28278 + Interview Questions in Maths in Class 12 Page 551 InterviewSolution

27501.	A straight line touches the circle described on the line joining the foci of the hyperbolax^(2)//a^(2) -y^(2)//b^(2) =1as diameter . The locus of polesw.r.t. the hyperbola is
Answer» ` (X^(2))/(a^(4)) +(y^(2))/( b^(4)) =(1)/( a^(2)+b^(2))` ` (x^(2) )/( a^(4)) +(y^(2))/( b^(4)) =(1)/(a^(2)-b^(2)) ` ` (x^(2))/(a^(4)) -(y^(2))/(b^(4))=(1)/(a^(2)+b^(2))` ` (x^(2))/(a^(4))-(y^(2))/(b^(4))=(1)/(a^(2)-b^(2))` Answer :A

Discussion

27502.	If overline(a), overline(b) and overline(c) are three coplanar vectors, then (overline(a)+overline(b))*(((overline(b)+overline(c))timesoverline(a)+(overline(b)+(overline(a))timesoverline(b)))=
Answer» `0` `[[OVERLINE(a), overline(b), overline(c)]]` `2[[overline(a), overline(b), overline(c)]]` `-[[overline(a), overline(b), overline(c)]]` Answer :A

Discussion

27503.	Show that subtraction and division are not binary opertions on N.
Answer» ANSWER :`3/5 NE N`

Discussion

27504.	If f(x) =x^2 +3x,x=10, deltax=0.01 then I: deltaf =02301 II : df = 023 III : relative error in x is 1
Answer» only I, III are TRUE only II,III are true only I,II are true I,II,III are true Answer :C

Discussion

27505.	Evaluate the following integrals int(3cosx+2sinx)/(4cosx+3sinx)dx
Answer» ANSWER :`(1)/(25)log\|4cosx+3sinx\|+(18)/(25)x+c`

Discussion

27506.	Consider g(x,y)=(2x^2y)/(x^2+y^2) . If (x,y) ne (0,0) and g (0,0) = 0Show that g is continuous on R^2.
Answer» ANSWER :G is CONTINUOUS at EVERY POINT of `R^2`.

Discussion

27507.	If 30 persons are sitting around a circle. In how many ways can 2 person out of them be selected so that they are not adjacent.
Answer» ANSWER :`""^(30)C_2-30`

Discussion

27508.	Prove that the pair of linesjoining the origin to the intersection ofthe curve (x^2)/(a^2)+(y^2)/(b^2)=1by the line lx+my+n=0 are coincident, if a a^2l^2+b^2m^2=n^2
Answer» ANSWER :`RARR a^2l^2+b^2m^2=n^2`

Discussion

27509.	Equation of a plane which passes through the line x+py+q=0=rz+s and makes equal intercepts on y and z axes is x+py+q+lambda(rz+s)=0 where lambda is equal to
Answer» `q//s` `p//r` `r//s` `p//q` ANSWER :B

Discussion

27510.	A man owns a field of area 1000 sq.m. He wants to plant fruit trees in it. He has a sum of Rs. 1400 to purchase young trees. He has the choice of two types of trees. Type A requires 10 sq.m. of ground per tree and costs Rs. 20 per tree and type B requires 20 sq.m. of ground per tree and costs Rs. 25 per tree. When fully grown type A produces an average of 20 kg. of fruit which can be sold at a profit of Rs. 2/ - per kg and type B produces an average of 40 kg of fruit which can be sold at a profit of Rs. 1.50/ - per kg. How many of each type should be planted to achieve maximum profit when the trees are fully grown ?
Answer» Answer :TYPE A : 20 plants, Type B : 40 plants Maximum profit = RS. 2200

Discussion

27511.	For the integral int_(0)^(pi) sin x dx find the upper and lower integral sums corresponding to the division oftheclosed interval [0,pi] into3 and 6 equal subintervals.
Answer» ANSWER :2

Discussion

27512.	The numbers t (t ^(2) +1) , t ^(2) and 6 are three consecutive terms of an A.P. If t be real, then find the the next two terms of A.P.
Answer» ANSWER :14,22

