14949 + Interview Questions in Maths in Class 11 Page 56 InterviewSolution

2751.	If a,b,c,d,e are +ve real number such thata+b+ c+ d+e= 8and a^(2) + b^(2) + c^(2) + d^(2) + e^(2)= 16 then the range of 'e' is
Answer» `[0, 16/5]` `[1, 5/3]` `(0, 5/16]` `[-1, 1]` ANSWER :A

Discussion

2752.	Solve : sqrt3 sin theta - cos theta = sqrt2.
Answer» ANSWER :` (PI)/(4) , N in I`

Discussion

2753.	Find the eccentricity, the semi-major axis, the semi-minor axis, the coordinates of the foci, the equationsof the directrices and the length of the latus rectum of the ellipse 3x^(2)+4y^(2)=12.
Answer» Answer :Semi-major axis = a = 2. Semi-minor axis = b = `sqrt(3)` Eccentricity = `1/2` The coordinates of the foci are `(pmae, 0) " or "(pm1, 0)` The equation of the DIRECTRICES are `x= pma/e =PM4` Length of the latus rectum = 3

Discussion

2754.	If bar(p) = xbar(i) + ybar(j) + zbar(k), find the value of \|bar(p) xx bar(k)\|^(2)
Answer» ANSWER :`X^(2) + y^(2)`

Discussion

2755.	Find thevalue of 'r': (i) .^(12)P_(r) = 1320 (ii) .^(56)P_(r+6): .^(54)P_(r+3) = 30800 :1 (iii) 5.^(4)P_(r) = 6.^(5)P_(r-1) (iv) .^(9)P_(5) +5 .^(9)P_(4) = 10 P_(r)
Answer» ANSWER :(i) 3 (ii) 41 (III) 3 (IV) 5

Discussion

2756.	How many signals can be formed with 4 green and 3 red flags arranged vertically?
Answer» ANSWER :35

Discussion

2757.	Find the centroid of the tetrahedron, whose vertices are (2,3,-4),(-3,3,2),(-1,4,2),(3,5,1)
Answer» ANSWER :`(1/4,15/4,1/4)`

Discussion

2758.	An examination is takenat three centres each of the of which has 100 candidates . The mean marks and standard devaition for the each centre are given below : Calculate the mean and standard deviation of all 300 candidates .
Answer» ANSWER :`46,10.26`

Discussion

2759.	If A, B, C are in A.P and and B=(pi)/(4) then tan A tan B tan C =
Answer» 1 2 3 4 Answer :A

Discussion

2760.	Prove the following ("sin"x-"sin"y)/(cosx+cosy)="tan""(x-y)/(2)
Answer» ANSWER :RHS

Discussion

2761.	Find Lt_(xto0)((sinx)/x)^((sinx)/(x-sinx)).
Answer» ANSWER :`E^(-1)`

Discussion

2762.	In triangle ABC , if cot A , cot B , cot Care in A.P., then a^(2), b^(2) , c^(2) are in…………
Answer» A.P G.P H.P A.G.P ANSWER :A

Discussion

2763.	There 12 points in a plane of which 5 are collinear . Find the number of straight lines obtained by joining these points in pairs.
Answer» ANSWER :` 57`

Discussion

2764.	Find the locus of the point of intersection of the lines x+y=3+lamda and 5x-y=7+3lamda, where lamda is a variable.
Answer» ANSWER : `rArrx-2y+=0`

Discussion

2765.	Let f(x){:{(2x+a",",x ge -1),(bx^(2)+3,x lt -1):} and g(x)={:{(x+4",",0 le x le 4),(-3x-2,-2 lt x lt 0):} g(f(x)) is not defined if
Answer» `a in (10, oo), B in (5, oo)` `a in (4, 10), b in (5, oo)` `a in (10, oo), b in (0, 1)` `a in (4, 10) , b in (1, 5)` Answer :A

Discussion

2766.	The equation of the circle passing through the point (4, 5) and having centre at (2, 2) is :
Answer» ANSWER :`X^(2)+y^(2)-4x-4y=5`

Discussion

2767.	If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find A ∩ (B ∪ C)
Answer» ANSWER :`{ 7, 9, 11 }`

Discussion

2768.	The period of f(x)=e^(x)-[x\|\|cos(pi x ) \| + \|cos(2 pi x)\| + ........\|cos( n pi x)\|) (where [.] is G.I.F) is
Answer» 1 `1/2` `1/4` `1/5` ANSWER :A

