28278 + Interview Questions in Maths in Class 12 Page 219 InterviewSolution

10901.	If \|(x,2),(18,x)\|=\|(6, 2),(18,6)\|, then x is equal toa) 6 b) pm6 c) -6 d) 0
Answer» 6 `PM6` `-6` 0 Solution :N/A

Discussion

10902.	The orthocentre of triangle formed by thelines x + 3y = 10 and 6x^(2) + xy - y^(2) = 0 is
Answer» `(1 , 3)` `(3 , 1)` `(-1 , 3)` `(1 , -3)` ANSWER :A

Discussion

10903.	Let A be a non-singular square matrix of order 3xx3.Then \|adj A\| is ...
Answer» \|A\| `\|A\|^2` `\|A\|^3` 3 \|A\| Answer :B

Discussion

10904.	If a is the number of ways of selecting 3 vowels, 2 consonents, b is the number of ways of selecting 2 vowels, 3 consonents and c is the number of ways of selecting 4 vowels, 1 consonent from the letters of the word EQUATION then descending order of a, b, c is
Answer» a, B, C b, c, a c, a, b a, c, b Answer :D

Discussion

10905.	Find the area of the region bounded by x^(2) = 4y, y = 2, y = 4and the y-axis in the first quadrant.
Answer» ANSWER :`(32-8sqrt2)/(3)`

Discussion

10906.	Find the values of the following integrals int_(0)^(5) x^(3) (25-x^(2))^(7//2) dx
Answer» ANSWER :`(2xx5^(11))/(99)`

Discussion

10907.	If I= int_(0)^(pi) (x^(2) sin x)/( (2x-1) (1+ cos^(2) x) ) dx then the value of I is (pi=3.14)
Answer» ANSWER :`2.46`

Discussion

10908.	A bond pays interest at a rate of 3% compounded annually. How long it take an initial investment to double ?
Answer» Solution :Each YEAR, the investment GROWS by factor of 1.03. Therefore, the growth factor after n year is `1.03^(n)`. SINCE the investment doubles when its growth factor is 2, we need to solve the EQUATION `1.03^(n)=2`. Take the log of both sides to get `nlog1.03=LOG2`. It follows that `n=(log2)/(log1.03)~~23.45` years.

Discussion

10909.	Find the remainder when polynomial P(x)=x^3+3x^2+3x+1 id divided by 5+2x
Answer» ANSWER :`5/6logabs(3X^(2)+2x+1)-11/(3sqrt2)TAN^(-1)((3x+1)/(sqrt2))+C`

Discussion

10910.	60 employees in an office were asked about their preference for tea and coffee. It was observed that for every 3 people who prefer tea, there are 2 who prefer coffee. For every 6 people who prefer tea, there are 2 who drink both of tea and coffee. For every 6 people who prefer tea, there are 2 who drink both of tea and coffee. The number of people who drink both is the same as those wo drink neither. How many people drink both tea adn coffee?
Answer» 10 12 14 16 Answer :B

Discussion

10911.	int [ (1)/(log x) - (1)/((log x)^(2))]dx =
Answer» x log x + C `(x)/(log x)` + c `x.(log x)^(2) ` +c `(x)/((log x)^(2)) + c ` Answer :B

Discussion

10912.	The vector equation of the plane passing through the intersection of the planes bar r.(3hati+4hatj)=1" and "bar r.(hati-hatj-hatk)=4 and the point (1,2,-1) is
Answer» `BARR.(11hati+3hatj+5hatk)=11` `barr.(11hati-3hatj-5hatk)=11` `barr.(11hati+3hatj+5hatk)=22` `barr.(11hati+3hatj-5hatk)=22` ANSWER :D

Discussion

10913.	Apoint A is on the line vec r = (1- 3mu ) hat i+ (mu - 1) hat j + (2 + 5 mu ) hat k. B(3,2,6) is a point of the plane . If the vector bar(AB) is parallel to the plane x-4y+3z = 1then the value of mu is ............
Answer» `1/4` `1/8` `1/2` `- (1)/(4)` ANSWER :A

