14949 + Interview Questions in Maths in Class 11 Page 246 InterviewSolution

12251.	If x,y,z are in A.P. and tan^(-1)x, tan^(-1)y and tan^(-1)z are also in A.P. then
Answer» `x=y=z` `2x=3y=6z` `6x=3y=2z` `6x=4y=3z` ANSWER :A

Discussion

12252.	Show thatLim_(x to pi/2)tanx does not exist .
Answer» ANSWER :Limit does not existas `Lim_(x to (PI^(+))/2`TAN x oo and LIM tan x = oo `

Discussion

12253.	Which of the following sentences are statements? Give reasons for your answer: The sum of 5 and 7 is greater than 10.
Answer» ANSWER :It is a STATEMENT.

Discussion

12254.	If the angles are in the ratio 1: 5: 6, then find the ratio of its sides .
Answer» ANSWER :` SQRT3 -1 ; sqrt3 + 1: 2 SQRT2`

Discussion

12255.	The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.
Answer» ANSWER :`16/7;2;16/7(2^(N)-1)`

Discussion

12256.	If (x+3+1, y-2/3)=(5/3, 1/3), find the values of x and y.
Answer» ANSWER :x=2 and y=1

Discussion

12257.	Forx in R , 3 cos (4x-5) +4 lies in the interval
Answer» `[1,7]` `[4,7]` `[0,7]` `[2,7]` ANSWER :1

Discussion

12258.	If bara " isperpendicular to " bari+barj+ bark " then the vector " bara is
Answer» ` BARI- barj+bark` `bari- barj-bark` `2BARI - 3barj+bark` `BAR0` ANSWER :D

Discussion

12259.	Find the stationary points and stationary values for the following functions. (x-2)^(4)(x+1)^(3)
Answer» ANSWER :`((1)/(E), e^(-1//e)), e^(-1//e)`

Discussion

12260.	If bara,barb are non-zero and non-collinear vectors then [bara barb bari]bari+[bara barb barj]barj+[bara barb bark]bark=
Answer» `BARAXXBARB` `barbxxbara` 0 `bara.barb` ANSWER :A

Discussion

12261.	Differentiate from first principles: 11. (x+1)(2x-3)
Answer» ANSWER :`4x-1`

Discussion

12262.	Find angles between the linessqrt3x + y = 1 " and " x + sqrt3y = 1.
Answer» ANSWER :`30^(@) " and " 150^(@)`

Discussion

12263.	Write the contrapositive and converse of the following statements. Something is cold implies that it has low temperature.
Answer» ANSWER :The contrapositive is If SOMETHING is not at low TEMPERATURE, then it is not cold The CONVERSE is If something is at low temperature, then it is cold

Discussion

12264.	Number of roots of cos^(2) x + (sqrt(3) + 1)/( 2) sin x - (sqrt(3))/(4) - 1 =0which lie in the interval [- pi, pi] is
Answer» 2 4 6 8 Answer :B

Discussion

12265.	In Delta ABC, if cos A cos B+ sin A sin B sin C=1, then a:b:c=
Answer» `1 : 1 : SQRT2` `1 : sqrt2 : 1` `sqrt2 : 1 : 1` `sqrt2 : sqrt2 : 1` ANSWER :A

Discussion

12266.	A spherical ballon is filled with 4500pi cubic meters of helium gas. If a leak in the ballon cause the gas to escape at the ratio of 72pi cubic meters per meters, then the rate (in meters per minute) at which the radius of the ballon decreases 49 minutes after the leakage bagan is
Answer» `2//9` `9//2` `9//7` `7//9` ANSWER :A

Discussion

12267.	If A(2, -1) and B(6, 5) are two points the ratio in which the foot of the perpendicular from (4, 1) to AB divides it is
Answer» `8:15` `5:8` `-5:8` `-8:5` ANSWER :B