Discussion

2769.	If g(x) = (x^(2)+2x+3), f(x) and f(0)=5 and lim_(xrarr0)(f(x)-5)/x = 4 then g'(o) is
Answer» 20 14 18 12 Answer :B

Discussion

2770.	Find the range of the following function f(x)= sqrt(x-3), x in R
Answer» ANSWER :`[0, OO)`

Discussion

2771.	The periodofSin^(n ) x cos^(n) xwhenn isodd inpi
Answer» `PI` `(pi)/(2)` `2pi` `(pi)/(4)` ANSWER :3

Discussion

2772.	Lim_( x to pi/2) (1-sin x)/((pi-2x)^(2))
Answer» ANSWER :`1/8`

Discussion

2773.	If a, b and A are given andc_(1) , c_(3) are two values of the side c in the ambiguous case, then c_(1)^(2) + c_(2)^(2) - 2c_(1)c_(2) * cos 2 A =
Answer» `4A^(2) COS^(2)A` `4a^(2)SIN^(2)A` `4a^(2)` `4a^(2) cos^(2)2A` Answer :a

Discussion

2774.	Find the coefficient of x^6 y^3 in the expansion of (x+2y)^9.
Answer» ANSWER :672

Discussion

2775.	Internal bisectors of DeltaABC meet the circumcircle at points D, E and Fthen area of DeltaDEF is
Answer» `2R^(2)COS^(2)((A)/(2))cos^(2)((B)/(2))cos^(2)((C)/(2))` `2R^(2)SIN((A)/(2))sin((B)/(2))sin((C)/(2))` `2R^(2)sin^(2)((A)/(2))sin^(2)((B)/(2))sin^(2)((C)/(2))` `2R^(2)cos((A)/(2))cos((B)/(2))cos((C)/(2))` ANSWER :D

Discussion

2776.	If z=(1)/((2+3i)^(2)) then \|z\|=...
Answer» `(1)/(13)` `(1)/(5)` `(1)/(12)` `(1)/(2)` ANSWER :A

Discussion

2777.	The no. of solutions of the equation 3x+3y-z=5,x+y=z=3,2x+2y-z=3 is
Answer» 1 0 infinite none Answer :C

Discussion

2778.	For any integer n ge 1, then sum_(k=1)^(n) k ( k+2) is equal to
Answer» `(N (n+1) (n+2) )/( 6)` `(n (n+1) (2n+1) )/( 6) ` `( n ( n+1) (2n+7) )/(6)` `(n (n+1) (2n+9) )/( 6)` ANSWER :C

Discussion

2779.	(bari-barj) xx (barj-bark).(bark-bari) =
Answer» 0 1 2 3 Answer :A

Discussion

2780.	If tanA=-3/4 and pi/2 lt A lt pi, find the values of the following: i) sinA/2 ii) cosA/2,iii) tanA/2
Answer» SOLUTION :i) `3/sqrt(10)`, II) `1/sqrt(10)`, III) 3

Discussion

2781.	Sinh (ix) =
Answer» ISINX SIN (IX) `-isinx` ISIN(ix) ANSWER :A

Discussion

2782.	Find at least two equations of the straight lines in the family of the lines y = 5x +b, for which b and thex - coordinate of the point of intersection of the lines with 3x - 4y = 6 are integers .
Answer» ANSWER :5X - 10

Discussion

2783.	Write a note on triangulation method and radar method to measure larger distances.
Answer» Solution :RADAR method (i) The word RADAR stands for radio detection and ranging. (ii) A radar can be used to measure accurately the distance of a nearby planet such as MARS. In this method, radio waves are sent from transmitters which, after reflection from the planet, are detected by the receiver. (iii) By measuring, the time interval (t) between the instants the radio waves are sent and received, the distance of the planet can be determined as (Speed is EXPLAINED in unit 2) Distance(d) = Speed of radio waves x time taken `d = ( v xx t)/(2)` (iv) where v is the speed of the radio wave. As the time taken (t) is for the distance covered during the FORWARD and backward path of the radio waves, it is divided by 2 to get the actual distance of the OBJECT. This method can also be used to determine the height, at which an aeroplane flies from the ground.