Discussion

27513.	A={(x,y,z):x,y,zinNandx+y+z=12}. The number of elements in A is
Answer» 54 55 7 `12^(3)` ANSWER :B

Discussion

27514.	int_0^1(log_e(1+x))/(1+x^2)dx=
Answer» `pi/4 log_e 2` `pi/6 log_e 6` `pi/2 log_e 8` `pi/8 log_e 2` ANSWER :D

Discussion

27515.	Write down the power set of{a,{a}}
Answer» SOLUTION :LET `A ={a,{a}} THENP(A)={{a},{{a}},PHI,A}`

Discussion

27516.	Find the volume of the Parallelepiped whose sides are given by the vectors. (1,0,0), (0,1,0), (0,0,1)
Answer» SOLUTION :

Discussion

27517.	If 5 letters are placed in 5 addressed envelopes and A,B,C defines the events that Exactly one letter is placed wrongly, atleast one placed wrongly, all are placed wrongly. Then the descending order of their probabilities is
Answer» <P>`p(A),p(B),p(C )` `p(B),p(C ),p(A)` `p(C ),p(B),p(A)` `p(A),p(C ),p(B)` ANSWER :B

Discussion

27518.	The range of x of which the expansion ( 9 + 25x^2)^(-6//5) is valid is
Answer» `(-3//5 , 3//5)` `[-3//5, 3//5]` `(-OO, 3//5)` `(-oo, - 3//5)CUP(3//5, oo)` ANSWER :A

Discussion

27519.	For 4 le r le n ((n),(r))+4((n),(r+1))+6((n),(r+2))=4((n),(r+3))+((n),(r+4)) equals
Answer» `((n+4),(R+4))` `((n+4),(r))` `((n+3),(r-1))` `((n+4),(r+3))` ANSWER :A

Discussion

27520.	Using differentials, find the approximate value of each of the following: (a) ((17)/(81))^((1)/(4))(b) (33)^(-(1)/(5))
Answer» ANSWER :(a) 0.677 (B) 0.497

Discussion

27521.	int(3sinx+5cosx+4)/(sinx+cosx+2)dx=
Answer» `LOG(sinx+cosx+2)+4x-4tan^(-1)(1+tan""(x)/(2))+c` `log(sinx+cosx+2)+4x-4sqrt2tan^(-1)((1+tan""(x)/(2))/(SQRT2))+c` `4LOG(sinx+cosx+2)+x-4sqrt2tan^(-1)((1+tan""(x)/(2))/(sqrt2))+c` `4log(sinx+cosx+2)+4x-4sqrt2tan^(-1)((1-tan""(x)/(2))/(sqrt2))+c` Answer :B

Discussion

27522.	Integrate the function 1/(sqrt(8+3x-x^(2)))
Answer» Answer :`SIN^(-1)((2x-3)/(SQRT(41)))+C`

Discussion

27523.	Let f(x) = {((x^(3)+x^(2)-16x+20)/((x-2)^(2)), ",","if" x != 2),(k, ",", "if" x = 2 ):}. If f(x) is continuous for all x, then k =
Answer» 7 -7 `+- 7` NONE of these Answer :A

Discussion

27524.	Let f (x) =1+ 1/2+ 1/3+ 1/4 + ……… + 1/n such that P (n) f (n+2) = P ( n) f (n) + q (n). Where P (n) Q(n) are polynomials of least possible degree and P (n) has leading coefficient unity. Then match the following Column-I with Column-II.
Answer» ANSWER :`ATOS; BtoP; CtoQ; DtoR`

Discussion

27525.	The set of values of x satisfying 2 le \| x-3\| lt 4is
Answer» `(-1,1] uu [5,7)` `-4 LE X le 2` `-1 LT x lt 7 ` or `x gt 5` `x lt 7 ` or ` x ge 5` ANSWER :A

