28278 + Interview Questions in Maths in Class 12 Page 188 InterviewSolution

9351.	If \|vec(a)\|=2,\|vec(b)\|=5 and vec(a).vec(b)=10 then find \|vec(a)-vec(b)\|.
Answer» ANSWER :3

Discussion

9352.	You are running out of time but have no idea about the route from Nepal to IIT Guwahati. The various cut-out parts of the map that can help you reach IIT Guwahati are hidden in the houses shown in the figure below. You will get the parts of the map only on delivering the right article(one per house) to all the houses. (i)An ‘X’ coloured ARTICLE should be delivered to an ‘X’ coloured HOUSE only by using an ‘X’ colouredTRUCK. (ii)A truck can also carry other coloured articles so that it can place them at any of the CHECKPOINTS from where other truck can later carry it to the destination. (iii) Trucks can carry any number of articles at a time. (iv) The main objective is to start all the trucks at the same time, with same speed and deliver the articles without collision of trucks. Also, a truck picks up every article that comes on its way. (v)Last and the most importantly, the PATHS of the trucks should not overlap at any point other thanjunctions.At junctions, the paths can though cross each other (but both trucks should not reach that junction at same time which leads to collision). The trucks can move only forward. Draw the final path of all the trucks and give the number of turns taken by the blue truck.
Answer» 8 7 6 None of the above Solution :C

Discussion

9353.	What did the chief astrologer say?
Answer» The king would die soon The King needs to SAVE himself from the 100th Tiger King would die due to CARDIAC arrest All of the above Answer :B

Discussion

9354.	A contractor submitted tenders for 2 works. If 0.4,0.6,0.1 are the respective probabilities that his first tender, atleast one tender, both the tenders are accepted, what is the probability that his second tender is accepted.
Answer» ANSWER :`0.3`

Discussion

9355.	Let ABCD be a parallelogram whose diagonals intersect at P and O be the origin, then OA+OB+OC+OD equals
Answer» `OP` `2 OP` `3 OP` `4 OP` SOLUTION :Since, thediagonals of a paralelogram bisect each other. Therefore, P is the middle point of AC and BD both. `:.""OA + OC = 2 OP" and "OB+OD=2OP` `rArr""OA+OB+OC+OD=4 OP`

Discussion

9356.	Find the Coefficient of x^(4) in (8-x)^(1//3)
Answer» SOLUTION :N/A

Discussion

9357.	When x is small, sqrt(1 + 2^(x)) is nearly equal to
Answer» `1 + X + x^(2)/2` `1 + x - x^(2)/2` `1 - x + x^(2)/2` `1 - x - x^(2)/2` ANSWER :B

Discussion

9358.	intsqrt(sec x - ) dx =
Answer» `2 tan^(-1)(sqrt(SEC x - 1)) + c ` `-2 " cosh"^(-1) (sqrt(2) cos" "(x)/(2)) + c ` `2"TANH"^(-1) ( sqrt(sec x - 1)) + c` `2 " cos"^(-1) ( sqrt(2) cos "" (x)/(2)) +c ` ANSWER :B

Discussion

9359.	Integrate the function (x^(2))/(1-x^(6))
Answer» ANSWER :`1/6logabs((1+x^(3))/(1-x^(3)))+C`

Discussion

9360.	The sets S_(1), S_(2), S_(3), …………. are given by S_(1) = {2/1},S_(2) = {3/2, 5/2},S_(3) = {4/3, 7/3, 10/3},S_(4) = {5/4, 9/4, 13/4, 17/4},........ . Then the sum of the set S_(25) is
Answer» 320 322 324 325 Answer :D

Discussion

9361.	Find the value of p if the lines 4x-3y-8=0, 2x+py+2=0, 6x+6y-1=0 are concurrent,.
Answer» SOLUTION :NA

Discussion

9362.	The solution of (x^(2) - y^(2) x^(2)) (dy)/(dx) + (y^(2) + x^(2) y^(2)) = 0 is
Answer» `X + (1)/(x) + y + (1)/(y) + C = 0` `x - (1)/(x) + y - (1)/(y) = c` `x + (1)/(x) - y- (1)/(y) + c = 0` `x-(1)/(x) - y - (1)/(y) = c` ANSWER :A