Discussion

2784.	If f and g are two real valued functions defined as f(x)= 2x+1 and g(x)= x^(2)+1, then find f+g
Answer» ANSWER :`X^(2) + 2X+ 2`

Discussion

2785.	If f and g are two real valued functions defined as f(x)= 2x+1 and g(x)= x^(2)+1, then find f-g
Answer» ANSWER :`X(2-x)`

Discussion

2786.	If f and g are two real valued functions defined as f(x)= 2x+1 and g(x)= x^(2)+1, then find (f)/(g).
Answer» ANSWER :`(2X + 1)/(X^(2) + 1)`

Discussion

2787.	If A is a 3xx3 matrix and B is its Adjoint matrix. If the determinent of B is 64 then the determinent of A is
Answer» `PM6` `pm8` `PM4` `pm16` ANSWER :B

Discussion

2788.	If range of the function f(x)=sin^(-1)x+2tan^(-1)x+x^(2)+4x+1 is [p,q], then the value of p+q is
Answer» ANSWER :4

Discussion

2789.	If S=ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents two straight lines equidistance from the origin show that f^(4)-g^(4)=c(bf^(2)-ag^(2))
Answer» ANSWER :`C(BF^(2)-AG^(2))`

Discussion

2790.	Locus of a point 'P' such that PA+PB =4, where A=(2,3,4), B=(-2,3,4) is
Answer» `y^(2)-Z^(2)+6y-8z+25 = 0` `y^(2)+z^(2)-6y-8z+25 = 0` `y^(2)-z^(2)-6y-8z+25 = 0` `y^(2)+z^(2)-6y-8z+25 = 0` ANSWER :B

Discussion

2791.	The number of the terms in the expansion(sqrt(3)+root(5)5)^(256) which are integar is ……….
Answer» 33 34 35 32 Answer :A

Discussion

2792.	If tanA = 12/5 and pi lt A lt (3pi)/(2), find the values of the following: i) sin2A ii) cos2A iii) tan2A
Answer» SOLUTION :i) `120/169`, II) `-119/169`, III) `-120/119`

Discussion

2793.	Change the following complex numbers into polar form (1+ 7i)/((2-i)^(2))
Answer» ANSWER :`SQRT2 ("cos" (3pi)/(4) + i "sin" (3pi)/(4))`

Discussion

2794.	Differentiate using 1^(st) principle : f(x)=(1)/(sqrt(2x+3))
Answer» ANSWER :`-(1)/((2x+3)^(3//2))`

Discussion

2795.	If the line x=a+m, y=-2 and y=mx are concurrent, then least value of absa is
Answer» 0 `SQRT2` `2sqrt32` 2 Answer :C

Discussion

2796.	A line is parallel to X-axis if all the points on the line have equal _____ .
Answer» ANSWER :y and Z COORDINATES

Discussion

2797.	Find the derivative of (1 - xsqrt(x))/(1+xsqrt(x)), (x > 0)
Answer» ANSWER :`(- 3 SQRTX)/((1+ x sqrtx) ^(2)) `

Discussion

2798.	If f(x) is differentiable in the interval [2,5] , where f(2) = ( 1)/(5) and f(5) = ( 1)/(2), then there exists a number 2 lt c lt 5 for which f(c ) is equal to
Answer» `(1)/(2)` `(1)/(5)` `(1)/(10)` `-(1)/(2)` ANSWER :C

Discussion

2799.	Find the valuesof other five trigonometric functions cotx=(3)/(4),x lies in third quadrant.
Answer» ANSWER :`SIN X =- 4/5, COSEC x =- 5/4, cos x =- 3/5, sec x =- 5/3, tan x =- 4/3`

Discussion

2800.	In the hexagon PQRSTU, RS\|\|PU\|\|QT. Which sides or diagonals have positive slope
Answer» Answer :QR, QS, PS, PT, PR

Discussion

Explore topic-wise InterviewSolutions in .

If a,b,c,d,e are +ve real number such thata+b+ c+ d+e= 8and a^(2) + b^(2) + c^(2) + d^(2) + e^(2)= 16 then the range of 'e' is

Solve : sqrt3 sin theta - cos theta = sqrt2.

Find the eccentricity, the semi-major axis, the semi-minor axis, the coordinates of the foci, the equationsof the directrices and the length of the latus rectum of the ellipse 3x^(2)+4y^(2)=12.

If bar(p) = xbar(i) + ybar(j) + zbar(k), find the value of |bar(p) xx bar(k)|^(2)

Find thevalue of 'r': (i) .^(12)P_(r) = 1320 (ii) .^(56)P_(r+6): .^(54)P_(r+3) = 30800 :1 (iii) 5.^(4)P_(r) = 6.^(5)P_(r-1) (iv) .^(9)P_(5) +5 .^(9)P_(4) = 10 P_(r)

How many signals can be formed with 4 green and 3 red flags arranged vertically?

Find the centroid of the tetrahedron, whose vertices are (2,3,-4),(-3,3,2),(-1,4,2),(3,5,1)

An examination is takenat three centres each of the of which has 100 candidates . The mean marks and standard devaition for the each centre are given below : Calculate the mean and standard deviation of all 300 candidates .