Discussion

27526.	For each opertion difined below, determine whether isw binary, commutative or associative. On Z, define a **b =a - b
Answer» ANSWER : `**` is BINARY but NEITHER COMMUTATIVE nor ASSOCIATIVE

Discussion

27527.	Resolve into Partial Fractions (i) (5x+1)/((x+2)(x-1))
Answer» `3/(x+2)+2/(x-1)` `2/(x+2)+3/(x-1)` `3/(x-2)+2/(x+1)` `2/(x-2)+3/(x+1)` ANSWER :A

Discussion

27528.	Show that of all rectangles inscribed in a given fixed circle, the square has the maximum area.
Answer» ANSWER :`x=y=sqrt(2)R`

Discussion

27529.	Let A={1,2,3} and Let R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}. then, R is
Answer» REFLEXIVE and SYMMETRIC but TRANSITIVE symmetric and transitive but not reflexive Reflexive and transitive but not symmetric An EQUIVALENCE relation Answer :A

Discussion

27530.	Using properties of determinant, if \|(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)\| = mua^2b^2c^2, find mu
Answer» ANSWER :`mu=4`

Discussion

27531.	If int_(0)^(x)f(t)dt=x+int_(x)^(1)tf(t)dt, then the value of f(1) is
Answer» 0 1 -1 `1/2` ANSWER :D

Discussion

27532.	If sum_(r=0)^(3n)a_(r)(x-4)^(r )=sum_(r=0)^(3n)A_(r)(x-5)^(r ) and a_( k)=1AA K ge 2n and sum_(r=0)^(3n)d_(r )(x-8)^(r )=sum_(r=0)^(3n)B_(r )(x-9)^(r ) and sum_(r =0)^(3n)d_(r )(x-12)^(r )=sum_(r=0)^(3n)D_(r )(x-13)^(r ) and d_(K)=1 AA K ge 2n. Then find the value of(A_(2n)+D_(2n))/(B_(2n)) .
Answer» ANSWER :2

Discussion

27533.	If a,b,c are in H.P.then which one of the following is true
Answer» `(1)/(B-a) + (1)/(b-c) = (1)/(b)` `(AC)/(a+c) = b` `(b+a)/(b-a) + (b+c)/(b-c) = 1` NONE of these Answer :D

Discussion

27534.	Which of the following options are incorrect.
Answer» Gravitational potential INSIDE a uniform solid is constant Gravitational field intensity inside a uniform solid SPHERE is ZERO Gravitational field intensity inside a uniform spherical shell is zero Gravitational potential inside a uniform spherical shell is constant Solution :`{:("Solid sphere",E=(GM)/(R^(3))*r,,rleR),(,V=-(GM)/(2R^(3))(3R^(2)-r^(2)),,rleR),("Spherical shell",E=0,,rltR),(,V=-(GM)/(R),,rleR):}` M `to` Mass of spherical shell R `to` Radius of the sphere r `to` DISTANCE of the point from the centre of spherical shell

Discussion

27535.	Findthe polynomial P(x) of the least degree that has a maximum equal to 6 at x = 1, and a minimum equal to 2 at x = 3
Answer» <P> ANSWER :`P(X) = x^(3) - 6x^(2) + 9x + 2`

Discussion

27536.	Solve the following problem graphically. Minimise and Maximise Z=3x+9y…………..1 subject to the constraints x+3yle60………….2 x+yge10…………..3 xley…………4 xge0,yge0…………..5
Answer» ANSWER :180

Discussion

27537.	A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals
Answer» `(1)/(2)` `(1)/(32)` `(31)/(32)` `(1)/(5)` Answer :A

Discussion

27538.	Discuss the continuity of the function f defined by f(x)= (1)/(x), x ne 0.
Answer» ANSWER :This MEANS F is a CONTINUOUS FUNCTION.

