28278 + Interview Questions in Maths in Class 12

1.	If f(x) = (ax+b)e^(x) satisfies the equation : f(x) = int_(0)^(x)e^(x)""^(y)f'(y)dy-(x^(2)-x+1) e^(x), find (a^(2)+ b^(2))
Answer» SOLUTION :N//A

Discussion

2.	LetZdenotethe setof allintegersand A = { (a,b) : a^2 +3b^2 = 28 ,a,b in Z } andB= {(a,b ):agtb, in Z} . Thenthe numberof elements inA nn Bis
Answer» 2 3 4 6 Answer :D

Discussion

3.	On Z, define R as follows: a, b in Z, aRb if 7\|(a^(2) -b^(2)), then R is
Answer» REFLEXIVE and TRANSITIVE only reflexive and SYMMETRIC only symmetric and transitive only an EQUIVALENCE relation Answer :D

Discussion

4.	Evaluate [[a,a^2-bc,1],[b,b^2-ac,1],[c,c^2-ab,1]]
Answer» SOLUTION :`[[a,a^2-bc,1],[B,b^2-ac,1],[C,c^2-ab,1]]` =`[[a-b,a^2-bc-b^2+ca,0],[b-c,b^2-ca-c^2+ab,0],[c,c^2-ab,1]]` `(R_1~~R_1-R_2, R_2~~R_2-R_3)` =`(a-b)(b-c)[[1,a+b+c,0],[1,a+b+c,0],[c,c^2-ab,1]]` =`(a-b)(b-c)xx0 (because R_1=R_2)`

Discussion

5.	lim_(x to 0) (e^(x) - e^(sin x)/ ((x - sin x))is equal to
Answer» `-1//2` `1//2` 1 `3//2` ANSWER :B

Discussion

6.	Statement 1 : There are infinite points from which two mutually perpendicular tangents can be drawn to the hyperbola(x^(2))/(9)-(y^(2))/(16) = 1 Statement 2: The locus of point of intersection of perpendicular tangent at one of the points of contact is
Answer» ` x+sqrt3y + 2=0 ` ` 3X- 2sqrt2y -3=0 ` ` 3x- sqrt2y + 6=0 ` `x-sqrt3y +2=0` ANSWER :D

Discussion

7.	One card is lost from a pack of 52 cards, then Statement-1 : If two cards are drawn then probability that lost card is Ace if both are Ace cards is 1/17 Statement-2 : If two cards are drawn then probability that lost card is Spade if both cards are Spade is (1)/(17).
Answer» STATEMENT-1 is TRUE, Statement-2 is true, Statement-2 is a correct EXPLANATION for statement -1 Statement-1 is true, Statement-2 is true, Statement-2 is Not acorrect explanation for statement -1 Statement-1 is true, Statement-2 is False Statement-1 is False, Statement-2 is true Answer :B

Discussion

8.	If the median and the range of four numbers {x,y,2x,+y,x-y}, where 0 lt y lt x lt 2y are 10 and 28 respectively, then the mean of numbers is
Answer» 18 10 5 14 Answer :D

Discussion

9.	cot^-1(-x) = pi - cot^-1x , x in R
Answer» ANSWER :T

Discussion

10.	If bar(a),bar(b) and bar( c ) are perpendicualr to bar(b)+bar( c ),bar( c )+bar(a) and bar(a)+bar(b) respectively and \|bar(a)+bar(b)\|=6,\|bar(b)+bar( c )\|=8 and \|bar( c )+bar(a)\|=10 then \|bar(a)+bar(b)+bar( c )\| =……………….
Answer» `5sqrt(2)` 50 `10sqrt(2)` 10 Answer :D

Discussion

11.	You note that your officer is happy with 60% of your calls, so, you assign a probability of his being happy on your visit of 0.6 . You havenoticed also that if he is happy, he accedesto your request with a probability 0 . 4 , whereasif he is not happy he accedes to the request with a probability of 0.1 . You call one day and he accedes to your request . What is the probability that your office was happy ?
Answer» ANSWER :`(6)/(7)= 0.86`

Discussion

12.	Following is the graph ofy = f(x). (##CEN_GRA_C01_S01_005_Q01.png" width="80%"> Find the roots of the equationf(x) = 0, f(x) = 4 and f(x) = 10.
Answer» Solution : (a) The root of the EQUATION F(x) = 0 occurs where graphy= f(x) meets the x-axis. From the graph, roots of f(x) = 0 are x =- 1 and x = 2. (b) The root of the equation f(x) = 4 occurs where the height of the graph is 4. HENCE the roots of f(x) = 0 are x = - 2 and x = 3. (c) The root of the equation f(x) = 10 occurs where the height of the graph is 10. Hence the roots of f(x) = 0are x =- 3 andx =4.

