28278 + Interview Questions in Maths in Class 12 Page 137 InterviewSolution

6801.	Find the vector and the cartesian equations of the lines that passes through the origin and (5, -2, 3).
Answer» ANSWER :`THEREFORE x/5=(y)/(-2)=z/3`

Discussion

6802.	Prove that: veca.{(vecb+vecx)xx(veca+2vecb+3vecc)}=[vecavecbvecc].
Answer»

Discussion

6803.	If \|(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2))\|=k then k=
Answer» `(2ABC)^2` `4` `2abc` `2` ANSWER :A

Discussion

6804.	If the lines 2x + y + 12 = 0, kx -3y - 10 = 0 are conjugate with respect to the circle x^(2) + y^(2) - 4x + 3y -1 = 0, then k =
Answer» 4 `-9` `-3` `-5` ANSWER :A

Discussion

6805.	Forces acting on a particle have magnitude 5,3 and 1 unit and act in the direction of the vectors 6 hati + 2hatj +3hatk, 3hati-2hatj+6hatk and 2hati-3hatj - 6hatk, respectively . Then, remain constant while the particle is displaced from the points A(2,-1,-3) to (5,-1,1) . The work done is
Answer» 11 UNIT 33 unit 10 unit 30 unit Answer :B

Discussion

6806.	Z is the set of integers, (Z, ) is a group with a b = 1 + b + 1, , b, in G. Then inverse of a is
Answer» `-a` `a + 1` `-2 -a` NONE of these Answer :C

Discussion

6807.	Let zt be the set of all 3 xx 3 summetric matrices whose entries are 1,1,1,0,0,0,-1,-1,.B is one of the matrix in set zt and X=[{:(,x),(,y),(,z):}] U=[{:(,0),(,0),(,0):}] V=[{:(,1),(,0),(,0):}] The equations BX=V
Answer» is inconsistent for ATLEAST 3 MATRICES, B. is inconsistent for all matrices, B. is inconsistent for all most 12 matrices, B. has infinite number of solutions for at LEAST 3 matrices, B Answer :A::C

Discussion

6808.	Let zt be the set of all 3 xx 3 summetric matrices whose entries are 1,1,1,0,0,0,-1,-1,.B is one of the matrix in set zt and X=[{:(,x),(,y),(,z):}] U=[{:(,0),(,0),(,0):}] V=[{:(,1),(,0),(,0):}]ltBRgt Number of matrices B in set is lambda, "then" lamda lies in the interval
Answer» (30,40) (38,40) (34,38) (25,35) ANSWER :A::C

Discussion

6809.	Let zt be the set of all 3 xx 3 summetric matrices whose entries are 1,1,1,0,0,0,-1,-1,.B is one of the matrix in set zt and X=[{:(,x),(,y),(,z):}] U=[{:(,0),(,0),(,0):}] V=[{:(,1),(,0),(,0):}] Number of matrices B such that equations BX=U has infinite solutions.
Answer» is at LEAST 6 is not more than 10 lie between 8 to 16 is zero Answer :A::C

Discussion

6810.	Using properties of definite integration evaluate : int_(a)^(b) (root(n)x)/(root(n)x+root(n)(a+b-x))dx
Answer» ANSWER :`(1)/(2)(b-a)`

Discussion

6811.	bar(a)=2bar(i)-3bar(j)+2bar(k) and bar(b)=2bar(i)+3bar(j)+bar(k) are the sides of triangle OAB. Then its area is …… seq. unit.
Answer» 340 `2sqrt(5)` `sqrt(229)` `(1)/(2)(sqrt(229))` ANSWER :D

Discussion

6812.	If P, Q are conjugate points with respect to a circles S -= x^2 + y^2 + 2gx + 2fy + c = 0then prove that the circle PQ as diameter cuts the circles S = 0 orthogonally.
Answer» ANSWER :`2g_1 g_2 + 2f_1 f_2 = c_1 + c_2`

Discussion

6813.	Consider the function f(x)=lim_(nto infty) ((1+cosx)^(n)+5lnx)/(2+(1+cosx)^(n)), then
Answer» `f(x)` is discontinous at positive even multiples of `pi` `f(x)` is CONTINUOUS at positive ODD multiples of `pi` `f(x)` is discontinuous at positive odd multiples of `(pi)/(2)` `f(x)` is continuous at positive even multiples of `(pi)/(2)` SOLUTION :`f(x)={{:(1,,, x in(20npi,2npi+(pi)/2),n in I^(+)CUP{0}),((1+5lnx)/3,,,x=(4n+1)(pi)/2,n in I^(+)cup{0}),((5lnx)/2,,,x in(2npi+(pi)/2,2npi+(3pi)/2),n in I^(+_)cup{0}),((1+5lnx)/3,,,x=2npi+(3pi)/2, n in I^(+)cup{0}):}` 1: `x in (2npi+(3pi)/(2),2npi+2pi)n in I^(+)cup{0}` `f(x)` is discontinuous at all positive odd multiples of `(pi)/(2)`

