28278 + Interview Questions in Maths in Class 12 Page 26 InterviewSolution

1251.	Let x it [0,2pi] The curve y=secx tanx +2tanx - sec x and the line y=0 intersect in
Answer» No POINTS 2 points 3 points 4 points SOLUTION :4

Discussion

1252.	Does the point (-2,5,3.5) lie inside, outside or on the circle x^2 + y^2 = 25?
Answer» ANSWER :`(-2,5,3.5)` LIE INSIDE the CIRCLE.

Discussion

1253.	In the given figure find minimum force (in N) required to move block up the incline.
Answer» ANSWER :`96.00`

Discussion

1254.	How many number of species are diamagnetic and have the order greater than 2.5. N_(2),N_(2)^(o+),NO^(o+),NO^(Θ),CO,CN^(Θ),KO_(2),Na_(2)O_(2)
Answer» SOLUTION :`{:("Species","Bond order","NUMBER of unpaired ELECTRON"),(N_(2),3,0),(N_(2)^(+),2.5,1),(NO^(+),3,0),(NO^(-),2,2),(CO,3,0),(CN^(-),3,0),(K^(+)//O_(2)^(-),1.5,1),(Na_(2)//O_(2)^(-2),1,0):}` Bond order of `N_(2),NO^(+),CO,CN^(-)` is GREATER than 2.5 and they are diamagentic species.]

Discussion

1255.	Method of integration by parts : The anti derivative of f(x) and e^(x) and the anti derivative of g(x) is cosx, then, intf(x)cosxdx+intg(x)e^(x)dx=............
Answer» `F(X)G(x)+C` `f(x)+g(x)+c` `e^(x)cosx+c` `f(x)-g(x)+c` Answer :C

Discussion

1256.	If the differential equation formed by eliminating a,b,c from the equaiton y = a e^(x) + b e^(2x) + c e^(3x) is Py_(3) + Qy_(2) + Ry_(1)+Sy = 0 then
Answer» P = 1, Q = 6, R=11, S = 6 P=1, Q=-6, R = 11, S=-6 P=1, Q=6, R = -11, S=6 P=1, Q = -6, R = 11, S=6 Answer :B

Discussion

1257.	Solve system of linear equations , using matrix method if exists 3x+2y-2z=3 x+2y+3z=6 2x-y+z=2
Answer» ANSWER :`THEREFORE x=1, y=1 and z=1`

Discussion

1258.	A particle moves along x-axis in such a way that its x-co-ordinate varies with time according to the equation x=8-4t+6t^2.The distance covered by particle between t=0 to t=2/3 sec is : (x is in meter & t is in seconds)
Answer» ZERO `8/3`m `8M` `4/3`m

Discussion

1259.	If sum_(r =0)^(n) ((r+2)/(r+1)) *""^(n)C_(r ) =(255)/(6). Find n.
Answer» SOLUTION :N/A

Discussion

1260.	Find the probability of throwing at most 2 sixes in 6 throws of a single dice.
Answer» ANSWER :`(35)/(18)((5)/(6))^(4)`

Discussion

1261.	Find the distance between the mid point of the line segment bar(AB)and the point (3,-1,2) where A = (6,3,-4), B = (-2,-1,2).
Answer» ANSWER :`SQRT14` UNITS

Discussion

1262.	The point of intersection of the tangents of the parabola y^(2)=16x at the extremities of the chord having (3,4) as its midpoint is
Answer» (1,4) (-1,4) (1,-4) (-1,-4) ANSWER :B

Discussion

1263.	Let x dy/dx + y -e^(x) =0 , y (a) = b. , The solution is given by xy = e^(x) + a, find true or false.
Answer»

Discussion

1264.	If the function f:R rarr R defined by {:{(a((1-cos2x)/(x))",","for" x lt 0 ),("b," ,"for "x=0),((sqrt(x))/(sqrt(4+sqrt(x))-2)",","for "x gt 0):} is continuous at x=0, then a+b=0
Answer» 2 4 6 8 Answer :C

Discussion

1265.	If A,B and C are angles of a triangle, then prove that E=(cos ((B-C)/(2)))/(cos ((B+C)/(2)))+ (cos ((C-A)/(2)))/(cos ((C+A)/(2)))+(cos ((A-B)/(2)))/(cos ((A+B)/(2)))ge6
Answer» ANSWER :`E GE 6`

Discussion

1266.	Show that the relation S in the set R of real numbersdefined as S={(a,b): a, b in R and a le b^(3) } is neither reflexive, nor symmetric, nor transitive.
Answer» ANSWER :Hence, S is NEITHER REFLEXIVE, nor symmetric, nor transitive.