Discussion

13.	Are the following sets relation ? phi from A to B . Determinethe domain range and inverse of each of the relations mentioned above.
Answer» SOLUTION :`PHI` from A to B is a RELATION.

Discussion

14.	Consider the family of planes x +y+z=c where c is is a parameter intersecting the coordinate axes at P,Q and R and alpha, beta and gamma are the angles made by each member of this family with positive x,y and z-axes. Which of the following interpretations hold good for this family?
Answer» Each member of this family is equally inclined with coordinate axes `sin ^(2) alpha + sin ^(2) beta + sin ^(2) gamma =1` `cos ^(2) alpha + cos ^(2) beta + cos ^(2) gamma =2` For `c=3` area of the `Delta PQR` is `3sqrt3` sq units ANSWER :A::B::C

Discussion

15.	a.b' + b.c' + c.a' =
Answer» 0 1 2 3 Answer :A

Discussion

16.	If the p^(th) term if an A.P. is q and the q^(th) term of an A.P is p then the r^(th) term is
Answer» <P>`Q - p + R` `p - q + r` `p + q + r` `p + q - r` ANSWER :D

Discussion

17.	Write the distance of the point (3,1,5) from y-axis.
Answer» SOLUTION :A LINE PERPENDICULAR to xy-plane MAKES an ANGLE `0orpi` with z-axis.

Discussion

18.	Find the area of the triangle whose vertices are (3,8),(-4,2) and (5,1)
Answer» ANSWER :`(61)/2`

Discussion

19.	Evaluate the following definite intergrals as limit of sums. overset(b) underset(a)(x+1)dx
Answer» ANSWER :`(35)/(2)`

Discussion

20.	Find the 5^("th")" term of "(7+(8y)/(3))^(7//4).
Answer» ANSWER :`(7^(7/4) .10y^4)/(3.(21)^3)`

Discussion

21.	For a 2^(nd) order determinant abs(A)=abs(a_(ij)), find a_(12)A_(11)+a_(22)A_(21)
Answer» `ABS(A)` 0 1 `-abs(A)` ANSWER :B

Discussion

22.	The value of 4sin85^@cos55^@cos65^@ is : -
Answer» `cos85^@` `cos5^@` `(sqrt3+1)/(2SQRT2)` `(sqrt3-1)/(2sqrt2)`

Discussion

23.	Solvethe equation 6x^3 -11 x^2 +6x -1=0
Answer» ANSWER :`-1/2,2,1/3`

Discussion

24.	If \|{:(ah+bg,g,ab+hc),(ab+bf,f,hb+bc),(af+bc,c,gb+fc):}\|=K\|{:(ah+bg,a,h),(ab+bf,h,b),(af+bc,g,f):}\| then find the value of k
Answer» ANSWER :a

Discussion

25.	Find the points on the curve y = x 3 at which the slope of the tangent is equal to the y-coordinate of the point.
Answer» ANSWER :(0, 0), (3, 27)

Discussion

26.	Let [{:(,a,o,b),(,1,e,1),(,c,o,d):}]=[{:(,0),(,0),(,0):}] where a,b,c,d,e in (0,1) then number of such matrix A which system of equationa AX=0 have unique solution.
Answer» 16 6 5 none of these Answer :B

Discussion

27.	A resonance tube is old and has jagged end. It is still used in the laboratory to determine. Velocity of sound in air. A tuning fork of frequency 512Hz produces first resonance when the tube is filled with wtaer to a mark11 cm below a reference mark, near the open end of the tube. the experiment is repeated with another fork of frequency 256Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. the velocity of sound in air, obtained in the experiment, is close to :
Answer» `322ms^(-1)` `341ms^(-1)` `335ms^(-1)` `328ms^(-1)` SOLUTION :NA

Discussion

28.	Prove that{:[( b+c,a,a), ( b,c+a,b),( c,c,b+a) ]:}
Answer» ANSWER :4ABC

Discussion

29.	16/(2!)+(64)/(3!) + (256)/(4!) + ..... oo=
Answer» `E^(4) -1 ` `e^(4) -2 ` `e^(4) -4 ` `e^(4) -5 ` ANSWER :D

Discussion

30.	Prove that \|[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]\| is independent of theta
Answer» SOLUTION :`X(-x^2-1)+x`, in which INDEPENDENT of `THETA`.