Discussion

9363.	a(x) =\|{:(1,2,3),(x+1, 2x+1, 3x+1),(x^(2)+1,2x ^(2) +1, 3x^(2)+1):}\|implies int _(0)^(1) A(x) dx=
Answer» 0 1 2 4 Answer :A

Discussion

9364.	If x!=0 the determinant Delta=\|(a_(0),a_(1),a_(2)),(-x,x,0),(0,-x,x)\| vanishes if
Answer» `a_(0)+a_(1)+a_(2)=0` `a_(0)+a_(1)=2a_(2)` `a_(0)+a_(2)=2a_(1)` NONE of these Answer :A

Discussion

9365.	Statement-I : The condition for the line y = mx+c to be a tangent to (x+a)^(2) = 4ay is c = am(1-m). Statement-II : The condition for tbe line y = mx + c to be a focal chord to y^(2) = 4ax is c+am=0 Statement-III : The condition for the line y = mx + c to be a tangent x^(2)=4ay is c = -am^(2) Which of above stattements is true
Answer» only I only III both I, II & III neither I nor II Answer :C

Discussion

9366.	If veca and vec b are unit vectors, then what is the angle between veca and vecb for sqrt3 veva - vecb to be a unit vectors ?
Answer» `30^(@)` `45^(@)` `60^(@)` `90^(@)` ANSWER :A

Discussion

9367.	Let A and B are square matrices of order 3. If \|A\|=4, \|B\|=6, B=A-2I and \|adj(I-2A^(-1))\|=k, then the value of k is equal to
Answer» ANSWER :2.25

Discussion

9368.	For any four vectorsveca,vecb,vecc,vecdwe have(vecaxxvecb)xx(veccxxvecd)=[veca,vecb,vecd]vecc-[veca,vecb,vecc]vecd=[veca,vecc,vecd]vecb-[vecb,vecc,vecd]veca.
Answer» ANSWER : ` [VECA,VECC,VECD]VECB-[vecb,vecc,vecd]veca ` .

Discussion

9369.	A line is drawn fromthe point P(1,1,1)and perpendicular to a line with direction ratios, (1,1,1) to intersect the plane x+2y+3z=4 at Q. The locus of point Q is
Answer» `x/1=(y-5)/-2=(z-+2)/1` `x/-2=(y-5)/1=(z+2)/1` `x=y=z` NONE of these Answer :A

Discussion

9370.	The mid point of the chord 3x - 2y + 8 = 0 of the ellipse 3x^(2) + 4y^(2) = 24 is
Answer» 1,-2 2,-1 `-2,1` 2,1 Answer :C

Discussion

9371.	Write the value of int1/(sqrt(x) e^sqrtx)dx
Answer» Solution :`INT1/(SQRT(xe^sqrtx))dx =2inte^-tdt` (where `sqrtx=trArr1/(2sqrtx)dx=dt)=-2e^-t+C=(-2)/(2sqrtx)+c`

Discussion

9372.	Match the following {:("I. Line passing through (-4, 3) and having intercepts in the" , (a) 2x-5y+4=0), ("ratio" 5:3 , ) ,("II. Line passing through P(2, -5) such that P bisects the part", (b) 5x-2y-20=0),("intercepted between the axes",),("III. Line parallel to "2x-3y+5=0" with x-intercept 2/5 is", (c) 3x+5y=3),("IV. Line perpendicularto " 5x+2y+7=0 " with x-intercept 4/5 is", (d)10x-15y=4):}
Answer» B,C, d, a c, b, d, a d, c, b, a a, b, c, d ANSWER :B

Discussion

9373.	Giventhat f(x)= xg (x)//[x], g(0) = g'(0)=0 and f(x) is continuousat x=-0thenthe valueof f'(0)
Answer» DOESNOT exist is-1 is 1 is 0 Answer :D

Discussion

9374.	If 0 le x le 1 and theta-sin^(-1)x+cos^(-1)x-tan^(-1)x, then
Answer» `THETA LE pi//2` `theta GE pi//4` `theta= pi//4` `pi//4 le theta le pi//2` ANSWER :D

