14949 + Interview Questions in Maths in Class 11 Page 274 InterviewSolution

13651.	Show that f(x) = (k-(1)/(k)-x)(4-3x^(2)) where k is a positive constant, has one and only one maximum value and only one minimum value and their difference is (4)/(9)(k+(1)/(k))^(3)
Answer» ANSWER :`4/9(k+1/k)^3`

Discussion

13652.	The wheel of a carriage is 91 cm in diameter andmake 5 revolution per second. How fast is the carrige running ?
Answer» ANSWER :51-48 km/h

Discussion

13653.	If sinx+cosx=1, then x=______
Answer» `2npi ,(4n+1)(PI)/2,nin Z` `n pi, (4n+1)(pi)/2, n in Z` `n pi (2n+1)(pi)/2,n in Z` `2npi,(2n+1)(pi)/2,n in Z` Answer :A

Discussion

13654.	.......... is the 20^(th) term of sequence a_(n)=(n-1)(2-n) (n-3).
Answer» ANSWER :`-5814`

Discussion

13655.	If f(x)=logx,x=2,deltax=0.02 then deltaf-df=
Answer» `LOG(1.01)` `log(1.01)-0.01` 0.01 0.001 Answer :B

Discussion

13656.	If the periodic function f(x) satisfies the equation f(x+1)+f(x-1)= sqrt(3)f(x) AA x in R and the period of f(x) is 4 lambda then lambda=
Answer» ANSWER :C

Discussion

13657.	Find the equation of the circle passing through the points (4,1) and(6,5) and whose centre is on the line 4x+y=16.
Answer» ANSWER :`X^(2)+y^(2)-6x-8y+15=0`

Discussion

13658.	If {i^(17)-((1)/(i))^(34)}^(2) = a + 2i, then the value of a is
Answer» 0 2 -1 1 Answer :A

Discussion

13659.	If x = tan h^(-1)(y) then log_(e)((1+y)/(1-y))
Answer» x 4x 2x 3x Answer :C

Discussion

13660.	Example 8 Insert 6 numbers between 3 and 24 such that the resulting sequence is an A.P.
Answer» ANSWER :6,9,12,15, 18 and 21

Discussion

13661.	If f(x)=(ax+b)/(a+bx)"then"f(x).f(x).f(1/x)=.... . (where x ne 0)
Answer» ANSWER :1

Discussion

13662.	The sum of n terms of two arithmetic progressions are in the ratio (3n+ 8): (7n+ 15). Find the ratio of their 12^(th) terms.
Answer» ANSWER :`7/16`

Discussion

13663.	Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (cosx)/(1+sinx)
Answer» ANSWER :`(-1)/(1+sinx)`

Discussion

13664.	Perpendicular distance between 3x+4y-5=0 and 6x + 8y - 15=0 is …....
Answer» `1` `(1)/(2)` `(22)/( 10)` `2` ANSWER :B

Discussion

13665.	If a right angled Delta ABCof maximum area is inscribed within a circle of radius R. then (Deltarepresents area of triangle ABC and r, r_(1), r_(2), r_(3)represent inradius and exradii, and s is the semi perimeter of then
Answer» `DELTA = R^(2)` `1/r_(1) + 1/r_(2) + 1/r_(3) = (SQRT 2 + 1)/R ` `r = (sqrt 2 - 1)R` `s = (1 + SQRT2) R` Answer :A::B::C::D

Discussion

13666.	The vertices A and B of a triangle ABC are (2,5),(4,-11),C moves on the line L=9x+7y+4=0. Then the locus of the centroid of the triangle ABC is parallel to
Answer» AB AC BC L Answer :D

Discussion

13667.	Ifcos (A-B)=3//5 and tan A tan B=2 , then which one of the followingis true ?
Answer» SIN (A + B) = `(1)/(5)` sin (A + B) `(-1)/(5)` COS (A- B) = `(1)/(5)` cos (A+B) = `(-1)/(5)` Answer :D