Discussion

27539.	Integrate the functions xsqrt(1+2x^(2))
Answer» ANSWER :`1/6(1+2x^(2))^(3/2)+C`

Discussion

27540.	For +veinteger n,n^3 +2nis alwaysdivisibleby
Answer» 3 7 5 6 Answer :A

Discussion

27541.	Consider the binary opertion ^^ on the set {1,2,3,4,5} defined by a ^^ b = min {a,b}. Write the opertion table of the opertion ^^.
Answer» ANSWER :`(##NCERT_BEN_MAT_XII_P1_C01_E04_003_A01##)`

Discussion

27542.	If int_(0)^(oo)(x^(2)dx)/((x^(2)+a^(2))(x^(2)+b^(2))(x^(2)+c^(2)))=(pi)/(2(a+b)(b+c)(c+a))" then "int_(0)^(oo)(dx)/((x^(2)+4)(x^(2)+9))=
Answer» `pi/60` `pi/20` `pi/40` `pi/80` ANSWER :A

Discussion

27543.	Evaluate : int_(0)^((pi)/(4)) log(1+tan theta ) d theta
Answer» SOLUTION :N/A

Discussion

27544.	Solve the following linear programming problem graphically : Minimise Z = 200 x + 500 y "…(1)" subject to the constraints : x+2y ge 10"…(2)" 3x+4y le 24"…(3)" x ge 0, y ge 0"...(4)"
Answer» ANSWER :MINIMUM value of Z is 2300, ATTAINED at the the POINT (4, 3)

Discussion

27545.	Evaluate (i) int_(a)^(b) (1)/(sqrt((x-a)(b-x)))dx
Answer» Answer :`2 int_(0)^((PI)/(2)) d THETA = pi`

Discussion

27546.	I : If the vectors a = (1, x, -2), b = (x, 3, -4) are mutually perpendicular, then x = 2 II : If a = I + 2j + 3k, b = - I + k, c = 3i + j and a + b is perpendicular to c then t = 5.
Answer» only I is ture Only II is ture both I and II are true Neither I nor II are true Answer :B

Discussion

27547.	If P = (0,1,2) , Q = (4,-2,1) , O = (0,0,0) then angle POQ is equal to
Answer» `pi/2` `pi/4` `pi/6` `pi/3` ANSWER :A

Discussion

27548.	If a_(1) x^(3) + b_(1)x^(2) + c_(1)x + d_(1) = 0 and a_(2)x^(3) + b_(2)x^(2) + c_(2)x + d_(2) = 0 a pair of repeated roots common, then prove that \|{:(3a_(1)","2b_(1)","c_(1)),(3a_(2)"," 2b_(2)","c_(1)),(a_(2)","b_(1)- a_(1)b_(2)","c_(2)a_(1)-c_(2)a_(1)","d_(1)a_(2)-d_(2)a_(1)):}\|=0
Answer» SOLUTION :If `f(x) = a_(1)x^(3) + b_(1) x^(2) + c_(1) x + d_(1) = ` has roots `alpha, alpha, beta,` then `g(x) = a_(2)x^(3) + b_(2)x^(2) + c_(2)x+ d_(2) = 0` must have roots `alpha, alpha, gamma` Hence,` a_(1) alpha^(3) + b_(1)alpha^(2)+ c_(1) alpha+ d_(1)= 0`(1) ` a_(2) alpha^(3) + b_(2)alpha^(2)+ c_(2) alpha+ d_(2)= 0`(2) Now, `alpha` is also a root of equation `f'(x) = 3a_(1)x^(2) + 2b_(1) x + c_(1) = 0` and `g'(x) = 3 a_(2) x^(2) + 2b_(2)x + c_(2)` = 0. Therefore, `3 a_(1) alpha^(2) + 2b_(1)alpha+ c_(1) = 0`(3) `3 a_(2) alpha^(2) + 2b_(2)alpha+ c_(2) = 0`(4) Also, from `a_(2) xx(1) - a_(1)xx(2)`, we have `(a_(2)b_(1)-a_(1)b_(2) )alpha^(2) + (c_(1) a_(2) - c_(2)a_(1))alpha + d_(1)a_(2) -d_(2)a_(1)= 0`(5) Eliminating `alpha` from (3),(4) and (5), we have `\|{:(3a_(1)","2b_(1)","c_(1)),(3a_(2)"," 2b_(2)","c_(1)),(a_(2)","b_(1)- a_(1)b_(2)","c_(2)a_(1)-c_(2)a_(1)","d_(1)a_(2)-d_(2)a_(1)):}\|=0` .