Discussion

10914.	Statement: For any△ABC, the expression (b+c-a)(c+a-b)(a+b-c)-abc is negative
Answer» TTT FTT TFT TTF ANSWER :A

Discussion

10915.	Simplify the following(cis5alpha)/(cis alpha)
Answer» ANSWER :`CIS 4 ALPHA`

Discussion

10916.	A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is ..........
Answer» `(3)/(28)` `(2)/(21)` `(1)/(28)` `(167)/(168)` Answer :A

Discussion

10917.	If A, B, C and D are the points with position vectors hati+hatj-hatk,2hati-hatj+3hatk,2hati-3hatk and 3hati-2hatj+hatk respectively, then find the projection of vec(AB) along vec(CD).
Answer» ANSWER :`SQRT(21)`

Discussion

10918.	Evaluate the determinants(i){:\|( 3,-1,-2),( 0,0,-1),( 3,-5,0) \|:} "" (ii) {:\|( 3,-4,5),( 1,1,-2),(2,3,1) \|:} (iii) {:\|( 0,1,2),(-1,0,-3),(-2,3,0)\|:}""(iv) {:\|(2,-1,-2),(0,2,-1),(3,-5,0)\|:}
Answer» ANSWER :` (i) -12, (ii) 46, (iii) 0, (IV) 5`

Discussion

10919.	If int (sin 2x + cos 2x) dx = (1)/(sqrt(2)) sin (2x - c) + a then c =
Answer» `pi//4` `pi//3` `pi//6` `pi//2` ANSWER :A

Discussion

10920.	Form the differential equation for the given solution: b^(2) x^(2) + a^(2) y^(2) =a^(2)b^(2)
Answer»

Discussion

10921.	If A and B are two events such that A sub B and P(B) ne 0, then which of the following is correct?
Answer» `P(A \| B)= (P(B))/(P(A))` `P(A \| B) LT P(A)` `P(A \| B) ge P(A)` NONE of these Answer :B

Discussion

10922.	Evaluate the following integrals int sec^2x/(cosec^2 x) dx
Answer» SOLUTION :`INT sec^2x/(cosec^2x) DX = int sin^2x/cos^2x dx = int tan^2x dx = int (sec^2x - 1) dx = tanx-x+c`

Discussion

10923.	The value of I=int(pi//2)^(5pi//2)(e^(tan^(-1)(sinx)))/(e^(tan^(-1)(sinx))+e^(tan^(-1)(cosx)))dx, is
Answer» 1 `PI` E `pi//2` ANSWER :B

Discussion

10924.	Erythroblastosis foetalis can occurs if :-
Answer» MOTHER is RH -ve and FOETUS is Rh +ve Both mother and foetus are Rh -ve Mother is Rh +ve and foetus is Rh -ve Both mother and foetus are Rh + ve Answer :A

Discussion

10925.	The determinant \|{:(b^2-ab,b-c,bc-ac),(ab-a^2,a-b,b^2-ab),(bc-ac,c-a,ab-a^2):}\| equals …….
Answer» ANSWER :`1/2(a^3+b^3+c^3-3abc)[(a-b)^2+(b-c)^2+(c-a)^2]`

Discussion

10926.	A letter is known to have come from either 'TATANAGAR' or 'CALCUTTA'. On the envelope just two consecutive letters, TA are visible. Find the probability that the letter has come from 'CALCUTTA'.
Answer» ANSWER :`(4)/(11)`

Discussion

10927.	Let I=int_0^1(x^3cos3x)/(2+x^2)dx. Then
Answer» `-(1)/(2)ltIlt(1)/(2)` `-(1)/(3)ltIlt(1)/(3)` `-1ltIlt1` `-(3)/(2)ltIlt(3)/(2)` ANSWER :A::B::C::D