Discussion

9375.	Let * be a binary operation on Q defind by ab= (ab)/(2), AAa,b in Q Determine whether is associative or not.
Answer» ANSWER :* is ASSOCIATIVE

Discussion

9376.	If int x(1 + x) log (1 + x^(2)) dx = F(x) log (1 + x^(2))-(2)/(3) tan^(-1)x - (2x^(3))/(9) - (x^(2))/(2) + (2x)/(3) + c, then F(x) =
Answer» `(x^(2))/(2) + (x^(3))/(3)` `(x^(2))/(2) + (x^(3))/(3) - (1)/(3)` `(x^(2))/(2) + (x^(3))/(3) + (1)/(2)` `(x^(2))/(2) + (x^(3))/(3) - (2)/(3)` Answer :C

Discussion

9377.	If the foot of the perpendicularfrom (0,0,0) to a planeis (1,2,3) then the equation of the plane is ,
Answer» `2x+y+3z=14` `x+2y+3z=14` `x+2y+3z+14=0` `x+2y-3z=14` ANSWER :B

Discussion

9378.	युग्मक सामान्यतः किस प्रकार के होते हैं?
Answer» हैप्लॉयड (एक गुणक) डिप्लॉयड (द्विगुणक) पौलीप्लॉइड (बहुगुणक) नलीप्लॉइड (अगुणक) ANSWER :A

Discussion

9379.	आवेशन का सही परिक्षण होता है -
Answer» प्रतिकर्षण आकर्षण उदासीनता केवल आकर्षण तथा प्रतिकर्षण Answer :A

Discussion

9380.	Show that semi latus rectum of the parabola y^(2) =4ax is the harmonic mean between the segments of any focal chord.
Answer» ANSWER :`2A= ( 2SPSQ)/( SP+SQ)`

Discussion

9381.	Projection of the line 8x-y-7z=8,x+y+z=1 on the plane 5x-4y-z=5 is
Answer» `(x-1)/(1)=(y-0)/(2)=(z-0)/(-3)` `(x-0)/(1)=(y-1)/(2)=(z-0)/(-3)` `(x-0)/(1)=(y-0)/(2)=(z-1)/(-3)` `x=y=t` ANSWER :A

Discussion

9382.	Two personsthrowa pairof dice alternativelytill onegets a totalof 9and wins the game . If A has the firstthrow ,then theprobabilitythat A winsthe game is :
Answer» `9/17` `8/17` `1/2` NONE of these ANSWER :A

Discussion

9383.	If vec(a) and vec(b) are two vectors in space given byvec(a) = (hat(i)-2hat(j))/(sqrt(5))and vec(b) = (2 hat(i) +hat(j)+ 3 hat(k))/(sqrt(14) )then the value of
Answer» ANSWER :8

Discussion

9384.	Let f(x)= x^(3)-x^(2) + x + 1 g(x) = {max (f(t)), 0 le t le x}, 0 le x le 1}{ 3-x, 1 lt x le 2} Then in [0, 2] the points where g(x) is not differentiable is………
Answer» 0 1 2 None of these Answer :B

Discussion

9385.	Let vec(a),vec(b), & vec(c) be three vectors such that \|vec(b)\| = 2\|vec(a)\| & \|vec(c)\| = 3\|vec(a)\|. The Angle between each pair of vectors is 60^(@) such that \|vec(a) + 2vec(b) + 3vec(c)\| = sqrt(21) then sqrt(7)\| vec(c)\| is equal to
Answer» Solution :`\|vec(a)\| = k` `\|vec(b)\| = 2k` `\|vec(C)\| = 3k` `\|vec(a) + 2vec(b) + 3vec(c)\| = sqrt(21)` `(\|vec(a) + 2vec(b) + 3vec(c)\|)^(2) = 21` `a^(2) + 4b^(2) + 9C^(2) + 2[2vec(a) cdot vec(b) + 6vec(b) cdot vec(c) + 3vec(c) cdot vec(a)] = 21` `k^(2) + 16k^(2) + 81k^(2) + 2[(4k^2)/2 + (36k^2)/2 + (9k^2)/2] = 21` `147k^(2)= 21 IMPLIES k = +- 1/(sqrt7)` `\|c\| = 3k = 3/(sqrt7)` [magnitude is ALWAYS +ve]`