Discussion

12268.	If a= ( 1)/( 5 cos x+ 12 sin x) then for all real x
Answer» the LEAST positive VALUE of a is `(1)/(13)` the greatest NEGATIVE value of a is `- (1)/(13)` ` a LE (1)/( 13)` `- (1)/( 13) le a le (1)/(13)` Answer :A::B

Discussion

12269.	Find the approximate value of root(3)(7.8)
Answer» ANSWER :1.9834

Discussion

12270.	If f^(1)(x) =g(x) and g^(1)(x) =-f (x) for all x and f(2) = 4 =f^(1) (2) then f^(2) (4) +g^(2)(4) is
Answer» 32 24 64 48 Answer :A

Discussion

12271.	If 5cos2theta+2cos^(2)""(theta)/(2)+1=0 and -piltthetaltpi, then find theta.
Answer» Answer :`PM(pi)/(3),pm[pi-cos^(-1)((3)/(5))]`

Discussion

12272.	If tan h^(2) x = cos theta then cos h 2x =
Answer» `tan^(2) ((theta)/(2))` `COT^(2) ((theta)/(2))` `SEC^(2) ((theta)/(2))` `SIN^(2) ((theta)/(2))` Answer :B

Discussion

12273.	Evaluate the following limits : Lim_(x to pi/2) (cos^(2)x)/(1-sinx )
Answer» ANSWER :2

Discussion

12274.	Iftanalpha=(1)/(7)andtanbeta=(1)/(3), then cos2alpha is equal to
Answer» `sin2beta` `sin4beta` `sin3beta` `COS2BETA` ANSWER :B

Discussion

12275.	If the chord joining the points where x=p, x=q on the curve y=ax^(2)+bx+c is parallel to the tangent to the curve (alpha, beta)( then alpha=
Answer» 2PQ `sqrt(PQ)` `(p+q)/(2)` `(p-q)/(2)` Answer :C

Discussion

12276.	The radius of the circumcircle of an isosceles triangle PQR is equal to PQ(=PR). Then the angle P is
Answer» ` 75^(@) ` ` 105 ^(@) ` ` 90 ^(@)` ` 120 ^(@) ` ANSWER :D

Discussion

12277.	If A and B are subsets of the universal set cup, then show that, (A cap B) sub A
Answer» ANSWER :`(A CAP B) SUB A`

Discussion

12278.	Define Coefficient of restitution
Answer» Solution :Co-efficient of resitution is defined as the RATIO of velocity of SEPARATION (relative velocity) after COLLISION to the velocity of approach (relative velocity) before collision, i.E., ` e = ("velocity of separation(after collision)")/("velocity of approach (before collision)")` ` = ((v_2 - v_1))/((u_1 - u_2))`

Discussion

12279.	A=(0,5),B = (0, -5) are the points and \|AP-PB\|=8 then the locus of P is
Answer» `16x^(2)-9Y^(2)+144=0` `16x^(2)+9y^(2)+144=0` `x^(2)+9y^(2)+144=0` `16x^(2)-9y^(2)-144=0` ANSWER :1

Discussion

12280.	P, Q, R and S are four points with the position vectors 3bar(i)-4bar(j)+5bar(k), 4bar(k), -4bar(i)+5bar(j)+bar(k) and -3bar(i)+4bar(j)+3bar(k) respectively. Then the line PQ meets the line RS at the point.
Answer» `3bar(i)+4bar(J)+3bar(k)` `-3bar(i)+4bar(j)+3bar(k)` `-BAR(i)+4bar(j)+bar(k)` `bar(i)+bar(j)+bar(k)` ANSWER :B

Discussion

12281.	underset(x to 1)(Lt) ((1+x)/(2+x))^(((1-sqrt(x))/(1-x)))=
Answer» `(2)/(3)` `SQRT((2)/(3))` `(2)/(sqrt(3))` `(sqrt(2))/(3)` ANSWER :B

Discussion

12282.	If (bara+barb)botbara, absbarb =sqrt2 absbara, then
Answer» `(2bara+barb)ABS()BARA` `(2bara+barb)botbarb` `(2bara-barb)botbarb` `(2bara+barb)BOT bara` ANSWER :B

