28278 + Interview Questions in Maths in Class 12 Page 186 InterviewSolution

9251.	Write all the unit vectors in XY-plane.
Answer» <P> Answer :`vec(OP')=cos THETA HATI` `vec(P'P)=SIN theta hatj`

Discussion

9252.	Integrate the functions (e^(2x)-1)/(e^(2x)+1)
Answer» ANSWER :`(:.t=E^(X)+e^(-x))`

Discussion

9253.	If A and B are symmetric matrices of same order , then AB is symmetric if and only if …….. .
Answer» ANSWER :`AB=BA`.

Discussion

9254.	A number n is chosen at random from S={1,2,3,…..50}. Let A={n in S :n+(50)/(n) gt 27}, B={n in S : n "is a prime"} and C={ n in S : n "is a square"} Then correct order of their probability is
Answer» <P>`P(A) lt P(B) lt P(C )` `P(A) GT P(B) gt P(C )` `P(B) lt P(A) lt P(C )` `P(A) gt P(C ) gt P(B)` ANSWER :B

Discussion

9255.	Express the -2 points geometrically in the Argrand plane.
Answer» SOLUTION :`-2=-2+i0=(-2,0)`

Discussion

9256.	The starting value of the model class of a distribution is 20. The frequency of the model class is 18. The frequencies of the classes preceeding and succeeding are 8,10 and the width of the model class is 5, then mode is
Answer» 18.5 20.5 21.4 22.78 Answer :D

Discussion

9257.	If \|z + 2i\| le 1 and z_(1) = 6-3i then the maximum value of \|iz + z_(1) - 4\| is ____
Answer» `(1)/(2)` 6 3 2 Answer :B

Discussion

9258.	An equivalent expression for (pimplies q ^^ r) vv (r hArr s) which contains neither the biconditional nor the conditional is
Answer» `(~p vv q ^^ R) ^^ [(~r vv s )^^ (r vv ~s)]` `(~p ^^ q ^^ r) vv [(~r vv s) ^^ (r vv ~s)]` `(~p vv q ^^ r ) ^^ [(~r vv s) vv (r vv ~s)]` NONE of the above Answer :A

Discussion

9259.	If 20! Were multiplied out, how many consecutive zeros would it have on the right?
Answer» Solution :If "20!" were MULTIPLIED out, then the number of consecutive zeros on the RIGHT is 4. due to presence of `4xx5,10,14xx15,20`.

Discussion

9260.	Show that the following vector are co-planar. hati-2hatj+2hatk, 3hati+4hatj+5hatk, -2hati+4hatj-4hatk.
Answer» Solution :Let `VECA = hati-2hatj+2hatk` `vecb = 3hati+4hatj+5hatk` `vecc = -2hati+4hatj-4hatk` The vectors `veca.vecb.vecc` are coplanar if `(VECAXXVECB).vecc = 0` HENCE as `(vecaxxvecb).vecc = 0 the GIVEN vectors are coplanar.

Discussion

9261.	1+(2x)/(1!) +(3x^2)/(2!) +(4x^3)/(3!) +.......oo =
Answer» `e^x` `(x+1) e^x` `(x-1) e^x` `(x+2)e^x` ANSWER :B

Discussion

9262.	Evaluate the integrals :I = int_(0)^(3) (x dx)/( sqrt(x + 1) + sqrt(5x + 1)),
Answer» ANSWER :`(14)/(15)`

Discussion

9263.	Find the number of non negative integral solutions of 2x + y + z = 21.
Answer» ANSWER :132

Discussion

9264.	If an equilateral Delta is inscribed in a parabola y^(2) = 12x with one of the vertex is at the vertex of the parabola then its height is
Answer» `24 SQRT(3)` `16sqrt(3)` 36 24 Answer :C

Discussion

9265.	Question 11 and 12 refer to the gaph above. Q. Which of the following is the best approximation for the decrease in the number of cars purchased per year between 2011 and 2014?
Answer» `105` `140` `300` `420` Answer :B

Discussion

9266.	Find the approximate value of f(2.01), where f(x)=4x^(2)+5x+2.
Answer» ANSWER :`=28.21`

Discussion

9267.	Evaluate the following integrals : int_(1)^(2)(1)/(x(1+x^(2)))dx
Answer» Answer :`(3)/(2)log2-(1)/(2)LOG5`

Discussion

9268.	Integrate the rational functions 2/((1-x)(1+x^(2)))
Answer» ANSWER :`-log\|1-x\|+(1)/(2) log\|1+x^(2)\|+TAN^(-1)x+c`

Discussion

9269.	Equation of the latusrectum of the ellipse 9x^(2)+4y^(2)-18x-8y-23=0 are
Answer» `y= PM SQRT5` `x=pm sqrt5` `y=1 pm sqrt5` `x=-1 pm sqrt5` ANSWER :C

Discussion

9270.	There are four doors leading to the inside of a cinema hall. In how many ways can a person enter into it an come out ?
Answer» Solution :There are four doors leading to the INSIDE of a CINEMA HALL. A person can enter into it and come out in `4^2=16`different ways .(By the principle of COUNTING.)