Discussion

27549.	The rate of change of the area of a circle with respect to its radius r at r = 6 cm is ……….
Answer» `10 PI` `12pi` `8pi` `11pi` ANSWER :B

Discussion

27550.	Let f(x)= (sqrt(3x^2+2)+root3(x^3+3))/(root4(x^4+5)-root(5)(x^4+6)) then lim_(x to oo) f(x) is equal to
Answer» ANSWER :0.67

Discussion

Explore topic-wise InterviewSolutions in .

A straight line touches the circle described on the line joining the foci of the hyperbolax^(2)//a^(2) -y^(2)//b^(2) =1as diameter . The locus of polesw.r.t. the hyperbola is

If overline(a), overline(b) and overline(c) are three coplanar vectors, then (overline(a)+overline(b))*(((overline(b)+overline(c))timesoverline(a)+(overline(b)+(overline(a))timesoverline(b)))=

Show that subtraction and division are not binary opertions on N.

If f(x) =x^2 +3x,x=10, deltax=0.01 then I: deltaf =0*2301 II : df = 0*23 III : relative error in x is 1

Evaluate the following integrals int(3cosx+2sinx)/(4cosx+3sinx)dx

Consider g(x,y)=(2x^2y)/(x^2+y^2) . If (x,y) ne (0,0) and g (0,0) = 0Show that g is continuous on R^2.

If 30 persons are sitting around a circle. In how many ways can 2 person out of them be selected so that they are not adjacent.

Prove that the pair of linesjoining the origin to the intersection ofthe curve (x^2)/(a^2)+(y^2)/(b^2)=1by the line lx+my+n=0 are coincident, if a a^2l^2+b^2m^2=n^2

Equation of a plane which passes through the line x+py+q=0=rz+s and makes equal intercepts on y and z axes is x+py+q+lambda(rz+s)=0 where lambda is equal to

For the integral int_(0)^(pi) sin x dx find the upper and lower integral sums corresponding to the division oftheclosed interval [0,pi] into3 and 6 equal subintervals.

The numbers t (t ^(2) +1) , t ^(2) and 6 are three consecutive terms of an A.P. If t be real, then find the the next two terms of A.P.

A={(x,y,z):x,y,zinNandx+y+z=12}. The number of elements in A is

int_0^1(log_e(1+x))/(1+x^2)dx=

Write down the power set of{a,{a}}

Find the volume of the Parallelepiped whose sides are given by the vectors. (1,0,0), (0,1,0), (0,0,1)

If 5 letters are placed in 5 addressed envelopes and A,B,C defines the events that Exactly one letter is placed wrongly, atleast one placed wrongly, all are placed wrongly. Then the descending order of their probabilities is

The range of x of which the expansion ( 9 + 25x^2)^(-6//5) is valid is

For 4 le r le n ((n),(r))+4((n),(r+1))+6((n),(r+2))=4((n),(r+3))+((n),(r+4)) equals

Using differentials, find the approximate value of each of the following: (a) ((17)/(81))^((1)/(4))(b) (33)^(-(1)/(5))

int(3sinx+5cosx+4)/(sinx+cosx+2)dx=

Integrate the function 1/(sqrt(8+3x-x^(2)))

Let f(x) = {((x^(3)+x^(2)-16x+20)/((x-2)^(2)), ",","if" x != 2),(k, ",", "if" x = 2 ):}. If f(x) is continuous for all x, then k =

Let f (x) =1+ 1/2+ 1/3+ 1/4 + ……… + 1/n such that P (n) f (n+2) = P ( n) f (n) + q (n). Where P (n) Q(n) are polynomials of least possible degree and P (n) has leading coefficient unity. Then match the following Column-I with Column-II.