Discussion

13668.	Find the point equlidistant from the four points (-1, 1, 3), (2, 1, 2), (0, 5, 6) and (3, 2, 2).
Answer» ANSWER :the POINT EQUIDISTANT from GIVEN points is (1, 3, 4)

Discussion

13669.	The point of intersection of the lines (x-5)/(3) = (y-7)/(-1) = (z+2)/(1) and (x+3)/(-36) = (y-3)/(2) = (z-6)/(4) is
Answer» `(21, (5)/(3), (10)/(3))` `(2, 10 , 4)` `(-3,36)` `(5,7,-2)` Answer :A

Discussion

13670.	Observe the following lists : (##AKS_NEO_CAO_MAT_XI_VIB_P02_C02_E04_038_Q01.png" width="80%">
Answer» `{:(A,B,C,D),(2,1,3,5):}` `{:(A,B,C,D),(1,2,3,4):}` `{:(A,B,C,D),(2,5,1,3):}` `{:(A,B,C,D),(2,4,3,5):}` ANSWER :B

Discussion

13671.	If absbara =5, absbarb =4, absbarc =3 and bara+barb+barc = bar0 ," then " abs(bara.barb+barb.barc+barc.bara)=
Answer» 25 50 -25 -50 Answer :A

Discussion

13672.	Evaluate the following limits : Lim_(xto 1) (1-x) (tan. (pix)/2)
Answer» ANSWER :`2/pi`

Discussion

13673.	Find the sum to n terms of each of the series in3 × 1^(2) + 5 × 2^(2) + 7 × 3^(2) +.........
Answer» ANSWER :`(N)/(6)(n+1)(3N^(2)+ 5n+1)`

Discussion

13674.	Find the multiplicative inverse of (3+4i)/(4-5i)
Answer» ANSWER :`(-8-31I)/(25) (-8)/(25)- (31i)/(25)`

Discussion

13675.	Given two vectors veca=-hati + 2hatj + 2hatk and vecb =- 2hati + hatj + 2hatk
Answer» <P> Solution :a. VECTOR `-3hati = 3hatj + 4hatk and hati + hatj` are coplanar with `veca and vecb`. b. `vecaxxvecb=\|{:(hati,hatj,HATK),(-1,2,2),(-2,1,2):}\|` `2hati-2hatj+3hatk` c. if `vecc` is equally inclined to `veca and vecb` , then we must have `veca.vecc= vecb.vecc`. which is true for vectors in options p,q,s d. vector is forming a TRIANGLE with `veca and vecb`. THUS `vecc= veca + vecb = -3hati + 3hatj + 4hatk`

Discussion

13676.	Show that \|{:(a,b,c),(b,c,a),(c,a,b):}\|^2=\|{:(2bc-a^(2),c^(2),b^(2)),(c^(2),2ac-b^(2),a^(2)),(b^(2),a^(2),2ab-c^(2)):}\|=(a^(3)+b^(3)+c^(3)-3abc)^(2)
Answer» ANSWER :`(a^(3)+B^(3)+C^(3)-2ABC)^(2)`

Discussion

13677.	If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements and Y has 15 elements , how many elements does X ∩ Y have?
Answer» ANSWER :5

Discussion

13678.	If e is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 (a lt b), then ……..
Answer» `B^(2) = a^(2) (1 - E^(2))` `a^(2) = b^(2) (1 - e^(2))` `a^(2) = b^(2) (e^(2) - 1)` `b^(2) = a^(2) (e^(2) - 1)` ANSWER :B