Discussion

1267.	Two different digits are selected at random from the digits 1 through 9 If 3 is one of the digits selected, what is the probability that the sum is odd?
Answer» <P> SOLUTION :`P(A/B)=(P(B CAPA))/(P(B))=(4/36)/(8/36)=1/2` [A and B is in (i)]

Discussion

1268.	Two different digits are selected at random from the digits 1 through 9 If 3 is one of the digits selected, what is the probability that the sum is even?
Answer» <P> SOLUTION :`THEREFORE P(A/B)=(P(BcapA))/(P(B))=(4/36)/(8/36)=1/2` [A NAD B as in (i)]

Discussion

1269.	If the planes vecr(2hati-lambda hatj+hatk)=3 and vecr(4hati+hatj-mu hatk)=5 are parallel, then the value of lambda and mu are:
Answer» `(1)/(2), -2` `-(1)/(2), 2` `-(1)/(2), -2` `(1)/(2), 2 ` SOLUTION :N/A

Discussion

1270.	If the directionratios of two linesare givenby 3lm - 4ln + mn = 0 and l + 2m + 3n = 0 , then the angle between the lines , is
Answer» `pi/6` `pi/4` `pi/6` `pi/2` ANSWER :D

Discussion

1271.	int(dx)/(4x^(2)+3)
Answer» ANSWER :`(1)/(2sqrt(3))tan^(-1)((2X)/(sqrt(3)))+C`

Discussion

1272.	How many line segments have both their endpoints located at the vertices of a given cube?
Answer» ANSWER :28

Discussion

1273.	Let A and B be independent events with P(A)= 0.3 and P( B)= 0.4. Find P( A cap B)
Answer» ANSWER :0.12

Discussion

1274.	On a festival day, a man plans to visit 4 holy temples A,B,C,D in a random order. Find the probability that he visits (i) A before B (ii) A before B and B before C.
Answer» ANSWER :`(i) (1)/(2)` `(II)(1)/(6)`

Discussion

1275.	Construct a 2xx3 matrix having element:a_(ij)= ixxj
Answer» SOLUTION :`a_ji=i+ij` THEMATRIX is `[[axx1,1xx2,1xx3],[2xx1,2xx2,2xx3]]=[[1,2,3],[2,4,6]]`

Discussion

1276.	If A is a (x + 2) × (y - 3) matrix and B is a 2 × 5 matrix AB is a 3 × 5,then values of x and y are
Answer» `5,1` `2,3` `1,5` `3,2` ANSWER :C

Discussion

1277.	The method of eliminating 'theta' from two given equations involving trigonometrical functions of 'theta'. By using given equations involving 'theta' and trigonometrical identities, we shall obtain an equation not involving 'theta'. On the basis of above information answer the following questions.After eliminating 'theta' from equations (x cos theta)/(a) + (y sin theta)/(b)=1 and x sin theta-y cos theta= sqrt((a^(2)sin^(2) theta+ b^(2) cos^(2) theta)), we get
Answer» `X^(2)+y^(2)=a^(2)+B^(2)` `(x^(2))/(a^(2)) (y^(2))/(b^(2))=1` `(x^(2))/(a(a+b))+(y^(2))/(b(a+b))=1` `x^(2)+y^(2)=(a+b)^(2)` Answer :C

Discussion

1278.	Let A(h, k), B (1, 1) and C(2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1 square unit, then the set of values which 'k' can take is given by
Answer» {-1, 3} {-3, -2} {1, 3} {0, 2} ANSWER :A

Discussion

1279.	Find the area of the right angled triangle with base b and altitude h, using the fundamental theorem of integral calculus.
Answer» ANSWER :`((1)/(2) BH)`

Discussion

1280.	Let f(x)=(ax^2+bx+c)/(x^2+1) such that y=-2 is an asymptote of the curve y=f(x). The curve y=f(x) is symmetric about Y-axis and its maximum values is 4. Let h(x)=f(x)-g(x),where f(x)=sin^4 pi x and g(x)=log_(e)x. Let x_(0),x_(1),x_(2)...x_(n+1) be the roots of f(x)=g(x) in increasing order Then, the absolute area enclosed by y=f(x) and y=g(x) is given by
Answer» `sum_(r=0)^n int_(x_r)^(x_(r+1))(-1)^rcdoth(x)DX` `sum_(r=0)^n int_(x_1)^(x_(r+1))(-1)^(r+1)CDOT h(x)dx` `2sum_(r=0)^n int_(x_r)^(x_(r__r+1))(-1)^rcdoth(x)dx` `1/2 cdot sum_(r=0)^n int_(x_1)^(x_(r+1))(-1)^(r+1)cdot h(x)dx` ANSWER :A