Discussion

12283.	Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : s ^^ q
Answer» ANSWER :T

Discussion

12284.	Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : r ^^ p
Answer» ANSWER :F

Discussion

12285.	Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : q vv s
Answer» ANSWER :T

Discussion

12286.	Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : ~r
Answer» ANSWER :T

Discussion

12287.	Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : ~q
Answer» ANSWER :F

Discussion

12288.	Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : p ^^ s
Answer» ANSWER :F

Discussion

12289.	Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : p vv s
Answer» ANSWER :T

Discussion

12290.	Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : q ^^ r
Answer» ANSWER :F

Discussion

12291.	Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : r vv p
Answer» ANSWER :F

Discussion

12292.	If y = "sin"^(-1)[xsqrt(1 - x) - sqrt(x) sqrt(1 - x^2)] and 0 lt x lt 1 then (dy)/(dx) at x = (sqrt3)/2 is
Answer» ANSWER :B

Discussion

12293.	If x = exp [ Tan ^(-1) ((y -x ^(2))/(x ^(2)))] then (dy )/(dx)=
Answer» `2x [1 + TAN(LOG x) + x.sec 2(log x)]` `x [1 + tan(log x) + sec^2(log x)]` `2x [1 + tan(log x) + x^2sec 2(log x)]` `2x [1 + tan(log x) + sec^2(log x)]` Answer :A

Discussion

12294.	A variable complex number z is such that the amplitude of (z-1)/(z+1) is always equal to (pi)/(4). Illustrate the locus of z in the Argand plane
Answer» ANSWER :`SQRT2`

Discussion

12295.	If the first three terms in the expansion of (1 + ax)^(n) in ascending powers of x are 1+ 12x + 64x^(2), find n and a.
Answer» ANSWER :`9, (4)/(3)`

Discussion

12296.	Find the approximate value of root(3)65
Answer» ANSWER :4.0208

Discussion

12297.	Find sin""(x)/(2),cos""(x)/(2)andtan""(x)/(2) in each of the following. sinx=(1)/(4),x in quadrant II.
Answer» ANSWER :`(SQRT ( 8 + 2 sqrt15))/(4) , (sqrt ( 8- 2 sqrt15))/(4), 4 + sqrt15`

Discussion

12298.	Evaluate the following limits : Lim_( x to 0) (3^(2x)-1)/(2^(3x)-1)
Answer» ANSWER :`(LOG 9)/( log 8)`

Discussion

12299.	Evaluate the following limits : Lim_( x to 0) (3^(2x)-1)/(2^(3x)-1)
Answer» ANSWER :`(log_(E)9)/(log_(e) 8)`

Discussion

12300.	If bara,barb,barc are three vector suchthat each is inclined at an angle pi/3 " with the other two and" absbara =1, absbarb =2, absbarc=3, " then the scalar product of the vectors " 2bara+3barb-5barc and 4bara-6barb+10barc is equal to
Answer» 333 334 -333 -334 Answer :D

Discussion

Explore topic-wise InterviewSolutions in .

If x,y,z are in A.P. and tan^(-1)x, tan^(-1)y and tan^(-1)z are also in A.P. then

Show thatLim_(x to pi/2)tanx does not exist .

Which of the following sentences are statements? Give reasons for your answer: The sum of 5 and 7 is greater than 10.

If the angles are in the ratio 1: 5: 6, then find the ratio of its sides .

The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.

If (x+3+1, y-2/3)=(5/3, 1/3), find the values of x and y.

Forx in R , 3 cos (4x-5) +4 lies in the interval

If bara " isperpendicular to " bari+barj+ bark " then the vector " bara is

Find the stationary points and stationary values for the following functions. (x-2)^(4)(x+1)^(3)

If bara,barb are non-zero and non-collinear vectors then [bara barb bari]bari+[bara barb barj]barj+[bara barb bark]bark=

Differentiate from first principles: 11. (x+1)(2x-3)

Find angles between the linessqrt3x + y = 1 " and " x + sqrt3y = 1.