Discussion

10928.	Let f:[2,infty) rarr [1, infty) defined by f(x)=2^(x^(4)-4x^(2)) and g:[pi/2,pi] rarr A defined by g(x)=(sinx+4)/(sinx-2) be two invertible functions. The domain of f^(-1)g^(-1)(x) is
Answer» [-5, sin 1] `[-5,(sin 1)/(2-sin1)]` `[-5,-((4+sin 1))/(2-sin1)]` `[-((4+sin 1))/(2-sin1), -2]` ANSWER :C

Discussion

10929.	If bar(a) = 2bar(i) +bar(j)-3bar(k), bar(b) = bar(i) -2bar(j)+bar(k), bar(C) =- bar(i) +bar(j)-4bar(k), bar(D) = bar(i) +bar(j)+bar(k), then compute \|(bar(a)xxbar(b))xx(bar(c)xxbar(d))\|.
Answer» ANSWER :`5sqrt(114)`

Discussion

10930.	An arch on a road is in the shape of semi-ellipse. The breadth of the road is 30 feet. A man 6 feet tall just touches the arch when he stands 2 feet the side . i. Assuming the road level as x-axis (major axis). Find the point C. ii. What is the maximum height of arch (minor axis)?
Answer» ANSWER :i. (13,6) `45/(SQRT14)` FEET.

Discussion

10931.	If 1,2,3aretherootsofax^3 +bx^2+ cx+d=0then therootsof ax sqrt(x) + bx +c sqrt (x )+d=0are
Answer» 2,3,4 1,4,9 `2,4,6` `1,sqrt(2) , sqrt(3)` ANSWER :B

Discussion

10932.	Show that the volume of the largest right circular cone that can beinscribed in a sphere of radius a is (8)/(27) (volume of the shpere).
Answer» ANSWER :The VOLUME is MAXIMUM when `y=(a)/(3)` and the maximum volume is

Discussion

10933.	Select the Correct Option If A is any matrix of order 2×3 and B is any matrix of order 3×4 in order of (AB)' is
Answer» 4×2 2×4 2×3 3×2 Answer :A

Discussion

10934.	Let R={ (1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A={1,2,3,4}. The relation R is
Answer» a FUNCTION REFLEXIVE not symmetric transitive ANSWER :C

Discussion

10935.	If a=hati+2hatk+3hatk, b=-hati+2hatj = hatk and c=3hati+hatj, then p such that a+pb is at right angle to c will be
Answer» 7 9 3 5 Solution :Given,`a+p b ` is at right ANGLE to c. `therefore (a+pb)c=0 RARR ac+p(bc)=0` `rArr 5-p=0 ` `[ because ac = 3+2 = 5 and b*c=-3+2 = -1] ` `therefore p = 5`

Discussion

10936.	If x in (pi, (3pi)/(2)) then int(sqrt(1+sinx)-sqrt(1-sinx))dx=
Answer» `4"COS"(X)/(2)+c` `-4"cos"(x)/(2)+c` `4"sin"(x)/(2)+c` `-4"sin"(x)/(2)+c` ANSWER :3

Discussion

10937.	Evaluate the integral underset(0)overset(4) int (16-x^(2))^(5//2) dx
Answer» ANSWER :`640 PI`

Discussion

10938.	If the straight line represented by ltbgt x cos alpha + y sin alpha = p"____ "(1) inersects the circle x^2 + y^2 = a ^2"____"(2) at the points A and B, then show that the equation of the circle with AB as diameter is (x^2 + y^2 - a^2 ) - 2p(x cos alpha + ysin alpha - p) = 0.
Answer» <P> Answer :(`x^2 + y^2 - a^2 ) - 2p(x cos ALPHA + ysin alpha - p) = 0`.