Discussion

13679.	If ""^(n)C_(8)=""^(n)C_(2), find ""^(n)C_(2).
Answer» ANSWER :45

Discussion

13680.	Express (-sqrt(3)+sqrt(-2))(2sqrt(3)-i)) in the form of a+ib.
Answer» ANSWER :`(-6+SQRT(2))+sqrt(3)(1+2sqrt(2))i`

Discussion

13681.	The numbers of proper subset of set A having n elements are…….
Answer» ANSWER :`2^(N)-2`

Discussion

13682.	1 to 7, describe the sample space for the indicated experiment. 2 boys and 2 girls are in Room X and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.
Answer» ANSWER :`{XB_(1), XB_(2), XG_(1), XG_(2), YB_(3), YG_(3), YG_(4), YG_(5)}`

Discussion

13683.	The longest distance of the point (a,0) from the curve 2x^2+y^2=2x is
Answer» `1+a` `\|1+a\|` `SQRT(1-2a+2a^(2))` `sqrt(1-2a+3a^(2))` ANSWER :C

Discussion

13684.	If A, B, C are three events associated with a random experiment, prove that P(A uu B uu C) = P(A) + P(B) + P(C) - P(A nn B) - P(A nn C) P(B nn C) + P (A nn B nn C)
Answer» ANSWER :` = 1/10`

Discussion

13685.	Three coins are tossed . Describe Two events which are mutually exclusive.
Answer» ANSWER :`:.` EVENTS A and B are MUTUALLY EXCLUSIVE events.

Discussion

13686.	cot^(2) theta - (1+ sqrt3) cot theta + sqrt3 = 0,0 lt theta lt (pi)/(2)
Answer» ANSWER :`(PI)/(6), (pi)/(4)`

Discussion

13687.	If vec(a)= 2vec(i)-vec(j) +vec(k), vec(b)= 3vec(i) + 4vec(j) -vec(k), then \|vec(a) xx vec(b)\|=
Answer» `sqrt135` `sqrt145` `sqrt155` `sqrt165` ANSWER :C

Discussion

13688.	A parabola reflector is 15 cm deep and its focus is at a distance of 5 cm from its vertex. Find the diameter of the reflector.
Answer» Solution :LET the vertex, focus and diameter of PARABOLIC reflecter are (0,0), S(5,0) and AB respectively. The diameter AB is at a distance of 15 cm from the vertex. Let the co-ordinates of A=(15,k) Equation of PARABOLA `y^(2)=4ax` Co-ordinates of focus = (a,0) = (5,0) `rArr""a=5` `:.""y^(2)=20x` `:.""k^(2)=20xx15=300` `rArr"" k=10sqrt(3)` Therefore, AB=2k=20sqrt(3)cm`.

Discussion

13689.	If A+B+C= 360^(@) " then " cot""(A)/(4)+ cot ""(B)/(4) + cot ""(C)/(4)=
Answer» `sin""(A)/(4)sin""(B)/(4)sin""(C )/(4)` `cos""(A)/(4)cos""(B)/(4)cos""(C )/(4)` `TAN""(A)/(4)tan""(B)/(4)tan""(C )/(4)` `cot""(A)/(4)cot""(B)/(4)cot""(C )/(4)` ANSWER :D

Discussion

13690.	a^(2)-b^(2)=bc rArr A:B
Answer» `2:1` `3:1` `4:1` `5:1` ANSWER :A

Discussion

13691.	Write the following sets in roster form: B = {x : x is a natural number less than 6}
Answer» ANSWER :`B = {1, 2, 3, 4, 5}`

Discussion

13692.	sin 765^(@)
Answer» ANSWER :`(1)/(SQRT2)`

Discussion

13693.	bara=bari-bark,barb=xbari+barj+(1-x)bark,barc=ybari+xbarj+(1+x-y)bark then [barabarbbarc] depends on
Answer» only X only y neither x nor y both x and y Answer :C

Discussion

13694.	If the function f(x)=4e^((1-x)/2)+1+x+(x^2)/2+x^2/3 and g(x) =f^(-1)(x) then the reciprocal of g((-7)/6) is .......
Answer»

Discussion

13695.	There are 2 red and 3 black balls in a bag . 3 balls are taken out at random from the bag . Find the probability of getting 2 red and 1 black balls or 1 red and 2 black balls .
Answer» ANSWER :`=(9)/(10)`.