If A, B, C are in A.P and and B=(pi)/(4) then tan A tan B tan C =

Prove the following ("sin"x-"sin"y)/(cosx+cosy)="tan""(x-y)/(2)

Find Lt_(xto0)((sinx)/x)^((sinx)/(x-sinx)).

In triangle ABC , if cot A , cot B , cot Care in A.P., then a^(2), b^(2) , c^(2) are in…………

There 12 points in a plane of which 5 are collinear . Find the number of straight lines obtained by joining these points in pairs.

Find the locus of the point of intersection of the lines x+y=3+lamda and 5x-y=7+3lamda, where lamda is a variable.

Let f(x){:{(2x+a",",x ge -1),(bx^(2)+3,x lt -1):} and g(x)={:{(x+4",",0 le x le 4),(-3x-2,-2 lt x lt 0):} g(f(x)) is not defined if

The equation of the circle passing through the point (4, 5) and having centre at (2, 2) is :

If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find A ∩ (B ∪ C)

The period of f(x)=e^(x)-[x||cos(pi x ) | + |cos(2 pi x)| + ........|cos( n pi x)|) (where [.] is G.I.F) is

If g(x) = (x^(2)+2x+3), f(x) and f(0)=5 and lim_(xrarr0)(f(x)-5)/x = 4 then g'(o) is

Find the range of the following function f(x)= sqrt(x-3), x in R

The periodofSin^(n ) x cos^(n) xwhenn isodd inpi

Lim_( x to pi/2) (1-sin x)/((pi-2x)^(2))

If a, b and A are given andc_(1) , c_(3) are two values of the side c in the ambiguous case, then c_(1)^(2) + c_(2)^(2) - 2c_(1)c_(2) * cos 2 A =

Find the coefficient of x^6 y^3 in the expansion of (x+2y)^9.

Internal bisectors of DeltaABC meet the circumcircle at points D, E and Fthen area of DeltaDEF is

If z=(1)/((2+3i)^(2)) then |z|=...

The no. of solutions of the equation 3x+3y-z=5,x+y=z=3,2x+2y-z=3 is

For any integer n ge 1, then sum_(k=1)^(n) k ( k+2) is equal to

(bari-barj) xx (barj-bark).(bark-bari) =

If tanA=-3/4 and pi/2 lt A lt pi, find the values of the following: i) sinA/2 ii) cosA/2,iii) tanA/2

Sinh (ix) =

Find at least two equations of the straight lines in the family of the lines y = 5x +b, for which b and thex - coordinate of the point of intersection of the lines with 3x - 4y = 6 are integers .

Write a note on triangulation method and radar method to measure larger distances.

If f and g are two real valued functions defined as f(x)= 2x+1 and g(x)= x^(2)+1, then find f+g

If f and g are two real valued functions defined as f(x)= 2x+1 and g(x)= x^(2)+1, then find f-g

If f and g are two real valued functions defined as f(x)= 2x+1 and g(x)= x^(2)+1, then find (f)/(g).

If A is a 3xx3 matrix and B is its Adjoint matrix. If the determinent of B is 64 then the determinent of A is

If range of the function f(x)=sin^(-1)x+2tan^(-1)x+x^(2)+4x+1 is [p,q], then the value of p+q is

If S=ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents two straight lines equidistance from the origin show that f^(4)-g^(4)=c(bf^(2)-ag^(2))

Locus of a point 'P' such that PA+PB =4, where A=(2,3,4), B=(-2,3,4) is

The number of the terms in the expansion(sqrt(3)+root(5)5)^(256) which are integar is ……….

If tanA = 12/5 and pi lt A lt (3pi)/(2), find the values of the following: i) sin2A ii) cos2A iii) tan2A

Change the following complex numbers into polar form (1+ 7i)/((2-i)^(2))

Differentiate using 1^(st) principle : f(x)=(1)/(sqrt(2x+3))

If the line x=a+m, y=-2 and y=mx are concurrent, then least value of absa is

A line is parallel to X-axis if all the points on the line have equal _____ .

Find the derivative of (1 - xsqrt(x))/(1+xsqrt(x)), (x > 0)

If f(x) is differentiable in the interval [2,5] , where f(2) = ( 1)/(5) and f(5) = ( 1)/(2), then there exists a number 2 lt c lt 5 for which f(c ) is equal to

Find the valuesof other five trigonometric functions cotx=(3)/(4),x lies in third quadrant.

In the hexagon PQRSTU, RS||PU||QT. Which sides or diagonals have positive slope