Discussion

10939.	int (x^(4) + x^(2) +1)/(x^(2) + 1)dx =
Answer» `(X^(3))/(3) + tan^(-1)`x +C `(x^(3))/(3) - tan^(-1)`x +C `(x^(3))/(2) + tan^(-1)`x +C `(x^(3))/(2) + tan^(-1)`x +C Answer :A

Discussion

10940.	{:(,"List-I",,"List-II"),((A),"If mean of 27, 31, 89, 107, 156 is 82, then mean of 130, 126, 68, 50, 1 is",(i),sqrt(2)),((B),"S. D. of scores 1, 2, 3, 4, 5 is",(ii),(n+1)/(2)),((C),"If mode is 18 and mean is 24, then median is" ,(iii),75),((D),"Mean of first n natural number is",(iv),22):}
Answer» Answer :(A) `IFF` (III), (B) `iff` (i), (C ) `iff` (iv), (D) `iff` (II)

Discussion

10941.	Prove that lines ax^2+2hxy+by^2+2gx+2fy+c=0 are equidistant from the origin , if f^4-g^4=c(bf^2-ag^2) . Also , find the product of their distances from the origin .
Answer» ANSWER :`(\|C\|)/SQRT((a-b)^2+4h^2)`

Discussion

10942.	The vector equation of the plane passing through the point (-1, 2,-5) and parallel to the vectors 4hati-hatj+3hatk and hati+hatj-hatk is
Answer» `VECR.(-2hati+7hatj+5hatk)=13` `vecr.(-2hati+7hatj+5hatk)=-13` `vecr.(-2hati+7hatj+5hatk)=-9` `vecr.(-2hati+7hatj+5hatk)=9` ANSWER :C

Discussion

10943.	(2)/(1).(1)/(3)+(3)/(2).(1)/(9)+(4)/(3).(1)/(27)+(5)/(4).(1)/(81)+…oo=
Answer» `log_(E )((3)/(2))` `(1)/(2)+log_(e )((3)/(2))` `(1)/(2)` `(1)/(2)-log_(e )((3)/(2))` ANSWER :B

Discussion

10944.	Determine the range of values of0 in [ 0,2 pi]for which (cos theta ,sin theta ) lies inside the triangle formed by the lines x+y-2=0, x - y - 1 = 0 and 6x + 2y - sqrt(10 = 0
Answer» ANSWER :`THETA in (0,(5pi)/6-tan^(-1)3)`

Discussion

10945.	If the parametric values of two points A and B lyingon the circle x^(2) + y^(2) - 6x + 4y - 12 = 0 are 30^(@) and 60^(@)respectively, then findthe equation of thechord joining A and B
Answer» ANSWER :`2X+ 2Y-(7+5sqrt3) =0`

Discussion

10946.	Evaluate the determinants below in examples number 1 and 2 \|{:(x^2-x+1,x-1),(x+1,x+1):}\|
Answer» ANSWER :`x^3-x^2+2`

Discussion

10947.	Find the values of each of the following : tan^(-1)[ 2 cos (2 "sin"^(-1)1/2)]
Answer» ANSWER :`(PI)/4`

Discussion

10948.	If (3,2) is one limiting point of a coaxal system of circles whose common radical axis is4x + 2y = 11, then the other limiting point is
Answer» (1,1) (2,2) (2,1) (3,2) ANSWER :A

Discussion

10949.	Find int(xdx)/((x+1)(x+2))
Answer» ANSWER :`LOG\|(x+2)/(x+1)\|+C`

Discussion

10950.	A tetrahedron is three dimensional figure bounded by four non coplanar triangular plane. So a tetrahedron has points A,B,C,D as its vertices, which have coordinates (x_(1),y_(1),z_(1)) (x_(2), y_(2), z_(2)) , (x _(3), y_(3) , z_(3)) and (x _(4), y _(4), z _(4)) respectively in a rectangular three –dimensional space. Then the coordinates of its centroid are ((x_(1)+ x_(2) + x _(3) + x_(4))/(4) , (y _(1) + y _(2) + y_(3) + y _(4))/(4), (z_(1) + z_(2) + z_(3)+ z_(4))/(4)). The circumcentre of the tetrahedron is the centre of a sphere passing through its vertices. So, the circumcentre is a point equidistant from each of the vertices of tetrahedron. Let tetrahedron has three of its vertices represented by the points (0,0,0) ,(6,-5,-1) and (-4,1,3) and its centroid lies at the point (1,-2,5). Now answer the following questions The equation of the triangular plane of tetrahedron that contains the given vertices is :
Answer» `x-2Y + z=0` ` 5x - 3y - 2z =0` `x+y+z=0` `x+ 2y + 3Z =0` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in .