Discussion

9271.	if f:R rarr R is defined bty f(x)={{:(\|[x-5]\|, "for" x lt 5),([\|x-5\|],"for" x ge5):} Then (fof)(-7/2)= (here [x] is the greatest integer not exceeding x)
Answer» `(FOF ) (-(11)/(2))` `(fof) (-(9)/(2))` `(fof) ( 3)` `(fof) ((9)/(2))` ANSWER :D

Discussion

9272.	Common tangents are drawn to the parabola y^2 = 4x & the ellipse 3x^2 + 8y^2 = 48 touching the parabola at A & B and the ellipse at C & D. Find the area of the quadrilateral.
Answer» ANSWER :`55sqrt2` sq.units

Discussion

9273.	A is a 3xx3 matrix , then \|3A\|=....\|A\|.
Answer» 3 6 9 27 Answer :D

Discussion

9274.	Three dailies A,B,C are published in a city. 20% of the city population read A,16% read B,14% read C,8% read both A and B , 5% both A and C , 4% both B and C ,2% read all the three. Find percentage of population that read atleast one news paper and find the percentage of population who read news paper A only.
Answer» ANSWER :`35,9`

Discussion

9275.	If (x + iy)^((1)/(3)) = 5+ 3i , then 3x + 5y =
Answer» 480 152 990 960 Answer :D

Discussion

9276.	Find the Lim_(nrarroo) ((""^(3n)C_(n))/(""^(2n)C_(n)))^(1/n) Where ""^(i)C_(j) is a binomial coefficient which means (i.(i-1)"…."(i-j+1))/(j.(j-1)"….."2.1)
Answer» SOLUTION :N//A

Discussion

9277.	Calculate without using trigonometric tables:
Answer» `4 cos 20^(@)-sqrt(3)cot20^(@)` `(2cos40^(@)-COS20^(@))/(sin20^(@))` `cos^(6)(pi)/(16)+cos^(6)(3pi)/(16)+cos^(6)(5pi)/(16)+cos^(6)(7pi)/(16)` `TAN10^(@)-TAN50^(@)+tan70^(@)` Answer :A::B::C::D

Discussion

9278.	Integrate the functions in exercise. (1)/(sqrt(1+4x^(2)))
Answer» ANSWER :`(1)/(2)log\|2x+sqrt(4X^(2)+1)\|+C`

Discussion

9279.	int (x^(2) + x)/((x^(2) + 1)(x - 1))dx =
Answer» `TAN^(-1)` x + LOG \|x - 1\| +c `-tan^(-1)` x - log \| x - 1\| + c `tan^(-1)` x -log \| x- 1\| none Answer :A

Discussion

9280.	Find the value of x and y so that the vectors 2hat(i)+3hat(j) and xhat(i)+yhat(j) are equal .
Answer» ANSWER :`=3`

Discussion

9281.	If vec(a)+vec(b)+vec( c )=0 and \|vec(a)\|=6,\|vec(b)\|=5,\|vec( c )\|=7 then find the angle between the vectors vec(b) and vec( c ).
Answer» ANSWER :`COS^(-1)(-(19)/(35))`

Discussion

9282.	int((sinx)^(99))/((cosx)^(101))dx=....+c
Answer» `((TANX)^(100))/(100)` `((tanx)^(2))/(100)` `((tanx)^(98))/(98)` `((tanx)^(97))/(97)` Answer :A

Discussion

9283.	Find the coefficient of a^(5) b^(3)c^(4) in the expansion of (ab+(bc)/(2)-(ca)/(3))^(6)
Answer» SOLUTION :N/A

Discussion

9284.	Statement I : f(x) = ax^(41) + bx^(-40) rArr (f'(x))/(f(x)) = 1640x^(-2) Statement II : (d)/(dx) tan^(-1) ((2x)/(1-x^(2))) = (1)/(1 + x^(2)) Which of the following is correct ?
Answer» I is TRUE, but II is FALSE Both I and II are true NEITHER I nor II is true I is false, but II is true ANSWER :A