The set of values of x satisfying 2 le | x-3| lt 4is

For each opertion ** difined below, determine whether ** isw binary, commutative or associative. On Z, define a **b =a - b

Resolve into Partial Fractions (i) (5x+1)/((x+2)(x-1))

Show that of all rectangles inscribed in a given fixed circle, the square has the maximum area.

Let A={1,2,3} and Let R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}. then, R is

Using properties of determinant, if |(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)| = mua^2b^2c^2, find mu

If int_(0)^(x)f(t)dt=x+int_(x)^(1)tf(t)dt, then the value of f(1) is

If sum_(r=0)^(3n)a_(r)(x-4)^(r )=sum_(r=0)^(3n)A_(r)(x-5)^(r ) and a_( k)=1AA K ge 2n and sum_(r=0)^(3n)d_(r )(x-8)^(r )=sum_(r=0)^(3n)B_(r )(x-9)^(r ) and sum_(r =0)^(3n)d_(r )(x-12)^(r )=sum_(r=0)^(3n)D_(r )(x-13)^(r ) and d_(K)=1 AA K ge 2n. Then find the value of(A_(2n)+D_(2n))/(B_(2n)) .

If a,b,c are in H.P.then which one of the following is true

Which of the following options are incorrect.

Findthe polynomial P(x) of the least degree that has a maximum equal to 6 at x = 1, and a minimum equal to 2 at x = 3

Solve the following problem graphically. Minimise and Maximise Z=3x+9y…………..1 subject to the constraints x+3yle60………….2 x+yge10…………..3 xley…………4 xge0,yge0…………..5

A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of head appearing on fifth toss equals

Discuss the continuity of the function f defined by f(x)= (1)/(x), x ne 0.

Integrate the functions xsqrt(1+2x^(2))

For +veinteger n,n^3 +2nis alwaysdivisibleby

Consider the binary opertion ^^ on the set {1,2,3,4,5} defined by a ^^ b = min {a,b}. Write the opertion table of the opertion ^^.

If int_(0)^(oo)(x^(2)dx)/((x^(2)+a^(2))(x^(2)+b^(2))(x^(2)+c^(2)))=(pi)/(2(a+b)(b+c)(c+a))" then "int_(0)^(oo)(dx)/((x^(2)+4)(x^(2)+9))=

Evaluate : int_(0)^((pi)/(4)) log(1+tan theta ) d theta

Solve the following linear programming problem graphically : Minimise Z = 200 x + 500 y "…(1)" subject to the constraints : x+2y ge 10"…(2)" 3x+4y le 24"…(3)" x ge 0, y ge 0"...(4)"

Evaluate (i) int_(a)^(b) (1)/(sqrt((x-a)(b-x)))dx

I : If the vectors a = (1, x, -2), b = (x, 3, -4) are mutually perpendicular, then x = 2 II : If a = I + 2j + 3k, b = - I + k, c = 3i + j and a + b is perpendicular to c then t = 5.

If P = (0,1,2) , Q = (4,-2,1) , O = (0,0,0) then angle POQ is equal to

If a_(1) x^(3) + b_(1)x^(2) + c_(1)x + d_(1) = 0 and a_(2)x^(3) + b_(2)x^(2) + c_(2)x + d_(2) = 0 a pair of repeated roots common, then prove that |{:(3a_(1)","2b_(1)","c_(1)),(3a_(2)"," 2b_(2)","c_(1)),(a_(2)","b_(1)- a_(1)b_(2)","c_(2)a_(1)-c_(2)a_(1)","d_(1)a_(2)-d_(2)a_(1)):}|=0

The rate of change of the area of a circle with respect to its radius r at r = 6 cm is ……….

Let f(x)= (sqrt(3x^2+2)+root3(x^3+3))/(root4(x^4+5)-root(5)(x^4+6)) then lim_(x to oo) f(x) is equal to

If f(x) =x^2 +3x,x=10, deltax=0.01 then I: deltaf =02301 II : df = 023 III : relative error in x is 1

For each opertion difined below, determine whether isw binary, commutative or associative. On Z, define a **b =a - b