Discussion

1281.	Let f(x)=(ax^2+bx+c)/(x^2+1) such that y=-2 is an asymptote of the curve y=f(x). The curve y=f(x) is symmetric about Y-axis and its maximum values is 4. Let h(x)=f(x)-g(x),where f(x)=sin^4 pi x and g(x)=log_(e)x. Let x_(0),x_(1),x_(2)...x_(n+1) be the roots of f(x)=g(x) in increasing order In above inquestion the value of n, is
Answer» 1 2 3 4 Answer :B

Discussion

1282.	Let f(x)=(ax^2+bx+c)/(x^2+1) such that y=-2 is an asymptote of the curve y=f(x). The curve y=f(x) is symmetric about Y-axis and its maximum values is 4. Let h(x)=f(x)-g(x),where f(x)=sin^4 pi x and g(x)=log_(e)x. Let x_(0),x_(1),x_(2)...x_(n+1) be the roots of f(x)=g(x) in increasing order The whole area bounded by y=f(x),y=g(x)x=0 is
Answer» `11/8` `8/3` `2` `13/3` ANSWER :A

Discussion

1283.	If A={1,2,3,4,5},B ={p,q,r,s} then n(A xxB ) =
Answer» 6 9 3 64 Answer :B

Discussion

1284.	Find the rank of the following matrices by row reduction method.[[1,2,-1],[3,-1,2],[1,-2,3],[1,-1,1]]
Answer» ANSWER :`RHO (B) = 3`

Discussion

1285.	The sum of the series (x-1)/(x+1)+1/2(x^(2)-1)/((x+1)^(2)+1/3(x^(3)-1)/(x+1)^(3)+…is equal to
Answer» `log_(e)X` `2 log_(e)x` `-log_(e)(x+1)` NONE of these Answer :a

Discussion

1286.	"Sinh"2x=70sqrt(2)if
Answer» SINH X = 5 sinh x = 7 COSH x = 5 cosh x = 7 Answer :B

Discussion

1287.	Consider f(x) = lim_(n to infty)(x^(n) - sin x^(n))/(x^(n) + sin x^(n)) , for x gt 0, x ne 1, f(1) =0, then
Answer» f is CONTINOUS at x=1 f has a finite DISCONTINUITY at x=1 f has an infinite or OSCILLATORY discontinuity at x=1 f has a removable TYPE of discontinuity at x=1. Answer :B

Discussion

1288.	Let AX =D be a system of three linear non-homogeneous equations. If \|A\|=0 and rank (A) = rank ([AD])=alpha, then
Answer» `AX=D` will have INFINITE NUMBER of solutions when `ALPHA=3` `AX=D` will have unique solution when `alpha LT 3` `AX =D` will have infinite number of solution when `alpha lt 3` `AX =D` will have no solution when `alpha lt 3` ANSWER :C

Discussion

1289.	Show that f(x)=tan^(-1)(sin x + cos x) is a decreasingfunction for x in ( pi/4, pi/2).
Answer» ANSWER :

Discussion

1290.	If A, B, C are mutually exclusive and exhaustive events such that P(B) = (3)/(2) P(A) and P(C) = (1)/(3) P(B). Find odds in favour of (A uu B).
Answer» ANSWER :`5 : 1`

Discussion

1291.	Find the perimeter of the triangle whose vertices are (0,1,2)(2,0,4) and (-4,-2,7).
Answer» Solution :Let A =(0,1,2)B =(2,0,4) and C =(-4,-2,7) ' "Then" AB = sqrt((2-0)^2+(0-1)^2+(4-2)^2)=sqrt(4+1+4) =3 ` `BC =sqrt((-4-2)^2+(-2-0)^2+(7-4)^2) =sqrt(36+4+9) =7` ` AC=sqrt((-4-0)^2 +(-2-1)^2+(7-2)^2) =sqrt(16+9+25)= sqrt(50) =5sqrt2` `:. "Perimetre of the TRIANGLE"=3 +7 +5 sqrt2 =10+5sqrt2`

Discussion

1292.	A plane intersects three co-ordinate axes at the points A, B, C. If (1, -2, 3) is the centroid of theDeltaABCthen find the equation of the plane.
Answer» ANSWER :`6x-3y+2z=18`