If |(x,2),(18,x)|=|(6, 2),(18,6)|, then x is equal toa) 6 b) pm6 c) -6 d) 0

The orthocentre of triangle formed by thelines x + 3y = 10 and 6x^(2) + xy - y^(2) = 0 is

Let A be a non-singular square matrix of order 3xx3.Then |adj A| is ...

If a is the number of ways of selecting 3 vowels, 2 consonents, b is the number of ways of selecting 2 vowels, 3 consonents and c is the number of ways of selecting 4 vowels, 1 consonent from the letters of the word EQUATION then descending order of a, b, c is

Find the area of the region bounded by x^(2) = 4y, y = 2, y = 4and the y-axis in the first quadrant.

Find the values of the following integrals int_(0)^(5) x^(3) (25-x^(2))^(7//2) dx

If I= int_(0)^(pi) (x^(2) sin x)/( (2x-1) (1+ cos^(2) x) ) dx then the value of I is (pi=3.14)

A bond pays interest at a rate of 3% compounded annually. How long it take an initial investment to double ?

Find the remainder when polynomial P(x)=x^3+3x^2+3x+1 id divided by 5+2x

int [ (1)/(log x) - (1)/((log x)^(2))]dx =

The vector equation of the plane passing through the intersection of the planes bar r.(3hati+4hatj)=1" and "bar r.(hati-hatj-hatk)=4 and the point (1,2,-1) is

Apoint A is on the line vec r = (1- 3mu ) hat i+ (mu - 1) hat j + (2 + 5 mu ) hat k. B(3,2,6) is a point of the plane . If the vector bar(AB) is parallel to the plane x-4y+3z = 1then the value of mu is ............

Statement: For any△ABC, the expression (b+c-a)(c+a-b)(a+b-c)-abc is negative

Simplify the following(cis5alpha)/(cis alpha)

A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is ..........

If A, B, C and D are the points with position vectors hati+hatj-hatk,2hati-hatj+3hatk,2hati-3hatk and 3hati-2hatj+hatk respectively, then find the projection of vec(AB) along vec(CD).

Evaluate the determinants(i){:|( 3,-1,-2),( 0,0,-1),( 3,-5,0) |:} "" (ii) {:|( 3,-4,5),( 1,1,-2),(2,3,1) |:} (iii) {:|( 0,1,2),(-1,0,-3),(-2,3,0)|:}""(iv) {:|(2,-1,-2),(0,2,-1),(3,-5,0)|:}

If int (sin 2x + cos 2x) dx = (1)/(sqrt(2)) sin (2x - c) + a then c =

Form the differential equation for the given solution: b^(2) x^(2) + a^(2) y^(2) =a^(2)b^(2)

If A and B are two events such that A sub B and P(B) ne 0, then which of the following is correct?

Evaluate the following integrals int sec^2x/(cosec^2 x) dx

The value of I=int(pi//2)^(5pi//2)(e^(tan^(-1)(sinx)))/(e^(tan^(-1)(sinx))+e^(tan^(-1)(cosx)))dx, is

Erythroblastosis foetalis can occurs if :-

The determinant |{:(b^2-ab,b-c,bc-ac),(ab-a^2,a-b,b^2-ab),(bc-ac,c-a,ab-a^2):}| equals …….

A letter is known to have come from either 'TATANAGAR' or 'CALCUTTA'. On the envelope just two consecutive letters, TA are visible. Find the probability that the letter has come from 'CALCUTTA'.