Discussion

6814.	Determine the differentials in each of the following cases. y = sin^2 x
Answer» SOLUTION :`y = sin^2 X` Then DY = `2 sin x cdot x dx = sin 2X dx`

Discussion

6815.	Statement-I : The number of ways of arranging the letters of the word TRIANGLE so that the relative positions of the vowels and consonents are not disturbed is 360. Statement-II : The number of ways of arranging the letters of the word MONDAY so that no vowel occupies even place is 144. Statement-III : The number of 3 letter words using the letters of the word MISTER in which atleast one letter is repeated is 96. Which of the above statements is true.
Answer» I & II are true II & III are true I & III are true I, II & III are true Answer :B

Discussion

6816.	X speaks truth in 60 % and Y in 50 % of the cases . The probability that they contradict each other while narrating the same fact isa) 1/4b)1/3c)1/2d)2/3
Answer» `1/4` `1/3` `1/2` `2/3` ANSWER :C

Discussion

6817.	The locus of z such that arg[(1-2i)z-2+5i]= (pi)/(4) is a
Answer» LINE not PASSING through the ORIGIN CIRCLE not possing through the origin line passing through the origin circle passing through the origin Answer :A

Discussion

6818.	Find the number of rational terms in the expansion of (2^((1)/(3)) + 3^((1)/(5)))^(600)
Answer» ANSWER :41

Discussion

6819.	Find the equation of locus of P, if the line segment joining (2,3) & (-1,5) subtends a right angle at P.
Answer» ANSWER :`X^(2)+y^(2)-x-8y+13=0`

Discussion

6820.	Differentiate.In cos e^x
Answer» SOLUTION :`y=In (COS e^x)` `dy/dx=1/(cos(e^x))CDOT d/dx(cose^x)` `1/((cose^x))(-sine^x)d/dx(e^x)`

Discussion

6821.	Differentiate.In (4x^2(2x-7)^3)/(3x^2-7)^5
Answer» SOLUTION :`y =In (4x^2(2x-7))/(3x^2+7)` `In 4+2In x+3In (2x-7)-5In(3x^2+7)` `thereforedy/dx=2/x+6/(2x-7)-5/(3x^2+7)6X` 2/x+6/(2x-7)-(5X)/(3x^2+7)cdot6x`

Discussion

6822.	int_0^(sqrt3)(dx)/(1+x^2)dx
Answer» Solution :`int_0^(SQRT3)(dx)/(1+X^2)dx=[tan^(-1)x]_0^(sqrt3)=pi/3`

Discussion

6823.	A cylinder is such that the sum of its height and circumference of its base is 10 metres. Findthe maximum volume of the cylinder.
Answer» SOLUTION :N/A

Discussion

6824.	IF b is two more than one-third of c, which of the following expresses the value of c in terms of b?
Answer» `C=(b-2)/3` `c=(b+3)/3` `c=3 (b-2)` `c=3(b-6)` ANSWER :C

Discussion

6825.	Let y = f(x) be defined parametrically as y = t^(2) + t\|t\|, x = 2t - \|t\|, t in R. Then, at x = find f(x) and discuss continuity.
Answer» ANSWER :`f(x) = {{:(2x^(2)",",x ge 0),(0",",x LT 0):}`

Discussion

6826.	Evalute the following integrals int(1)/(4 cos x + 3 sin x )dx
Answer» ANSWER :`(1)/(5)" log " \| (2 tan (X)/(2) + 1)/((tan" "(x)/(2) -2)) \| + c `

Discussion

6827.	int (2x)/(1+x^2) dx
Answer» ANSWER :`LOG(1+x^(2))+C`

Discussion

6828.	The value of int_(1)^(a) [x] f'(x) dx, a gt 1, where [x] denotes the greatest integer not exceeding x is
Answer» `AF([a])-{F(1) + f(2) +…+ f(a) ]` `a f(a) - { f(1) + f(2)+ …+ f([a] }` `[a] f(a) - {f(1) + f(2) +…+ f([a])}` `[a] f([a]) - {f(1) + f(2) +…+ f(a) }` ANSWER :C