Discussion

31.	Solve the following linear programming problems graphically : Maximise : Z = 5x +7y subject to constraints x+y le 4, 3x+8y le 24, 10x+7y le 35, x, y ge 0.
Answer» ANSWER :MAXIMUM Z = 24.8 at `(8/5, 12/5)`

Discussion

32.	If A =[(3,2),(0,1)] then A^(-3) is
Answer» `(1)/(27) [(1,-26),(0,-27)]` `(1)/(27) [(-1,-26),(0,-27)]` `(1)/(27) [(1,-26),(0,27)]` `(1)/(27) [(-1,26),(0,-27)]` ANSWER :C

Discussion

33.	Straight line \|(2-x-y,4,4),(2x,x-y-2,2x),(2y,2y,y-2-x)\|=0 passes through the fixed point
Answer» (-2,-2) (-2,0) (0,-2) (-1,-1) ANSWER :D

Discussion

34.	If x^(2)+y^(2)=25, "then" log_(5)["max"(3x+4y)] is
Answer» 2 3 4 5 Answer :A

Discussion

35.	Differentiate the following with respect to x: log [log (log x^(5))]
Answer» Answer :`(5x^(4))/(LOG (x^(5)).log (log x^(5)))`

Discussion

36.	(1+cos""(pi)/(8))(1+cos""(2pi)/(8))(1+cos""(3pi)/(8))(1+cos""(4pi)/(8))(1+cos""(5pi)/(8))(1+cos""(6pi)/(8))(1+cos""(7pi)/(8))=
Answer» `(1)/(8)` `(1)/(16)` `(1)/(32)` `(1)/(64)` Answer :B

Discussion

37.	If {(alpha+1)(beta-1)+(beta+1)(alpha-1)}a+(alpha-1)(beta-1)=0 and a(alpha+1)(beta+1)-(alpha-1)(beta-1)=0 Also, let A={(alpha+1)/(alpha-1),(beta+1)/(beta-1)} and B={(2alpha)/(alpha+1),(2beta)/(beta+1)}. If A cap B != phithen find all the permissible values of the parameter 'a'.
Answer» ANSWER :`ain {-1,1+i,1-i}`

Discussion

38.	The value of ((50),(6))-((5),(1))((40),(6))+((5)/(2))((30),(6))-((5),(3))((20),(6))+((5),(4))((10),(6)) where ((n),(r )) denotes "^(n)C_(r ), is
Answer» `15625` `0` `1000000` `2250000` Solution :`(d)` `'^(50)C_(6)-^(5)C_(1)^(40)C_(6)+^(5)C_(2)^(30)C_(6)-^(5)C_(3)^(20)C_(6)+^(5)C_(4)^(10)C_(6)` `="coefficient of" x^(6) "in" ['^(5)C_(0)(1+x)^(50)-^(5)C_(1)(1+x)^(40)+^(5)C_(2)(1+x)^(30)-^(5)C_(3)(1+x)^(20)+^(5)C_(4)(1+x)^(10)-^(5)C_(5)(1+x)^(0)]` `="coefficient" x^(6) "in" [(1+x)^(10)-1]^(5)` `="coefficient" x^(6) "in" ('^(10)C_(1)x+^(10)C_(2)x^(2)+....)^(5)` `="coefficient" x "in" ('^(10)C_(1)x+^(10)C_(2)x+....)^(5)` `='^(5)C_(1)('^(10)C_(2))('^(10)C_(1))^(4)=2250000`

Discussion

39.	Let vec(a)=hati+hatj+hatk,vec(b)=hati and vec( c )=c_(1)hati+c_(2)hatj+c_(3)hatk. Then If c_(2)=-1 and c_(3)=1. Show that no value of c_(1) can make vec(a),vec(b) and vec( c ) coplanar.
Answer» Answer :Hence, no VALUE of `c_(1)` can make `vec(a),vec(B)` and `vec( C )` COPLANAR.