Discussion

9285.	The sum S_(n)=sum_(k=0)^(n)(-1)^(k)*^(3n)C_(k), where n=1,2,…. is
Answer» `(-1)^(n)"^(3N-1)C_(n-1)` `(-1)^(n)"^(3n-1)C_(n)` `(-1)n"^(3n-1)C_(n+1)` None of these Solution :`(b)` `S_(n)=^(3n)C_(0)-^(3n)C_(1)+^(3n)C_(2)+….+(-1)^(n)^(3n)C_(n)` But `.^(3n)C_(0)=.^(3n-1)C_(0)` `-^(3n)C_(1)=-^(3n-1)C_(0)-^(3n-1)C_(1)` `-^(3n)C_(2)=^(3n-1)C_(1)+^(3n-1)C_(2)` `-^(3n)C_(3)=-^(3n-1)C_(2)-^(3n-1)C_(3)` `…………....................................` `(-1)^(n)^(3n)C_(n)=(-1)^(n)^(3n-1)C_(n-1)+(-1)^(n)^(3n-1)C_(n)` On ADDING we get `S_(n)=(-1)^(n)^(3n-1)C_(n)`

Discussion

9286.	Find the coefficient of x^(50) in (2-3x)/((1-x)^(3))
Answer» ANSWER :`-1173`

Discussion

9287.	Consider the following two statements:P: If 7 is an odd number , then 7 is divisible by 2 Q: If 7 is a prime number , then 7 is an odd number .If V_1 is the truth value of the contrapositive of P and V_2 is the truth value of contrapositive of Q, then the ordered pair (V_1,V_2) equals:
Answer» (F,F) (F,T) (T,F) (T,T) SOLUTION :TRUTH VALUE of P and its CONTRAPOSITIVE is F. Truth value of Q and its contrapositive is T.

Discussion

9288.	If xin((3pi)/4,pi) what is dy/dxfor y = \| cos x \| + \| sin x \| ?
Answer» SOLUTION :y = \| COS X \| + \| sin x \| As x `in ((3PI)/4,pi)` we have y = - cos x + sin x `therefore dy/dx=`sin x + cos x

Discussion

9289.	Period of (sin theta + sin 2 theta)/( cos theta + cos 2 theta)is
Answer» `2PI` `PI` `(2pi)/(3)` `pi/3` ANSWER :C

Discussion

9290.	The shortest distance between the lines r=(-2hat(i)+hat(j)-hat(k))+r(3hat(i)+3hat(j)-hat(k)) and r=(hat(i)-hat(j)+2hat(k))+k(-1hat(i)+2hat(j)+4hat(k)) is
Answer» 0 `(10)/(sqrt(6))` `(11)/(sqrt(6))` `(13)/(sqrt(6))` ANSWER :C

Discussion

9291.	If x = tan 15^(@), y = cosec 75^(@)and z =4 sin 18^(@) then,
Answer» `X LT y lt z` `y lt z lt x` `z lt x lt y` `xlt ZLT y` ANSWER :A

Discussion

9292.	if(5x^(2) +2)/(x^(3)+x)=(A_(1))/(x)+(A_(2)x+A_(3))/(x^(2)+1), then(A_(1), A_(2), A_(3))=
Answer» no IMAGINARY ROOTS no positive roots no NEGATIVE roots no real roots Answer :1

Discussion

9293.	If F(x)=[(cos^(2)x,cosxsinx),(cosxsinx,sin^(2)x)] and the difference of x and y is the odd Multipleof (pi)/(2),thenF(x)F(y) is :
Answer» ZERO matrix unit matrix diagonal matrix None of these SOLUTION :N/a

Discussion

9294.	If cottheta=5//12andtheta lies in the third quadrant , then what is (2sintheta+3costheta) equal to?
Answer» `-4` `-p^(2)`for some odd prime p `(-q//p)`where p is an odd prime and q a positive integer with `(q//p)` not an integer `-p`for some odd prime p Solution :Let`cottheta=(5)/(12)` `rArrtantheta=(12)/(5)=("perpendicular"(P))/("base"(b))` `therefore"Hypotenuse"(H)=sqrt(p^(2)+b^(2))` `=sqrt((12)^(2)+(5)^(2))=sqrt(144+255)=sqrt(169)=13` Consider 2 `2sintheta+3costheta` `=2((p)/(H))+3((b)/(H))`""(H- Height) But`theta`lies in `3^(rd)`QUADRANT and sin `theta , costheta` both are negative in `3^(rd)` quadrant `therefore2sintheta+3costheta=2((-p)/(H))+3((-b)/(H))` `=2((-12)/(13))+3((-5)/(13))` `=(-24-15)/(13)=(-39)/(13)=-3` WHICHIS an odd prime.