Discussion

6829.	Show that+ 1/4 + (1.3)/(4.8) + (1.3.5)/(4.8.12) + …….= sqrt2
Answer» ANSWER :`SQRT2`

Discussion

6830.	Statement -1 : The quadratic equationax^(2)+bx+c=0 has real roots if(a+c)^(2) gt b^(2) , AA , a,b,c in R . and Statement -2 :The quadratic equation ax^(2) +bx+c=0 has real roots ifb^(2) -4ac ge 0
Answer» STATEMENT -1 is True, Statement -2 is True, Statement -2 is a correct EXPLANATION for statement -14 Statement -1 is True, Statement -2 is True , Statement -2 is NOT a correct explanation for Statement -14 Statement -1 is True, Statement -2 isFalse Statement -1 is Flase, Statement -2 is True ANSWER :D

Discussion

6831.	int_(0)^(pi//8) cos^(6) 4 x dx=
Answer» `(5PI)/(128)` `(35pi)/(128)` `(25pi)/(128)` `(5)/(128)` ANSWER :A

Discussion

6832.	The slope of the straight line which does not intersect x-axis is equal to
Answer» `(1)/(2)` `(1)/(SQRT2)` `SQRT3` 0 Answer :D

Discussion

6833.	Find the area bounded between the curves y^(2)-1=2x and x =0
Answer» ANSWER :`((2)/(3))`

Discussion

6834.	The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.
Answer» ANSWER :`x=2r, (d^(2)A)/(DX^(2))GT 0`

Discussion

6835.	Six dice are thrown 729times. The numbers of times you expect atleast 3 dice to show either 5 or 6 is
Answer» 233 249 396 433 Answer :A

Discussion

6836.	Let G donate the set of all nxxn non-singular matrices with rational numbers as entries. Then under matrix multiplication.
Answer» G is a subgroup G is an infinite, non-A belian group G is a FINITE A belian group G is infinite, A belian ANSWER :B

Discussion

6837.	Evaluate int_(2)^(3)(2x^(5)+x^(4)-2x^(3)+2x^(2)+1)/((x^(2)+1)(x^(4)-1))dx
Answer» ANSWER :`[1/2 (LOG 6 - 1/5)]`

Discussion

6838.	A pole is standing at a point O between two milestones at A and B such that the angles of elevation of the top of the pole at A and B are respectively alpha and beta. If the distance between the milestones is half the height of the pole then
Answer» `2 sin (ALPHA + BETA) = sin alpha sin beta` `2 sin (alpha + beta) = COS alpha cos beta` `sin (alpha + beta) = 2 sin alpha sin beta` `sin (alpha + beta) = 2 cos alpha cos beta` ANSWER :A

Discussion

6839.	Evaluate the integerals. int e^(log (1+tan^(2)x )) dx " on " I sub R\\ {((2n+1)pi)/2: n in Z} .
Answer» Answer :`int SEC^(2) X dx = TAN x +c`

Discussion

6840.	Classify the follwing as scalar and vector quantities : (i) 5 second (ii) 1000" cm"(3) (iii) 50" m"//"sec"^(2) (iv) 10 Newton (v) 20 m/sec towards north (vi) 15 Kg.
Answer» Answer :Scalar : (i), (ii), (IV), (VI) VECTOR : (III), (V)

Discussion

6841.	Let int(5+f(sinx)+f(cosx))/(sinx+cosx)dx=h(x)+lamda, where h (1) = -1. Find the value of tan^(-1)(h(2))+tan^(-1)(h(3)). (where lamda is indefinite integration constant.)
Answer» `(3PI)/4` `pi/4` `-(3pi)/4` `-pi/4` ANSWER :C

Discussion

6842.	The value of the integral int_(1)^(5)[\|x-3\|+\|1-x\|]dx is equal to
Answer» 4 8 12 16 Answer :C

Discussion

6843.	If area of the triangle with vertices (-2, 0), (0, 4) and (0, k) is 4 square units, find the value of 'k' using determinants.
Answer» ANSWER :`k=0`

Discussion

6844.	If a right circular cone, having maximum volume is inscribed in a sphere of radius 3cm, then the curved surface area (in cm^(2)) of this cone is
Answer» `6 sqrt(3pi)` `6 sqrt2 pi` `8 sqrt2 pi` `8 SQRT3 pi` ANSWER :D

