underset(0leiltjlen)(sumsum)((1)/(.^(n)C_(i))+(1)/(.^(n)C_(j)))-S` `rArr S = n/2underset(0leiltjlen)(sumsum) ((1)/(.^(n)C_(i))+(1)/(.^(n)C_(j)))` `=n/2(underset(r=0)OVERSET(n-1)SUM(n-r)/(.^(n)C_(r))+underset(r=1)overset(n)sum(r)/(.^(n)C_(r)))` `= n/2(overset(n)underset(r=0)sum(n)/(.^(n)C_(r))) = (n^(2)a)/(2)`

Discussion

30.	If A+B+C=270^(@) then cos2A+cos2B+cos2C=
Answer» `1-4sinA SINB sinC` `1-4cosA cosB COSC` `4sinA sinB sinC` `1+2 cos A cos B cosC` ANSWER :A

Discussion

31.	A quadrilateral ABCD is divided by the diagonal AC into two triangles of equal areas. If A, B, C are respectively, (3,4),(-3,6),(-5,1), then the locus of D is
Answer» `(x-8y-57)(x-8y+11)=0` `(x-8y-57)(x-8y-11)=0` `(3x-8y-57)(3x-8y+11)=0` `(3x-8y-11)(3x-8y+57)=0` ANSWER :D

Discussion

32.	Statement I The incentre of a triangle formed by the line xcos(pi/9) + y sin (pi/9) = pi x cos ((8pi)/9)+ y sin ((8pi)/9)= pi and x cos ((13pi)/9) + y sin ((13pi)/9) = piis (0,0) Statement ifAny point equisdistant from the given three non - concurrent straight lines in the plane is the incentre of the triangle .
Answer» Statement I is true ,statement II is true , statement II is a CORRECT EXPLANATION for statement I Statement I is true ,STATEMENTII is true statement II is not a correct explanation for statement I Statement I is true ,statement II is false Statement I is false ,statement II is true ANSWER :C

Discussion

33.	The value of sqrt(2-1)/sqrt(2)+3-2sqrt(2)/(4)+5sqrt(2-7)/6sqrt(2)+17-12sqrt(2)/(16)+..+++..+ add.inftyis
Answer» `log_(E)2` `log_(e)sqrt(2)` `log_(e)3` `log_(e)sqrt(3)` ANSWER :a

Discussion

34.	Find the number of partial fractions of (x+2)/(x^(2)(x^(2)-1))
Answer» ANSWER :4

Discussion

35.	Find the matrix X so that X[(1,2,3),(4,5,6)]=[(-7,-8,-9),(2,4,6)]
Answer» ANSWER :`X=[(1,-2),(2,0)]`

Discussion

36.	Find the derivative of x^(2)+x+1 from first principles.
Answer» ANSWER :`2x+1`

Discussion

37.	A bag contans 2017 red balls and 2017 black balls. We remove two balls at a time repeatedly and (1) discard them if they are of some colour (2) discard the black ball and return to the bag the red ball if they are of different colours. Then the probability that thisprocess will terminate with one red ball is 'p' where 3p is______
Answer» SOLUTION :It's a SURE EVENT so `p=1`

Discussion

38.	Integration by partial fraction : int(x^(3)dx)/(x^(2)+a^(2))=....+c
Answer» `(X^(2))/(2)+(a^(2))/(2)log\|x^(2)+a^(2)\|` `(x^(2))/(2)+a^(2)log\|x^(2)+a^(2)\|` `x^(2)+(a^(2))/(2)log\|x^(2)+a^(2)\|` `(x^(2))/(2)-(a^(2))/(2)log\|x^(2)+a^(2)\|` ANSWER :D

Discussion

39.	Prove the tan10^@+tan35^@+tan10^@.tan35^@ = 1
Answer» SOLUTION :We have `TAN45^@=1` or `(TAN35^@+TAN10^@)/(1-tan35^@tan10^@)=1` or `tan35^@+tan10^@=1-tan35^@tan10^@=1`

Discussion

40.	Find dy/dx x^2 + 3y^2 = 5
Answer» Solution :`x^2 + 3y^2 = 5 implies d/dx(x^2) + 3 d/dx(y^2) = 0 implies 2x + 6y dy/dx = 0 implies dy/dx = -x/(3y)`