Discussion

9295.	int (cot x)/(1+sin^(2)x)dx=
Answer» `LOG \|(sin X)/(sqrt(1 + sin^(2)x))\| ` + C `log \|(sqrt(1 + sin^(2) x))/(sin x) \| + c ` `(1)/(2) log \| (sin x)/(sqrt(1 + sin^(2) x))\| + C` `(1)/(2) log \| (sqrt(1 + sin^(2) x))/(sin x) \| +c ` ANSWER :A

Discussion

9296.	Differentiate (1-cosx)/(1+cosx)
Answer» SOLUTION :`y=(1-cosx)/(1+cosx)` `d/dx(1-cosx)(1+cosx)` `dy/dx=(-(1-cosx)d/dx(1+cosx))/(1+cosx)^2` `=(SINX(1+cosx)+(1-cosx)sinx)/(1+cosx)^2` `(2sinx)/(1+cosx)^2`

Discussion

9297.	The slope of the tangent to the curve y = 3x^(2) + 4 cos x " at " x = 0 is
Answer» 4 2 3 `-1` ANSWER :A

Discussion

9298.	Equation of tangent of the curve y = 1 - e^(x//2) at that point at which the curve crosses the y-axis, is :
Answer» `x+y=1` `2x+y = 1` `x=-2y` NONE of these Answer :C

Discussion

9299.	log(1+x+x^(2)+...oo)=
Answer» `X+(x^(2))/(2)+(x^(3))/(3)+(x^(4))/(4)+…oo` `x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+…oo` `1+x+(x^(2))/(2)+(x^(3))/(3)+(x^(4))/(4)+….oo` `1-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+…oo` Answer :A

Discussion

9300.	If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0respresent the pair of parallel straight lines , then prove that h^(2)=abandabc+2fgh-af^(2)-bg^(2)-ch^(2)=0.
Answer» SOLUTION :Let the given equation represent PAIR of parallel straigh lines `lx+my+n=0andlx+my+n'=0` `:. ax^(2)+2HXY+b^(2)+2gx+2fy+c` `=(lx+my+n)(lx+my+n')` `=(lx+my)^(2)+L(n+n')x+m(n+n')y+nn'=0` Thus , expression`(lx+my)^(2)` is same as `ax^(2)+by^(2)_2hxy`. Therefore , `ax^(2)+2hxy+by^(2)`must be perfect SQUARE of liner expression inx and y. So `(2h)^(2)-4ab=0` `:. h^(2)=ab` Also , `abc+2ghf-af^(2)-bg^(2)-ch^(2)=0`.

Discussion

Explore topic-wise InterviewSolutions in .

Write all the unit vectors in XY-plane.

Integrate the functions (e^(2x)-1)/(e^(2x)+1)

If A and B are symmetric matrices of same order , then AB is symmetric if and only if …….. .

A number n is chosen at random from S={1,2,3,…..50}. Let A={n in S :n+(50)/(n) gt 27}, B={n in S : n "is a prime"} and C={ n in S : n "is a square"} Then correct order of their probability is

Express the -2 points geometrically in the Argrand plane.

The starting value of the model class of a distribution is 20. The frequency of the model class is 18. The frequencies of the classes preceeding and succeeding are 8,10 and the width of the model class is 5, then mode is

If |z + 2i| le 1 and z_(1) = 6-3i then the maximum value of |iz + z_(1) - 4| is ____

An equivalent expression for (pimplies q ^^ r) vv (r hArr s) which contains neither the biconditional nor the conditional is

If 20! Were multiplied out, how many consecutive zeros would it have on the right?

Show that the following vector are co-planar. hati-2hatj+2hatk, 3hati+4hatj+5hatk, -2hati+4hatj-4hatk.

1+(2x)/(1!) +(3x^2)/(2!) +(4x^3)/(3!) +.......oo =

Evaluate the integrals :I = int_(0)^(3) (x dx)/( sqrt(x + 1) + sqrt(5x + 1)),

Find the number of non negative integral solutions of 2x + y + z = 21.