Discussion

9386.	If the intercepts made by tangent, normal to a rectangular hyperbola x^(2)-y^(2)=a^(2) with x-axis are a_(1),a_(2) and with y-axis are b_(1)b_(2) when a_(1)a_(2)+b_(1)b_(2)=
Answer» 0 1 `-1` `a^2` ANSWER :A

Discussion

9387.	Which of the following options is the only correct combination ?
Answer» (II) (III) (S) (II) (iv) (Q) (III) (i) (R ) (I) (ii) (P) ANSWER :D

Discussion

9388.	If (1+sqrt(1+a))tan alpha= 1 +sqrt(1-a), then sin 4 alpha=.......
Answer» `(a)/(2)` a 2a `a^(2/3)` Solution :LET `a=sin4thetaimpliessqrt(1+a)=cos2theta+sin2theta` and `sqrt(1-a)=cos2theta-sin2theta` `because(1+sqrt(1+a))TAN ALPHA=1+sqrt(1-a)` `implies(1+cos2theta+sin2theta)tanalpha=1+cos2theta-sin2theta` `=2costheta(costheta+sintheta)tan alpha=2costheta(costheta-sintheta)` `implies(costheta+sintheta)/(costheta-sintheta)=cotalphaimplies(1+tantheta)/(1-tantheta)=COTALPHA` `impliestan((pi)/(4)+theta)=tan((pi)/(2)-alpha)=alpha=(pi)/(4)-theta` `=sin4alpha=sin(pi-4theta)=sin4theta=a`

Discussion

9389.	Which of the following options is the only correct combination ?
Answer» (II) (i) (Q) (I) (ii) (R ) (IV) (iv) (P) (IV) (iv) (S) Answer :A

Discussion

9390.	Which of the following options is the only correct combination ?
Answer» <P>(III) (i) (P) (III) (i) (S) (IV) (iii) (R ) (IV) (i) (R ) ANSWER :C

Discussion

9391.	For number N=35700, find (i) number of divisors (ii) number of proper divisors (iii) number of even divisors (iv) number of odd divisors (v) sum of all divisors
Answer» Solution :`N=35700=5^(2)xx2^(2)xx3^(1)xx7^(1)xx17^(1)` (i) Number of divisors `=(2+1)xx(2+1)xx(1+1)xx(1+1)xx(1+1)` `=3xx3xx2xx2xx2` =72 (II) Number of proper divisors =72-2=70 (III) Number of even divisors `=3xx2xx2xx2xx2` (as 2 MUST occur at least once) =48 (iv) Number of ODD divisors =72-48=24 (v) Sum of divisors `=(5^(@)+5^(1)+5^(2))(2^(@)+2^(1)+2^(2))(3^(@)+3^(1))(7^(@)+7^(1))(17^(@)+17^(1))` `=31xx7xx4xx8xx18` =124992

Discussion

9392.	int(dx)/[(3x+2]^((2)/(3))+(3x+2)^((4)/(5)))=
Answer» `(5)/(3)root5(3x+2)+5root15(3x+2)+5TAN^(-1)root15(3x+2)+C` `(5)/(3)root5(3x+2)+5root15(3x+2)-5tan^(-1)root15(3x+2)+c` `(5)/(3)root5(3x+2)-5root15(3x+2)+5tan^(-1)root15(3x+2)+c` `(5)/(3)root5(3x+2)-5root15(3x+2)-5tan^(-1)root15(3x+2)+c` Answer :C

Discussion

9393.	Find themagnitude of two vectors vecaandvecb , having the same magnitude and such that the angle between them is 60^(@) and their scalar product is (1)/(2).
Answer» ANSWER :`\|veca\|=1,\|vecb\|=1`

Discussion

9394.	Determine k and solve the equation 2x^3 - 6x^2 + 3x+k = 0 if one of its roots is twice the sum of the other two roots.
Answer» ANSWER :`(1pmsqrt3)/2`