Discussion

6845.	The locus of the middle points of portions of the tangents to the circle x^(2)+y^(2)=a^(2) terminated by the axes is
Answer» `X^(2)+y^(2)=2a^(2)` `x^(2)+y^(2)=4A^(2)` `x^(-2)+y^(-2)=4a^(-2)` `x^(-2)+y^(-2)=a^(-2)` ANSWER :C

Discussion

6846.	A fair coin is tossed n times and x be the number of heads. If P(x=4), P(x=5), P(x=6) are in A.P. then which of the following are correct. Statement-I : n = 7Statement-II : n = 9 Statement-III : n = 2Statement-IV : n = 14 correct statements are
Answer» only I both I and III both III and IV both I and IV Answer :D

Discussion

6847.	If veca= hati + hatj - hatk, vecb = hati - hatj + hatk and vecc is unit vector perpendicular to the vector vecaand coplanar with veca and vecb, then a unit vector vecd perpendicular to both veca and vecc is :
Answer» `(1)/(sqrt6) (2 hati - AHTJ + hatk)` `(hati+ hatj)/(sqrt2)` `(hatj + hatk)/(sqrt2)` `(hati +hatk)/(sqrt2).` ANSWER :C

Discussion

6848.	Find the ratio in which the XZ-plane divides line joining A(-2,3,4) and B(1,2,3)
Answer» ANSWER :`-3:2`

Discussion

6849.	The probability that the two digit number formed by digits 1, 2, 3, 4, 5 is divisible by 4 is
Answer» `(1)/(30)` `(1)/(20)` `(1)/(5)` NONE of these Answer :C

Discussion

6850.	The vector having initial and terminal points as (2, 5, 0) and (-3, 7, 4) respectively is ……..
Answer» `-bar(i)+12bar(j)+4bar(K)` `5bar(i)+2BAR(j)-4bar(k)` `-5bar(i)+2bar(j)+4bar(k)` `bar(i)+bar(j)+bar(k)` ANSWER :C

Discussion

Explore topic-wise InterviewSolutions in .

Find the vector and the cartesian equations of the lines that passes through the origin and (5, -2, 3).

Prove that: veca.{(vecb+vecx)xx(veca+2vecb+3vecc)}=[vecavecbvecc].

If |(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2))|=k then k=

If the lines 2x + y + 12 = 0, kx -3y - 10 = 0 are conjugate with respect to the circle x^(2) + y^(2) - 4x + 3y -1 = 0, then k =

Forces acting on a particle have magnitude 5,3 and 1 unit and act in the direction of the vectors 6 hati + 2hatj +3hatk, 3hati-2hatj+6hatk and 2hati-3hatj - 6hatk, respectively . Then, remain constant while the particle is displaced from the points A(2,-1,-3) to (5,-1,1) . The work done is

Z is the set of integers, (Z, **) is a group with a ** b = 1 + b + 1, , b, in G. Then inverse of a is

Let zt be the set of all 3 xx 3 summetric matrices whose entries are 1,1,1,0,0,0,-1,-1,.B is one of the matrix in set zt and X=[{:(,x),(,y),(,z):}] U=[{:(,0),(,0),(,0):}] V=[{:(,1),(,0),(,0):}] The equations BX=V

Let zt be the set of all 3 xx 3 summetric matrices whose entries are 1,1,1,0,0,0,-1,-1,.B is one of the matrix in set zt and X=[{:(,x),(,y),(,z):}] U=[{:(,0),(,0),(,0):}] V=[{:(,1),(,0),(,0):}]ltBRgt Number of matrices B in set is lambda, "then" lamda lies in the interval

Let zt be the set of all 3 xx 3 summetric matrices whose entries are 1,1,1,0,0,0,-1,-1,.B is one of the matrix in set zt and X=[{:(,x),(,y),(,z):}] U=[{:(,0),(,0),(,0):}] V=[{:(,1),(,0),(,0):}] Number of matrices B such that equations BX=U has infinite solutions.

Using properties of definite integration evaluate : int_(a)^(b) (root(n)x)/(root(n)x+root(n)(a+b-x))dx

bar(a)=2bar(i)-3bar(j)+2bar(k) and bar(b)=2bar(i)+3bar(j)+bar(k) are the sides of triangle OAB. Then its area is …… seq. unit.

If P, Q are conjugate points with respect to a circles S -= x^2 + y^2 + 2gx + 2fy + c = 0then prove that the circle PQ as diameter cuts the circles S = 0 orthogonally.