Discussion

1293.	If s is the sum to infnity of a G.P, whose first term is a, then the sum of the first n terms of the G.P. is
Answer» `s[1-(1-(a)/(s))^(N)]` `s(1-(a)/(s))^(n)` `a[1-(1-(a)/(s))^(n)]` `(a)/(s)[1-(1-(a)/(s))^(n)]` ANSWER :A

Discussion

1294.	Represent graphically a displacement of 40 km, 30^(@) west of south.
Answer» Answer :The vector `VEC(OP)` REPRESENTS the required displacement shown in FIGURE) `(##KPK_AIO_MAT_XII_P2_C10_E08_001_A01##)`

Discussion

1295.	The median of a set of 13 distinct observation is 187. 3. If each of the five larger observation is increased by 12.5 and each of the five smaller observations are decreased by 7.5 then the median of the new set of obervation is __________
Answer» ANSWER :`7.5`

Discussion

1296.	int_(1)^(e)(ln x)/(x^(2))dx=
Answer» `1 - 2/e` `2/e` `2/e +1` `e/2 -1` ANSWER :A

Discussion

1297.	The mean and standard deviations (s.d.)of five observations are 9 and 0 respectively. If one observations is changed such that mean of the new set of five observations becomes 10, then their s.d. is
Answer» 0 1 2 4 Answer :C

Discussion

1298.	Match the following
Answer» SOLUTION :A(q,t),B(p),C(R),D(s)

Discussion

1299.	If sqrt(1 + (1)/(1 ^(2)) + (1)/( 2 ^(2))) + sqrt (1 + (1)/( 2 ^(2)) + (1)/( 3 ^(2))) + sqrt (1 + (1)/( 3 ^(2)) + (1)/( 4 ^(2))) +...+ sqrt (1 + (1)/((1999) ^(2) +(2000) ^(2))) = x - (1)/(x),then find the value of x
Answer» ANSWER :`X = 2000 - (1)/( 2000)`

Discussion

1300.	A (2, 5), B (-1, 3) and C (5, -1) are the vertices of a triangle. The image of the point (1,2) with respect to the median through A is
Answer» (2, 1) (3, 2) `((3)/(2), (7)/(2))` (-1, -2) Answer :B

Discussion

Explore topic-wise InterviewSolutions in .

Let x it [0,2pi] The curve y=secx tanx +2tanx - sec x and the line y=0 intersect in

Does the point (-2,5,3.5) lie inside, outside or on the circle x^2 + y^2 = 25?

In the given figure find minimum force (in N) required to move block up the incline.

How many number of species are diamagnetic and have the order greater than 2.5. N_(2),N_(2)^(o+),NO^(o+),NO^(Θ),CO,CN^(Θ),KO_(2),Na_(2)O_(2)

Method of integration by parts : The anti derivative of f(x) and e^(x) and the anti derivative of g(x) is cosx, then, intf(x)cosxdx+intg(x)e^(x)dx=............

If the differential equation formed by eliminating a,b,c from the equaiton y = a e^(x) + b e^(2x) + c e^(3x) is Py_(3) + Qy_(2) + Ry_(1)+Sy = 0 then

Solve system of linear equations , using matrix method if exists 3x+2y-2z=3 x+2y+3z=6 2x-y+z=2

A particle moves along x-axis in such a way that its x-co-ordinate varies with time according to the equation x=8-4t+6t^2.The distance covered by particle between t=0 to t=2/3 sec is : (x is in meter & t is in seconds)

If sum_(r =0)^(n) ((r+2)/(r+1)) *""^(n)C_(r ) =(255)/(6). Find n.

Find the probability of throwing at most 2 sixes in 6 throws of a single dice.

Find the distance between the mid point of the line segment bar(AB)and the point (3,-1,2) where A = (6,3,-4), B = (-2,-1,2).

The point of intersection of the tangents of the parabola y^(2)=16x at the extremities of the chord having (3,4) as its midpoint is

Let x dy/dx + y -e^(x) =0 , y (a) = b. , The solution is given by xy = e^(x) + a, find true or false.

If the function f:R rarr R defined by {:{(a((1-cos2x)/(x))",","for" x lt 0 ),("b," ,"for "x=0),((sqrt(x))/(sqrt(4+sqrt(x))-2)",","for "x gt 0):} is continuous at x=0, then a+b=0

If A,B and C are angles of a triangle, then prove that E=(cos ((B-C)/(2)))/(cos ((B+C)/(2)))+ (cos ((C-A)/(2)))/(cos ((C+A)/(2)))+(cos ((A-B)/(2)))/(cos ((A+B)/(2)))ge6

Show that the relation S in the set R of real numbersdefined as S={(a,b): a, b in R and a le b^(3) } is neither reflexive, nor symmetric, nor transitive.