Discussion

41.	The solution of the equation (dy)/(dx) = e^(-2x) is
Answer» `(e^(-2X))/(4) = y` `(e^(-2x))/(-2) +c = y` `(1)/(4) e^(-2x) + CX^(2) + d = y` `(1)/(4)e^(-2x) + cx + d = y` Answer :B

Discussion

42.	If P-=(a,a,) and Q=(-a,-a,-a), then the equation of the right bisecting plane of seg PQ is
Answer» x-y+z=a x+y+z=3a x+y+z=0 x+y+z+3a=0 Answer :C

Discussion

43.	Three persons A,B,C in order cut a pack of cards replacing them after each cut. The person who first cuts a club shall win a prize. Find the probabilities of their winning.
Answer» ANSWER :`(16)/(37), (12)/(37), (9)/(37)`

Discussion

44.	A public opinion polling agency surveyed 200 government empolyees . The following table shows the ages of the empolyees interviewed.(i) Calculate the mean age of empolyees interviewed. (ii)Compute the mean deviation of the ages about the mean age.
Answer» ANSWER :(i) `=36.5` (II) `=6.65`

Discussion

45.	Fill int the blanks choosing correct answer from the bracket. In Delta ABC if A = 60^@, B = 45^@ , a:b = _____.
Answer» `(SQRT2:SQRT3)` `(sqrt6:2)` `(sqrt3:2)` ANSWER :B

Discussion

46.	Integrate the function 1/(((x-1)(x-2)))
Answer»

Discussion

47.	Let the statement r^2gt100, the statement P(k+1) will he true if
Answer» <P>`P(1)` is true P(2)is true P(K )is true NONEOF these Answer :C

Discussion

48.	Steve uses a certain copy machine that reduces an image by 13%. {:("Quantity A","Quantity B"),("The percent of the original if",75%),("Steve reduces the image by",),("another 13%",):}
Answer» ANSWER :QUANTITY A is LARGER.

Discussion

49.	Find (dy)/(dx) in the following y= sin^(-1) (2x sqrt(1-x^(2))), -(1)/(sqrt2) lt x lt (1)/(sqrt2)
Answer» ANSWER :`(2)/(SQRT(1-x^(2)))`

Discussion

50.	Solve (dy)/(dx) + 3ytan x = 3x^(2) cos^(3) x
Answer» ANSWER :`y SEC^(3) X = x^(3) + C`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

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

If a=a_(1)i+a_(2)j+a_(3)k, b=b_(1)i+b_(2)j+b_(3)k, c=c_(1)i+c_(2)j+c_(3)k, d=d_(1)i+d_(2)j+d_(3)k and k(a times b) times (c times d)=|{:(-a, -b, c, d), (a_(1), b_(1), c_(1), d_(1)), (a_(2), b_(2), c_(2), d_(2)), (a_(3), b_(3), c_(3), d_(3)):}| (formal expression) then

If ax^(2) + 2hxy + by^(2) + 2gx + 2f y + c = 0, then show that (dy)/(dx).(dx)/(dy)=1

For the triangle whose sides are x+y-6=0, 7x+y-6=0 and x-7y=6, the co-ordinates of the incentre are:

If A={a,b,c,d} mention the type of relations on A given below, which of them are equivalence relations? {(a,a),b,b),(c,c),(d,d),(a,d),(a,c),(d,a),(c,a),(c,d),(d,c)}

Classify 20 m/s towards north measures as scalar and vector.

The sum of the 9 AM's between 2 & 24 is

Find values of k if area of triangle is 4 sq. units and vertices are ( i) (k,0),(4,0) ,( 0,2) "" ( -2,0),( 0,4),( 0,k )

If f(x)=3x^2 +2x-5, then find f(0)

The vector in the direction of the vector vec(a)=bar(i)-2bar(j)+2bar(k) that has magnitude 9 is ……..

If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume

For the binomial distribution X with parameters n=12,p=(1)/(2), compute i) P(10leXle12)""ii) P(3 lt X lt 6)

Which of the following volume or capacity of lungs can't be measured directly by the spirometer ?