Discussion

9395.	If x-1/x=2i sin theta," then "x^4-(1)/(x^4)=
Answer» `2I SIN 4theta` `2cos5 THETA` `2i cos^5theta` `2cos^5theta` ANSWER :A

Discussion

9396.	Let A be the area between co-ordinate axis, y ^(2) =x -1,x ^(2) =y -1 and the line which makes the shortest distance between two parabolas and A be the area between x =0, x ^(2)=y -1,x =y and the shortest distance between y ^(2) =x -1 and x ^(2) = y-1,then
Answer» ` A= A'` `A = (A')^(1//2)` `A = 2A'` can't SAY anything ANSWER :C

Discussion

9397.	lim_(x to 0) (1 -e^(x) sin x)/ ( x^(2) + x^(3) )is equal to
Answer» `-1` 0 1 2 Answer :C

Discussion

9398.	A point is moving on y=4-2x^2. The x-coordinate of the point is decreasing at the rate of 5 units per second. Then the rate at which y coordinate of the point is changing when the point is at (1, 2), is
Answer» 5 unit/s 10 unit/s 15 unit/s 20 unit/s Answer :D

Discussion

9399.	For natural numbers m, n if (1-y)^m (1+y)^n=1+a_1 y +a_2 y^2 + …, and a_1 = a_2 = 10, then(m,n) is
Answer» SOLUTION :N/A

Discussion

9400.	If the quadratic equation x^(2)-ax+30=0 and x^(2)-12x+20=0 have exactly one root common, find the sum of the possible values of a.
Answer» 3 10 13 17 Answer :C

Discussion

Explore topic-wise InterviewSolutions in .

If |vec(a)|=2,|vec(b)|=5 and vec(a).vec(b)=10 then find |vec(a)-vec(b)|.

What did the chief astrologer say?

A contractor submitted tenders for 2 works. If 0.4,0.6,0.1 are the respective probabilities that his first tender, atleast one tender, both the tenders are accepted, what is the probability that his second tender is accepted.

Let ABCD be a parallelogram whose diagonals intersect at P and O be the origin, then OA+OB+OC+OD equals

Find the Coefficient of x^(4) in (8-x)^(1//3)

When x is small, sqrt(1 + 2^(x)) is nearly equal to

intsqrt(sec x - ) dx =

Integrate the function (x^(2))/(1-x^(6))

The sets S_(1), S_(2), S_(3), …………. are given by S_(1) = {2/1},S_(2) = {3/2, 5/2},S_(3) = {4/3, 7/3, 10/3},S_(4) = {5/4, 9/4, 13/4, 17/4},........ . Then the sum of the set S_(25) is

Find the value of p if the lines 4x-3y-8=0, 2x+py+2=0, 6x+6y-1=0 are concurrent,.

The solution of (x^(2) - y^(2) x^(2)) (dy)/(dx) + (y^(2) + x^(2) y^(2)) = 0 is

a(x) =|{:(1,2,3),(x+1, 2x+1, 3x+1),(x^(2)+1,2x ^(2) +1, 3x^(2)+1):}|implies int _(0)^(1) A(x) dx=

If x!=0 the determinant Delta=|(a_(0),a_(1),a_(2)),(-x,x,0),(0,-x,x)| vanishes if

If veca and vec b are unit vectors, then what is the angle between veca and vecb for sqrt3 veva - vecb to be a unit vectors ?

Let A and B are square matrices of order 3. If |A|=4, |B|=6, B=A-2I and |adj(I-2A^(-1))|=k, then the value of k is equal to

For any four vectorsveca,vecb,vecc,vecdwe have(vecaxxvecb)xx(veccxxvecd)=[veca,vecb,vecd]vecc-[veca,vecb,vecc]vecd=[veca,vecc,vecd]vecb-[vecb,vecc,vecd]veca.