Two different digits are selected at random from the digits 1 through 9 If 3 is one of the digits selected, what is the probability that the sum is odd?

Two different digits are selected at random from the digits 1 through 9 If 3 is one of the digits selected, what is the probability that the sum is even?

If the planes vecr*(2hati-lambda hatj+hatk)=3 and vecr*(4hati+hatj-mu hatk)=5 are parallel, then the value of lambda and mu are:

If the directionratios of two linesare givenby 3lm - 4ln + mn = 0 and l + 2m + 3n = 0 , then the angle between the lines , is

int(dx)/(4x^(2)+3)

How many line segments have both their endpoints located at the vertices of a given cube?

Let A and B be independent events with P(A)= 0.3 and P( B)= 0.4. Find P( A cap B)

On a festival day, a man plans to visit 4 holy temples A,B,C,D in a random order. Find the probability that he visits (i) A before B (ii) A before B and B before C.

Construct a 2xx3 matrix having element:a_(ij)= ixxj

If A is a (x + 2) × (y - 3) matrix and B is a 2 × 5 matrix AB is a 3 × 5,then values of x and y are

Let A(h, k), B (1, 1) and C(2, 1) be the﻿ vertices of a right angled triangle with AC﻿ as its hypotenuse. If the area of the triangle﻿ is 1 square unit, then the set of values which﻿ 'k' can take is given by﻿

Find the area of the right angled triangle with base b and altitude h, using the fundamental theorem of integral calculus.

If A={1,2,3,4,5},B ={p,q,r,s} then n(A xxB ) =

Find the rank of the following matrices by row reduction method.[[1,2,-1],[3,-1,2],[1,-2,3],[1,-1,1]]

The sum of the series (x-1)/(x+1)+1/2(x^(2)-1)/((x+1)^(2)+1/3(x^(3)-1)/(x+1)^(3)+…is equal to

"Sinh"2x=70sqrt(2)if

Consider f(x) = lim_(n to infty)(x^(n) - sin x^(n))/(x^(n) + sin x^(n)) , for x gt 0, x ne 1, f(1) =0, then

Let AX =D be a system of three linear non-homogeneous equations. If |A|=0 and rank (A) = rank ([AD])=alpha, then

Show that f(x)=tan^(-1)(sin x + cos x) is a decreasingfunction for x in ( pi/4, pi/2).

If A, B, C are mutually exclusive and exhaustive events such that P(B) = (3)/(2) P(A) and P(C) = (1)/(3) P(B). Find odds in favour of (A uu B).

Find the perimeter of the triangle whose vertices are (0,1,2)(2,0,4) and (-4,-2,7).

A plane intersects three co-ordinate axes at the points A, B, C. If (1, -2, 3) is the centroid of theDeltaABCthen find the equation of the plane.

If s is the sum to infnity of a G.P, whose first term is a, then the sum of the first n terms of the G.P. is

Represent graphically a displacement of 40 km, 30^(@) west of south.

The median of a set of 13 distinct observation is 187. 3. If each of the five larger observation is increased by 12.5 and each of the five smaller observations are decreased by 7.5 then the median of the new set of obervation is __________

int_(1)^(e)(ln x)/(x^(2))dx=

The mean and standard deviations (s.d.)of five observations are 9 and 0 respectively. If one observations is changed such that mean of the new set of five observations becomes 10, then their s.d. is

Match the following

If sqrt(1 + (1)/(1 ^(2)) + (1)/( 2 ^(2))) + sqrt (1 + (1)/( 2 ^(2)) + (1)/( 3 ^(2))) + sqrt (1 + (1)/( 3 ^(2)) + (1)/( 4 ^(2))) +...+ sqrt (1 + (1)/((1999) ^(2) +(2000) ^(2))) = x - (1)/(x),then find the value of x

A (2, 5), B (-1, 3) and C (5, -1) are the﻿ vertices of a triangle. The image of the point﻿ (1,2) with respect to the median through A﻿ is

If the planes vecr(2hati-lambda hatj+hatk)=3 and vecr(4hati+hatj-mu hatk)=5 are parallel, then the value of lambda and mu are:

Let A(h, k), B (1, 1) and C(2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1 square unit, then the set of values which 'k' can take is given by

A (2, 5), B (-1, 3) and C (5, -1) are the vertices of a triangle. The image of the point (1,2) with respect to the median through A is