Discussion

13696.	If one root of the equation x^(2)+ax+8=0 is 4 while the equation x^(2)+ax+b=0 has equal roots, find b.
Answer» ANSWER :9

Discussion

13697.	Consider DeltaABC with incentre l(1,0). Equation of the straight lines AI,BI,CI are x=1, y+1= x and x+3y=1 respectively andcot A//2=2 If point A liea above the x-axis and area of DeltaABC is30 sq, units then the in radius of DeltaABC is
Answer» `SQRT3` `SQRT5` 2 `3sqrt2` ANSWER :A

Discussion

13698.	Consider DeltaABC with incentre l(1,0). Equation of the straight lines AI,BI,CI are x=1, y+1= x and x+3y=1 respectively andcot A//2=2 Slope of side Bc is
Answer» `1/2` `(-1)/3` `1/4` `2/3` ANSWER :B

Discussion

13699.	Consider DeltaABC with incentre l(1,0). Equation of the straight lines AI,BI,CI are x=1, y+1= x and x+3y=1 respectively andcot A//2=2 Equation of the locus of centroid of Delta ABC is
Answer» `x=8y+1` `x=2y+1` `2x-3y=1` `3x=5y` ANSWER :A

Discussion

13700.	A ray of light coming from the point (1,2) is reflected at a point A on the axes of x and then passes through the point (5,3). Find the co ordinates of the point A.
Answer» ANSWER :`(13/5,0)`

Discussion

Explore topic-wise InterviewSolutions in .

Show that f(x) = (k-(1)/(k)-x)(4-3x^(2)) where k is a positive constant, has one and only one maximum value and only one minimum value and their difference is (4)/(9)(k+(1)/(k))^(3)

The wheel of a carriage is 91 cm in diameter andmake 5 revolution per second. How fast is the carrige running ?

If sinx+cosx=1, then x=______

.......... is the 20^(th) term of sequence a_(n)=(n-1)(2-n) (n-3).

If f(x)=logx,x=2,deltax=0.02 then deltaf-df=

If the periodic function f(x) satisfies the equation f(x+1)+f(x-1)= sqrt(3)f(x) AA x in R and the period of f(x) is 4 lambda then lambda=

Find the equation of the circle passing through the points (4,1) and(6,5) and whose centre is on the line 4x+y=16.

If {i^(17)-((1)/(i))^(34)}^(2) = a + 2i, then the value of a is

If x = tan h^(-1)(y) then log_(e)((1+y)/(1-y))

Example 8 Insert 6 numbers between 3 and 24 such that the resulting sequence is an A.P.

If f(x)=(ax+b)/(a+bx)"then"f(x).f(x).f(1/x)=.... . (where x ne 0)

The sum of n terms of two arithmetic progressions are in the ratio (3n+ 8): (7n+ 15). Find the ratio of their 12^(th) terms.

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (cosx)/(1+sinx)

Perpendicular distance between 3x+4y-5=0 and 6x + 8y - 15=0 is …....

If a right angled Delta ABCof maximum area is inscribed within a circle of radius R. then (Deltarepresents area of triangle ABC and r, r_(1), r_(2), r_(3)represent inradius and exradii, and s is the semi perimeter of then

The vertices A and B of a triangle ABC are (2,5),(4,-11),C moves on the line L=9x+7y+4=0. Then the locus of the centroid of the triangle ABC is parallel to

Ifcos (A-B)=3//5 and tan A tan B=2 , then which one of the followingis true ?

Find the point equlidistant from the four points (-1, 1, 3), (2, 1, 2), (0, 5, 6) and (3, 2, 2).