A line is drawn fromthe point P(1,1,1)and perpendicular to a line with direction ratios, (1,1,1) to intersect the plane x+2y+3z=4 at Q. The locus of point Q is

The mid point of the chord 3x - 2y + 8 = 0 of the ellipse 3x^(2) + 4y^(2) = 24 is

Write the value of int1/(sqrt(x) e^sqrtx)dx

Giventhat f(x)= xg (x)//[x], g(0) = g'(0)=0 and f(x) is continuousat x=-0thenthe valueof f'(0)

If 0 le x le 1 and theta-sin^(-1)x+cos^(-1)x-tan^(-1)x, then

Let * be a binary operation on Q defind by a*b= (ab)/(2), AAa,b in Q Determine whether * is associative or not.

If int x(1 + x) log (1 + x^(2)) dx = F(x) log (1 + x^(2))-(2)/(3) tan^(-1)x - (2x^(3))/(9) - (x^(2))/(2) + (2x)/(3) + c, then F(x) =

If the foot of the perpendicularfrom (0,0,0) to a planeis (1,2,3) then the equation of the plane is ,

युग्मक सामान्यतः किस प्रकार के होते हैं?

आवेशन का सही परिक्षण होता है -

Show that semi latus rectum of the parabola y^(2) =4ax is the harmonic mean between the segments of any focal chord.

Projection of the line 8x-y-7z=8,x+y+z=1 on the plane 5x-4y-z=5 is

Two personsthrowa pairof dice alternativelytill onegets a totalof 9and wins the game . If A has the firstthrow ,then theprobabilitythat A winsthe game is :

If vec(a) and vec(b) are two vectors in space given byvec(a) = (hat(i)-2hat(j))/(sqrt(5))and vec(b) = (2 hat(i) +hat(j)+ 3 hat(k))/(sqrt(14) )then the value of

Let f(x)= x^(3)-x^(2) + x + 1 g(x) = {max (f(t)), 0 le t le x}, 0 le x le 1}{ 3-x, 1 lt x le 2} Then in [0, 2] the points where g(x) is not differentiable is………

Let vec(a),vec(b), & vec(c) be three vectors such that |vec(b)| = 2|vec(a)| & |vec(c)| = 3|vec(a)|. The Angle between each pair of vectors is 60^(@) such that |vec(a) + 2vec(b) + 3vec(c)| = sqrt(21) then sqrt(7)| vec(c)| is equal to

If the intercepts made by tangent, normal to a rectangular hyperbola x^(2)-y^(2)=a^(2) with x-axis are a_(1),a_(2) and with y-axis are b_(1)b_(2) when a_(1)a_(2)+b_(1)b_(2)=

Which of the following options is the only correct combination ?

If (1+sqrt(1+a))tan alpha= 1 +sqrt(1-a), then sin 4 alpha=.......

Which of the following options is the only correct combination ?

Which of the following options is the only correct combination ?

For number N=35700, find (i) number of divisors (ii) number of proper divisors (iii) number of even divisors (iv) number of odd divisors (v) sum of all divisors

int(dx)/[(3x+2]^((2)/(3))+(3x+2)^((4)/(5)))=

Find themagnitude of two vectors vecaandvecb , having the same magnitude and such that the angle between them is 60^(@) and their scalar product is (1)/(2).

Determine k and solve the equation 2x^3 - 6x^2 + 3x+k = 0 if one of its roots is twice the sum of the other two roots.

If x-1/x=2i sin theta," then "x^4-(1)/(x^4)=

Let A be the area between co-ordinate axis, y ^(2) =x -1,x ^(2) =y -1 and the line which makes the shortest distance between two parabolas and A be the area between x =0, x ^(2)=y -1,x =y and the shortest distance between y ^(2) =x -1 and x ^(2) = y-1,then

lim_(x to 0) (1 -e^(x) sin x)/ ( x^(2) + x^(3) )is equal to

A point is moving on y=4-2x^2. The x-coordinate of the point is decreasing at the rate of 5 units per second. Then the rate at which y coordinate of the point is changing when the point is at (1, 2), is

For natural numbers m, n if (1-y)^m (1+y)^n=1+a_1 y +a_2 y^2 + …, and a_1 = a_2 = 10, then(m,n) is

If the quadratic equation x^(2)-ax+30=0 and x^(2)-12x+20=0 have exactly one root common, find the sum of the possible values of a.

Let * be a binary operation on Q defind by ab= (ab)/(2), AAa,b in Q Determine whether is associative or not.