Discussion

40.	Construct a 3xx2 matrix whose elements are given by a_(ij)=(1)/(2)\|i-3j\|.
Answer» Answer :`A=[(1,(5)/(2)),((1)/(2), 2),(0,(3)/(2))]`

Discussion

41.	A couple has two children. Find the probability that both are male if it is known that atleast one of them is a male child.
Answer» ANSWER :`(1)/(3)`

Discussion

42.	Find the derivative of the following functions 'ab initio', that is, using the definition.1/x
Answer» SOLUTION :LET y=1/x Then `dy/dx=lim_(deltaxto0)(1/(x+deltax)-1/x)/(deltax)` `=lim_(deltaxto0)(x-(x+deltax))/(x(x+deltax)cdotdelta x)` `=lim_(deltaxto0)1/(x(x+deltax))=-1/x^2`

Discussion

43.	Simple living and high thinking' is the base of -
Answer» AMERICAN Civilization Indian Civilization European Civilization None of these Answer :B

Discussion

44.	Show that the points A(1, -2, -8) B (5, 0, -2) and C(11, 3, 7) are collinear and find the ratio in which B divides AC.
Answer» ANSWER :`2:3`

Discussion

45.	If costheta+cosphi=alpha,cos2theta+cos2phi=beta and cos3theta+cos3phi=gamma, then
Answer» `cos^(2)theta+cos^(2)phi=1+(beta)/(2)` `costheta.cosphi=(ALPHA^(2))/(2)-(beta+2)/(4)` `2alpha^(2)+gamma=3alpha(1+beta)` `alpha+beta+gamma=2alphabetagamma` ANSWER :A::B::C

Discussion

46.	Using L Hospital rule evaluate lim_(xrarr0) (e^(x)-1-x)/(x(e^(x)-1))
Answer» ANSWER :`(1)/(2)`

Discussion

47.	If two cards are drawn from pack, find the probability atleast one king card.
Answer» ANSWER :`(33)/(221)`

Discussion

48.	If a circle passes through (1,2) and cuts x^2+y^2=4,orthogonally then the locus of the centre is
Answer» 2x+4y-9=0 x+y+3=0 x+y-9=0 2x+3y=7 Answer :A

Discussion

49.	A solution of 8% boric acid is to be diluted. By adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid . If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added ?
Answer» ANSWER :`320 LT X lt 1280`

Discussion

50.	Find the number of terms in the sequence 4,7,10,13…….,82.
Answer» ANSWER :`N =27`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If f(x) = (ax+b)e^(x) satisfies the equation : f(x) = int_(0)^(x)e^(x)""^(y)f'(y)dy-(x^(2)-x+1) e^(x), find (a^(2)+ b^(2))

LetZdenotethe setof allintegersand A = { (a,b) : a^2 +3b^2 = 28 ,a,b in Z } andB= {(a,b ):agtb, in Z} . Thenthe numberof elements inA nn Bis

On Z, define R as follows: a, b in Z, aRb if 7|(a^(2) -b^(2)), then R is

Evaluate [[a,a^2-bc,1],[b,b^2-ac,1],[c,c^2-ab,1]]

lim_(x to 0) (e^(x) - e^(sin x)/ ((x - sin x))is equal to

Statement 1 : There are infinite points from which two mutually perpendicular tangents can be drawn to the hyperbola(x^(2))/(9)-(y^(2))/(16) = 1 Statement 2: The locus of point of intersection of perpendicular tangent at one of the points of contact is

One card is lost from a pack of 52 cards, then Statement-1 : If two cards are drawn then probability that lost card is Ace if both are Ace cards is 1/17 Statement-2 : If two cards are drawn then probability that lost card is Spade if both cards are Spade is (1)/(17).

If the median and the range of four numbers {x,y,2x,+y,x-y}, where 0 lt y lt x lt 2y are 10 and 28 respectively, then the mean of numbers is

cot^-1(-x) = pi - cot^-1x , x in R

If bar(a),bar(b) and bar( c ) are perpendicualr to bar(b)+bar( c ),bar( c )+bar(a) and bar(a)+bar(b) respectively and |bar(a)+bar(b)|=6,|bar(b)+bar( c )|=8 and |bar( c )+bar(a)|=10 then |bar(a)+bar(b)+bar( c )| =……………….

Following is the graph ofy = f(x). (##CEN_GRA_C01_S01_005_Q01.png" width="80%"> Find the roots of the equationf(x) = 0, f(x) = 4 and f(x) = 10.

Are the following sets relation ? phi from A to B . Determinethe domain range and inverse of each of the relations mentioned above.