If an equilateral Delta is inscribed in a parabola y^(2) = 12x with one of the vertex is at the vertex of the parabola then its height is

Question 11 and 12 refer to the gaph above. Q. Which of the following is the best approximation for the decrease in the number of cars purchased per year between 2011 and 2014?

Find the approximate value of f(2.01), where f(x)=4x^(2)+5x+2.

Evaluate the following integrals : int_(1)^(2)(1)/(x(1+x^(2)))dx

Integrate the rational functions 2/((1-x)(1+x^(2)))

Equation of the latusrectum of the ellipse 9x^(2)+4y^(2)-18x-8y-23=0 are

There are four doors leading to the inside of a cinema hall. In how many ways can a person enter into it an come out ?

if f:R rarr R is defined bty f(x)={{:(|[x-5]|, "for" x lt 5),([|x-5|],"for" x ge5):} Then (fof)(-7/2)= (here [x] is the greatest integer not exceeding x)

Common tangents are drawn to the parabola y^2 = 4x & the ellipse 3x^2 + 8y^2 = 48 touching the parabola at A & B and the ellipse at C & D. Find the area of the quadrilateral.

A is a 3xx3 matrix , then |3A|=....|A|.

If (x + iy)^((1)/(3)) = 5+ 3i , then 3x + 5y =

Find the Lim_(nrarroo) ((""^(3n)C_(n))/(""^(2n)C_(n)))^(1/n) Where ""^(i)C_(j) is a binomial coefficient which means (i.(i-1)"…."(i-j+1))/(j.(j-1)"….."2.1)

Calculate without using trigonometric tables:

Integrate the functions in exercise. (1)/(sqrt(1+4x^(2)))

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

Find the value of x and y so that the vectors 2hat(i)+3hat(j) and xhat(i)+yhat(j) are equal .

If vec(a)+vec(b)+vec( c )=0 and |vec(a)|=6,|vec(b)|=5,|vec( c )|=7 then find the angle between the vectors vec(b) and vec( c ).

int((sinx)^(99))/((cosx)^(101))dx=....+c

Find the coefficient of a^(5) b^(3)c^(4) in the expansion of (ab+(bc)/(2)-(ca)/(3))^(6)

Statement I : f(x) = ax^(41) + bx^(-40) rArr (f'(x))/(f(x)) = 1640x^(-2) Statement II : (d)/(dx) tan^(-1) ((2x)/(1-x^(2))) = (1)/(1 + x^(2)) Which of the following is correct ?

The sum S_(n)=sum_(k=0)^(n)(-1)^(k)*^(3n)C_(k), where n=1,2,…. is

Find the coefficient of x^(50) in (2-3x)/((1-x)^(3))

Consider the following two statements:P: If 7 is an odd number , then 7 is divisible by 2 Q: If 7 is a prime number , then 7 is an odd number .If V_1 is the truth value of the contrapositive of P and V_2 is the truth value of contrapositive of Q, then the ordered pair (V_1,V_2) equals:

If xin((3pi)/4,pi) what is dy/dxfor y = | cos x | + | sin x | ?

Period of (sin theta + sin 2 theta)/( cos theta + cos 2 theta)is

The shortest distance between the lines r=(-2hat(i)+hat(j)-hat(k))+r(3hat(i)+3hat(j)-hat(k)) and r=(hat(i)-hat(j)+2hat(k))+k(-1hat(i)+2hat(j)+4hat(k)) is

If x = tan 15^(@), y = cosec 75^(@)and z =4 sin 18^(@) then,

if(5x^(2) +2)/(x^(3)+x)=(A_(1))/(x)+(A_(2)x+A_(3))/(x^(2)+1), then(A_(1), A_(2), A_(3))=

If F(x)=[(cos^(2)x,cosxsinx),(cosxsinx,sin^(2)x)] and the difference of x and y is the odd Multipleof (pi)/(2),thenF(x)F(y) is :

If cottheta=5//12andtheta lies in the third quadrant , then what is (2sintheta+3costheta) equal to?

int (cot x)/(1+sin^(2)x)dx=

Differentiate (1-cosx)/(1+cosx)

The slope of the tangent to the curve y = 3x^(2) + 4 cos x " at " x = 0 is

Equation of tangent of the curve y = 1 - e^(x//2) at that point at which the curve crosses the y-axis, is :

log(1+x+x^(2)+...oo)=

If the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=0respresent the pair of parallel straight lines , then prove that h^(2)=abandabc+2fgh-af^(2)-bg^(2)-ch^(2)=0.