The point of intersection of the lines (x-5)/(3) = (y-7)/(-1) = (z+2)/(1) and (x+3)/(-36) = (y-3)/(2) = (z-6)/(4) is

Observe the following lists : (##AKS_NEO_CAO_MAT_XI_VIB_P02_C02_E04_038_Q01.png" width="80%">

If absbara =5, absbarb =4, absbarc =3 and bara+barb+barc = bar0 ," then " abs(bara.barb+barb.barc+barc.bara)=

Evaluate the following limits : Lim_(xto 1) (1-x) (tan. (pix)/2)

Find the sum to n terms of each of the series in3 × 1^(2) + 5 × 2^(2) + 7 × 3^(2) +.........

Find the multiplicative inverse of (3+4i)/(4-5i)

Given two vectors veca=-hati + 2hatj + 2hatk and vecb =- 2hati + hatj + 2hatk

Show that |{:(a,b,c),(b,c,a),(c,a,b):}|^2=|{:(2bc-a^(2),c^(2),b^(2)),(c^(2),2ac-b^(2),a^(2)),(b^(2),a^(2),2ab-c^(2)):}|=(a^(3)+b^(3)+c^(3)-3abc)^(2)

If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements and Y has 15 elements , how many elements does X ∩ Y have?

If e is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 (a lt b), then ……..

If ""^(n)C_(8)=""^(n)C_(2), find ""^(n)C_(2).

Express (-sqrt(3)+sqrt(-2))(2sqrt(3)-i)) in the form of a+ib.

The numbers of proper subset of set A having n elements are…….

1 to 7, describe the sample space for the indicated experiment. 2 boys and 2 girls are in Room X and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

The longest distance of the point (a,0) from the curve 2x^2+y^2=2x is

If A, B, C are three events associated with a random experiment, prove that P(A uu B uu C) = P(A) + P(B) + P(C) - P(A nn B) - P(A nn C) P(B nn C) + P (A nn B nn C)

Three coins are tossed . Describe Two events which are mutually exclusive.

cot^(2) theta - (1+ sqrt3) cot theta + sqrt3 = 0,0 lt theta lt (pi)/(2)

If vec(a)= 2vec(i)-vec(j) +vec(k), vec(b)= 3vec(i) + 4vec(j) -vec(k), then |vec(a) xx vec(b)|=

A parabola reflector is 15 cm deep and its focus is at a distance of 5 cm from its vertex. Find the diameter of the reflector.

If A+B+C= 360^(@) " then " cot""(A)/(4)+ cot ""(B)/(4) + cot ""(C)/(4)=

a^(2)-b^(2)=bc rArr A:B

Write the following sets in roster form: B = {x : x is a natural number less than 6}

sin 765^(@)

bara=bari-bark,barb=xbari+barj+(1-x)bark,barc=ybari+xbarj+(1+x-y)bark then [barabarbbarc] depends on

If the function f(x)=4e^((1-x)/2)+1+x+(x^2)/2+x^2/3 and g(x) =f^(-1)(x) then the reciprocal of g((-7)/6) is .......

There are 2 red and 3 black balls in a bag . 3 balls are taken out at random from the bag . Find the probability of getting 2 red and 1 black balls or 1 red and 2 black balls .

If one root of the equation x^(2)+ax+8=0 is 4 while the equation x^(2)+ax+b=0 has equal roots, find b.

Consider DeltaABC with incentre l(1,0). Equation of the straight lines AI,BI,CI are x=1, y+1= x and x+3y=1 respectively andcot A//2=2 If point A liea above the x-axis and area of DeltaABC is30 sq, units then the in radius of DeltaABC is

Consider DeltaABC with incentre l(1,0). Equation of the straight lines AI,BI,CI are x=1, y+1= x and x+3y=1 respectively andcot A//2=2 Slope of side Bc is

Consider DeltaABC with incentre l(1,0). Equation of the straight lines AI,BI,CI are x=1, y+1= x and x+3y=1 respectively andcot A//2=2 Equation of the locus of centroid of Delta ABC is

A ray of light coming from the point (1,2) is reflected at a point A on the axes of x and then passes through the point (5,3). Find the co ordinates of the point A.