Write the following function in the simplest form : "tan"^(-1)1/(sqrt(x^(2)-1)),|x|gt1

Two parabolas with a common vertex and with axes along x-axis and y-axis respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is:

Solve (dy)/(dx) = (xy-2y^(2))/(x^(2)-3xy)

LetA=[[1,-1,1],[2,1,-3],[1,1,1]] Using A^-1 solve the system of equations x-y+z=4 2x+y-3z=0 x+y+z=2

A bag contains 4 white and 3 black balls. Another bag contains 5 white and 2 black balls. A pair of dice is rolled. If the sum on the dice is 10,1^(st) bag is selected. Otherwise 2^(nd) bag is selected. Find the probability of drawing white ball if one ball is drawn from the selected bag at random.

Find the middle term (s) in the expansion of (4x^2 + 5x^3)^17

For the differential equation xy(dy)/(dx) = (x + 2)( y + 2), find the solution curve passing through the point (1, -1).

If x in [0, pi/2]" and " 1 + log_(2) sin x + log_(2) sin 3x gt 0 then x does not belongs to

If |{:(1,2,x),(1,1,1),(2,1,-1):}|=0 then find x.

if 2x+y=16 , x+2z=14 , and 2y+z=12 find the arithmetic mean of x, y and z.

Minimize and Maximizez=5x+2y subject to constrains -2x-3yle-6,x-2yle 2,3x+2yle 12,-3x+2yle3 and x,yge0

If f(x)={(2x+3,x,le1),(k,,x>):} is continuous at x=1 then k=

Arrange the folloiwng in the ascendingorder Maximum value of 3 sin^(2) x+ 4 cos^(2) x(B) Maximum value of2 sin^(2) x - cos 2x (C) Maximum value of cos^(4) x- sin^(4) x(D) Maximum value ofcos^4 x- sin^(4) x

For continuous function f,f'(log_(e)(x)) ={{:(1 ,0lt x le1),(x",",x gt1):}. then f(x)=.....

If a_(n) = sum_(r=0)^(n) (1)/(""^(n)C_(r)), then the value of (sumsum)_(0leiltjlen) (i/(""^(n)C_(i))+j/(""^(n)C_(j)))

If A+B+C=270^(@) then cos2A+cos2B+cos2C=

A quadrilateral ABCD is divided by the diagonal AC into two triangles of equal areas. If A, B, C are respectively, (3,4),(-3,6),(-5,1), then the locus of D is

The value of sqrt(2-1)/sqrt(2)+3-2sqrt(2)/(4)+5sqrt(2-7)/6sqrt(2)+17-12sqrt(2)/(16)+..+++..+ add.inftyis

Find the number of partial fractions of (x+2)/(x^(2)(x^(2)-1))

Find the matrix X so that X[(1,2,3),(4,5,6)]=[(-7,-8,-9),(2,4,6)]

Find the derivative of x^(2)+x+1 from first principles.

Integration by partial fraction : int(x^(3)dx)/(x^(2)+a^(2))=....+c

Prove the tan10^@+tan35^@+tan10^@.tan35^@ = 1

Find dy/dx x^2 + 3y^2 = 5

The solution of the equation (dy)/(dx) = e^(-2x) is

If P-=(a,a,) and Q=(-a,-a,-a), then the equation of the right bisecting plane of seg PQ is

Three persons A,B,C in order cut a pack of cards replacing them after each cut. The person who first cuts a club shall win a prize. Find the probabilities of their winning.

A public opinion polling agency surveyed 200 government empolyees . The following table shows the ages of the empolyees interviewed.(i) Calculate the mean age of empolyees interviewed. (ii)Compute the mean deviation of the ages about the mean age.

Fill int the blanks choosing correct answer from the bracket. In Delta ABC if A = 60^@, B = 45^@ , a:b = _____.

Integrate the function 1/(((x-1)(x-2)))

Let the statement r^2gt100, the statement P(k+1) will he true if

Steve uses a certain copy machine that reduces an image by 13%. {:("Quantity A","Quantity B"),("The percent of the original if",75%),("Steve reduces the image by",),("another 13%",):}

Find (dy)/(dx) in the following y= sin^(-1) (2x sqrt(1-x^(2))), -(1)/(sqrt2) lt x lt (1)/(sqrt2)

Solve (dy)/(dx) + 3ytan x = 3x^(2) cos^(3) x