Write the contrapositive and converse of the following statements. Something is cold implies that it has low temperature.

Number of roots of cos^(2) x + (sqrt(3) + 1)/( 2) sin x - (sqrt(3))/(4) - 1 =0which lie in the interval [- pi, pi] is

In Delta ABC, if cos A cos B+ sin A sin B sin C=1, then a:b:c=

A spherical ballon is filled with 4500pi cubic meters of helium gas. If a leak in the ballon cause the gas to escape at the ratio of 72pi cubic meters per meters, then the rate (in meters per minute) at which the radius of the ballon decreases 49 minutes after the leakage bagan is

If A(2, -1) and B(6, 5) are two points the ratio in which the foot of the perpendicular from (4, 1) to AB divides it is

If a= ( 1)/( 5 cos x+ 12 sin x) then for all real x

Find the approximate value of root(3)(7.8)

If f^(1)(x) =g(x) and g^(1)(x) =-f (x) for all x and f(2) = 4 =f^(1) (2) then f^(2) (4) +g^(2)(4) is

If 5cos2theta+2cos^(2)""(theta)/(2)+1=0 and -piltthetaltpi, then find theta.

If tan h^(2) x = cos theta then cos h 2x =

Evaluate the following limits : Lim_(x to pi/2) (cos^(2)x)/(1-sinx )

Iftanalpha=(1)/(7)andtanbeta=(1)/(3), then cos2alpha is equal to

If the chord joining the points where x=p, x=q on the curve y=ax^(2)+bx+c is parallel to the tangent to the curve (alpha, beta)( then alpha=

The radius of the circumcircle of an isosceles triangle PQR is equal to PQ(=PR). Then the angle P is

If A and B are subsets of the universal set cup, then show that, (A cap B) sub A

Define Coefficient of restitution

A=(0,5),B = (0, -5) are the points and |AP-PB|=8 then the locus of P is

P, Q, R and S are four points with the position vectors 3bar(i)-4bar(j)+5bar(k), 4bar(k), -4bar(i)+5bar(j)+bar(k) and -3bar(i)+4bar(j)+3bar(k) respectively. Then the line PQ meets the line RS at the point.

underset(x to 1)(Lt) ((1+x)/(2+x))^(((1-sqrt(x))/(1-x)))=

If (bara+barb)botbara, absbarb =sqrt2 absbara, then

Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : s ^^ q

Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : r ^^ p

Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : q vv s

Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : ~r

Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : ~q

Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : p ^^ s

Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : p vv s

Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : q ^^ r

Let p,q,r and s represent simple statements. Assume thatp is false, q is true, r is false, and s is true. Determine the truth valueof each statement expressed below : r vv p

If y = "sin"^(-1)[xsqrt(1 - x) - sqrt(x) sqrt(1 - x^2)] and 0 lt x lt 1 then (dy)/(dx) at x = (sqrt3)/2 is

If x = exp [ Tan ^(-1) ((y -x ^(2))/(x ^(2)))] then (dy )/(dx)=

A variable complex number z is such that the amplitude of (z-1)/(z+1) is always equal to (pi)/(4). Illustrate the locus of z in the Argand plane

If the first three terms in the expansion of (1 + ax)^(n) in ascending powers of x are 1+ 12x + 64x^(2), find n and a.

Find the approximate value of root(3)65

Find sin""(x)/(2),cos""(x)/(2)andtan""(x)/(2) in each of the following. sinx=(1)/(4),x in quadrant II.

Evaluate the following limits : Lim_( x to 0) (3^(2x)-1)/(2^(3x)-1)

Evaluate the following limits : Lim_( x to 0) (3^(2x)-1)/(2^(3x)-1)

If bara,barb,barc are three vector suchthat each is inclined at an angle pi/3 " with the other two and" absbara =1, absbarb =2, absbarc=3, " then the scalar product of the vectors " 2bara+3barb-5barc and 4bara-6barb+10barc is equal to