Consider the function f(x)=lim_(nto infty) ((1+cosx)^(n)+5lnx)/(2+(1+cosx)^(n)), then

Determine the differentials in each of the following cases. y = sin^2 x

X speaks truth in 60 % and Y in 50 % of the cases . The probability that they contradict each other while narrating the same fact isa) 1/4b)1/3c)1/2d)2/3

The locus of z such that arg[(1-2i)z-2+5i]= (pi)/(4) is a

Find the number of rational terms in the expansion of (2^((1)/(3)) + 3^((1)/(5)))^(600)

Find the equation of locus of P, if the line segment joining (2,3) & (-1,5) subtends a right angle at P.

Differentiate.In cos e^x

Differentiate.In (4x^2(2x-7)^3)/(3x^2-7)^5

int_0^(sqrt3)(dx)/(1+x^2)dx

A cylinder is such that the sum of its height and circumference of its base is 10 metres. Findthe maximum volume of the cylinder.

IF b is two more than one-third of c, which of the following expresses the value of c in terms of b?

Let y = f(x) be defined parametrically as y = t^(2) + t|t|, x = 2t - |t|, t in R. Then, at x = find f(x) and discuss continuity.

Evalute the following integrals int(1)/(4 cos x + 3 sin x )dx

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

The value of int_(1)^(a) [x] f'(x) dx, a gt 1, where [x] denotes the greatest integer not exceeding x is

Show that+ 1/4 + (1.3)/(4.8) + (1.3.5)/(4.8.12) + …….= sqrt2

Statement -1 : The quadratic equationax^(2)+bx+c=0 has real roots if(a+c)^(2) gt b^(2) , AA , a,b,c in R . and Statement -2 :The quadratic equation ax^(2) +bx+c=0 has real roots ifb^(2) -4ac ge 0

int_(0)^(pi//8) cos^(6) 4 x dx=

The slope of the straight line which does﻿ not intersect x-axis is equal to

Find the area bounded between the curves y^(2)-1=2x and x =0

The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

Six dice are thrown 729times. The numbers of times you expect atleast 3 dice to show either 5 or 6 is

Let G donate the set of all nxxn non-singular matrices with rational numbers as entries. Then under matrix multiplication.

Evaluate int_(2)^(3)(2x^(5)+x^(4)-2x^(3)+2x^(2)+1)/((x^(2)+1)(x^(4)-1))dx

A pole is standing at a point O between two milestones at A and B such that the angles of elevation of the top of the pole at A and B are respectively alpha and beta. If the distance between the milestones is half the height of the pole then

Evaluate the integerals. int e^(log (1+tan^(2)x )) dx " on " I sub R\\ {((2n+1)pi)/2: n in Z} .

Classify the follwing as scalar and vector quantities : (i) 5 second (ii) 1000" cm"(3) (iii) 50" m"//"sec"^(2) (iv) 10 Newton (v) 20 m/sec towards north (vi) 15 Kg.

Let int(5+f(sinx)+f(cosx))/(sinx+cosx)dx=h(x)+lamda, where h (1) = -1. Find the value of tan^(-1)(h(2))+tan^(-1)(h(3)). (where lamda is indefinite integration constant.)

The value of the integral int_(1)^(5)[|x-3|+|1-x|]dx is equal to

If area of the triangle with vertices (-2, 0), (0, 4) and (0, k) is 4 square units, find the value of 'k' using determinants.

If a right circular cone, having maximum volume is inscribed in a sphere of radius 3cm, then the curved surface area (in cm^(2)) of this cone is

The locus of the middle points of portions of the tangents to the circle x^(2)+y^(2)=a^(2) terminated by the axes is

A fair coin is tossed n times and x be the number of heads. If P(x=4), P(x=5), P(x=6) are in A.P. then which of the following are correct. Statement-I : n = 7Statement-II : n = 9 Statement-III : n = 2Statement-IV : n = 14 correct statements are

If veca= hati + hatj - hatk, vecb = hati - hatj + hatk and vecc is unit vector perpendicular to the vector vecaand coplanar with veca and vecb, then a unit vector vecd perpendicular to both veca and vecc is :

Find the ratio in which the XZ-plane divides line joining A(-2,3,4) and B(1,2,3)

The probability that the two digit number formed by digits 1, 2, 3, 4, 5 is divisible by 4 is

The vector having initial and terminal points as (2, 5, 0) and (-3, 7, 4) respectively is ……..

Z is the set of integers, (Z, ) is a group with a b = 1 + b + 1, , b, in G. Then inverse of a is

The slope of the straight line which does not intersect x-axis is equal to