Consider the family of planes x +y+z=c where c is is a parameter intersecting the coordinate axes at P,Q and R and alpha, beta and gamma are the angles made by each member of this family with positive x,y and z-axes. Which of the following interpretations hold good for this family?

a.b' + b.c' + c.a' =

If the p^(th) term if an A.P. is q and the q^(th) term of an A.P is p then the r^(th) term is

Write the distance of the point (3,1,5) from y-axis.

Find the area of the triangle whose vertices are (3,8),(-4,2) and (5,1)

Evaluate the following definite intergrals as limit of sums. overset(b) underset(a)(x+1)dx

Find the 5^("th")" term of "(7+(8y)/(3))^(7//4).

For a 2^(nd) order determinant abs(A)=abs(a_(ij)), find a_(12)A_(11)+a_(22)A_(21)

The value of 4sin85^@cos55^@cos65^@ is : -

Solvethe equation 6x^3 -11 x^2 +6x -1=0

If |{:(ah+bg,g,ab+hc),(ab+bf,f,hb+bc),(af+bc,c,gb+fc):}|=K|{:(ah+bg,a,h),(ab+bf,h,b),(af+bc,g,f):}| then find the value of k

Find the points on the curve y = x 3 at which the slope of the tangent is equal to the y-coordinate of the point.

Let [{:(,a,o,b),(,1,e,1),(,c,o,d):}]=[{:(,0),(,0),(,0):}] where a,b,c,d,e in (0,1) then number of such matrix A which system of equationa AX=0 have unique solution.

Prove that{:[( b+c,a,a), ( b,c+a,b),( c,c,b+a) ]:}

16/(2!)+(64)/(3!) + (256)/(4!) + ..... oo=

Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is independent of theta

Solve the following linear programming problems graphically : Maximise : Z = 5x +7y subject to constraints x+y le 4, 3x+8y le 24, 10x+7y le 35, x, y ge 0.

If A =[(3,2),(0,1)] then A^(-3) is

Straight line |(2-x-y,4,4),(2x,x-y-2,2x),(2y,2y,y-2-x)|=0 passes through the fixed point

If x^(2)+y^(2)=25, "then" log_(5)["max"(3x+4y)] is

Differentiate the following with respect to x: log [log (log x^(5))]

(1+cos""(pi)/(8))(1+cos""(2pi)/(8))(1+cos""(3pi)/(8))(1+cos""(4pi)/(8))(1+cos""(5pi)/(8))(1+cos""(6pi)/(8))(1+cos""(7pi)/(8))=

If {(alpha+1)(beta-1)+(beta+1)(alpha-1)}a+(alpha-1)(beta-1)=0 and a(alpha+1)(beta+1)-(alpha-1)(beta-1)=0 Also, let A={(alpha+1)/(alpha-1),(beta+1)/(beta-1)} and B={(2alpha)/(alpha+1),(2beta)/(beta+1)}. If A cap B != phithen find all the permissible values of the parameter 'a'.

The value of ((50),(6))-((5),(1))((40),(6))+((5)/(2))((30),(6))-((5),(3))((20),(6))+((5),(4))((10),(6)) where ((n),(r )) denotes "^(n)C_(r ), is

Let vec(a)=hati+hatj+hatk,vec(b)=hati and vec( c )=c_(1)hati+c_(2)hatj+c_(3)hatk. Then If c_(2)=-1 and c_(3)=1. Show that no value of c_(1) can make vec(a),vec(b) and vec( c ) coplanar.

Construct a 3xx2 matrix whose elements are given by a_(ij)=(1)/(2)|i-3j|.

A couple has two children. Find the probability that both are male if it is known that atleast one of them is a male child.

Find the derivative of the following functions 'ab initio', that is, using the definition.1/x

Simple living and high thinking' is the base of -

Show that the points A(1, -2, -8) B (5, 0, -2) and C(11, 3, 7) are collinear and find the ratio in which B divides AC.

If costheta+cosphi=alpha,cos2theta+cos2phi=beta and cos3theta+cos3phi=gamma, then

Using L Hospital rule evaluate lim_(xrarr0) (e^(x)-1-x)/(x(e^(x)-1))

If two cards are drawn from pack, find the probability atleast one king card.

If a circle passes through (1,2) and cuts x^2+y^2=4,orthogonally then the locus of the centre is

A solution of 8% boric acid is to be diluted. By adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid . If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added ?

Find the number of terms in the sequence 4,7,10,13…….,82.