Let I=int_0^1(x^3cos3x)/(2+x^2)dx. Then

Let f:[2,infty) rarr [1, infty) defined by f(x)=2^(x^(4)-4x^(2)) and g:[pi/2,pi] rarr A defined by g(x)=(sinx+4)/(sinx-2) be two invertible functions. The domain of f^(-1)g^(-1)(x) is

If bar(a) = 2bar(i) +bar(j)-3bar(k), bar(b) = bar(i) -2bar(j)+bar(k), bar(C) =- bar(i) +bar(j)-4bar(k), bar(D) = bar(i) +bar(j)+bar(k), then compute |(bar(a)xxbar(b))xx(bar(c)xxbar(d))|.

An arch on a road is in the shape of semi-ellipse. The breadth of the road is 30 feet. A man 6 feet tall just touches the arch when he stands 2 feet the side . i. Assuming the road level as x-axis (major axis). Find the point C. ii. What is the maximum height of arch (minor axis)?

If 1,2,3aretherootsofax^3 +bx^2+ cx+d=0then therootsof ax sqrt(x) + bx +c sqrt (x )+d=0are

Show that the volume of the largest right circular cone that can beinscribed in a sphere of radius a is (8)/(27) (volume of the shpere).

Select the Correct Option If A is any matrix of order 2×3 and B is any matrix of order 3×4 in order of (AB)' is

Let R={ (1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A={1,2,3,4}. The relation R is

If a=hati+2hatk+3hatk, b=-hati+2hatj = hatk and c=3hati+hatj, then p such that a+pb is at right angle to c will be

If x in (pi, (3pi)/(2)) then int(sqrt(1+sinx)-sqrt(1-sinx))dx=

Evaluate the integral underset(0)overset(4) int (16-x^(2))^(5//2) dx

If the straight line represented by ltbgt x cos alpha + y sin alpha = p"____ "(1) inersects the circle x^2 + y^2 = a ^2"____"(2) at the points A and B, then show that the equation of the circle with AB as diameter is (x^2 + y^2 - a^2 ) - 2p(x cos alpha + ysin alpha - p) = 0.

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

{:(,"List-I",,"List-II"),((A),"If mean of 27, 31, 89, 107, 156 is 82, then mean of 130, 126, 68, 50, 1 is",(i),sqrt(2)),((B),"S. D. of scores 1, 2, 3, 4, 5 is",(ii),(n+1)/(2)),((C),"If mode is 18 and mean is 24, then median is" ,(iii),75),((D),"Mean of first n natural number is",(iv),22):}

Prove that lines ax^2+2hxy+by^2+2gx+2fy+c=0 are equidistant from the origin , if f^4-g^4=c(bf^2-ag^2) . Also , find the product of their distances from the origin .

The vector equation of the plane passing through the point (-1, 2,-5) and parallel to the vectors 4hati-hatj+3hatk and hati+hatj-hatk is

(2)/(1).(1)/(3)+(3)/(2).(1)/(9)+(4)/(3).(1)/(27)+(5)/(4).(1)/(81)+…oo=

Determine the range of values of0 in [ 0,2 pi]for which (cos theta ,sin theta ) lies inside the triangle formed by the lines x+y-2=0, x - y - 1 = 0 and 6x + 2y - sqrt(10 = 0

If the parametric values of two points A and B lyingon the circle x^(2) + y^(2) - 6x + 4y - 12 = 0 are 30^(@) and 60^(@)respectively, then findthe equation of thechord joining A and B

Evaluate the determinants below in examples number 1 and 2 |{:(x^2-x+1,x-1),(x+1,x+1):}|

Find the values of each of the following : tan^(-1)[ 2 cos (2 "sin"^(-1)1/2)]

If (3,2) is one limiting point of a coaxal system of circles whose common radical axis is4x + 2y = 11, then the other limiting point is

Find int(xdx)/((x+1)(x+2))

If the straight line represented by ltbgt x cos alpha + y sin alpha = p" "(1) inersects the circle x^2 + y^2 = a ^2""(2) at the points A and B, then show that the equation of the circle with AB as diameter is (x^2 + y^2 - a^2 ) - 2p(x cos alpha + ysin alpha - p) = 0.