14949 + Interview Questions in Maths in Class 11 Page 37 InterviewSolution

1801.	Letf (x) = { tan "" ((pi)/(4) + x)}^(1/x) , x ne 0 " and " f(0) = k .For what value of k, f(x) is
Answer» ANSWER :`E^(2)`

Discussion

1802.	Find the n^(th) term of the series 2+(5)/(9)+(7)/(27) +…… . Hence find sum to n terms.
Answer» SOLUTION :N/A

Discussion

1803.	Ifcos A =-3//5 , sin B=7//25 and 90^(@) lt A lt 180^@,0^(@) lt B lt 90^(@) , "then " tan (A+B)=
Answer» `3//4` `-3//4` `3//5` `(-3)/(5)` ANSWER :B

Discussion

1804.	Find the values of each of the following : tan225^(@),sin315^(@),tan(-1742^(@)),cos(-1760^(@)).
Answer» ANSWER :`0.7660`.

Discussion

1805.	Let H be the ortho centre of Delta^("le") ABC,then angle subtended by the side BC at the centre of in circle of Delta^("le') BHCis
Answer» `A/2 + pi/2` `(B+C)/2 + pi/2` `(B - C)/2 + pi/2` `(B + C)/2 + pi/4` ANSWER :b

Discussion

1806.	Let f(x)=x(2-x), 0 le x le 2. If the definition of 'f' is extended over the set R-[0, 2] by f(x+1)=f(x) then f is a periodic function with period.
Answer» 1 2 3 4 Answer :B

Discussion

1807.	Find the equation of the line passing through the points (-1, 1) " and " (2, - 4).
Answer» ANSWER :`5X - y + 20 = 0 `

Discussion

1808.	The coefficient of x^(m) and x^n in the expansion of (1+x)^(m+n) are ...........
Answer» ANSWER :` = 1: 1 `

Discussion

1809.	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

1810.	n points are given of which r points are collinear, then the number of straightlines that can be found =(a) ""^(n)C_(2)-""^(r)C_(2)(b) ""^(n)C_(2)-""^(r)C_(2)+1(c) ""^(n)C_(2)-""^(r)C_(2)-1(d) None of these
Answer» `""^(n)C_(2)-""^(r)C_(2)` `""^(n)C_(2)-""^(r)C_(2)+1` `""^(n)C_(2)-""^(r)C_(2)-1` None of these ANSWER :B

Discussion

1811.	Evaluate the following limits : Lim_(x to 0) (sin ax)/(sin bx)
Answer» ANSWER :`a/b`

Discussion

1812.	p vec(a) is a vector perpendicular to vec(i) and vec(j) whose magnitude is 2 where 'p' is a scalar, then
Answer» <P>`vec(a) = vec(K) and \|vec(a)\|=p` `vec(a) = (2)/(p) vec(k) and \|vec(a)\| = (2)/(p)` `vec(a)= 2p vec(k) and \|vec(a)\|= 2p` `vec(a) =p vec(k) and \|vec(a)\|= (p)/(2)` Answer :B

Discussion

1813.	Evaluate the following limits : Lt_(xto7/2)(2x^(2)-9x+8)^(cot(2x-7))
Answer» ANSWER :`E^(5//2)`

Discussion

1814.	Find the number of even positive integers which have three digits?
Answer» ANSWER :` 450`

Discussion

1815.	The price of six different commodities for years 2009 and year 2011 are as follows: The index number for the year 2011 taking 2009 as the base year for the above data was calculated to be 125. Find the values of x and y if the total price in 2009 is Rs. 360.
Answer» ANSWER :`X=` RS. 110, `y=` Rs. 60.

Discussion

1816.	Find the modulus and the arguments of the following complex numbers : 1+i sqrt(3)
Answer» ANSWER :MODULUS =2 ARGUMENT `=(PI)/(3)`

Discussion

1817.	If f (x) ={{:( 3x+ 1,0le xle2"") ,( 1+ 9x ,2lt xlt3 "then "),( 3 0+ 2x ,xge 3"") :}
Answer» Answer :` F( 4) =30 + 2( 4) =38`

Discussion

1818.	(4x+5sinx)/(3x+7cosx)
Answer» ANSWER :`(35+28cosx+28x sinx+15x COSX-15sinx)/((3x+7 cosx)^(2))`

Discussion

1819.	Check the continuity of the function f defined by f(x)={{:((x^(2)-9)/(x^(2)-2x-3),if 0 lt x lt 5 and x ne 3):} at the point x =3
Answer» ANSWER :discontinous

Discussion

1820.	Area of triangle ABC isa^(2) - (b-c)^(2)then tan A =
Answer» ` 8 //15` `1// 16` ` 3//4` ` 4//3` ANSWER :A

Discussion

1821.	Let f'(sinx)lt0andf''(sinx)gt0AAx in(0,(pi)/(2))andg(x)=f(sinx)+f(cosx). Which of the following is true in (0,(pi)/(2))?
Answer» G ' is increasing g' is decreasing g' has a POINT of minima g ' has a point of maxima Answer :A

Discussion

1822.	If t_(n)= sum_(1)^(n) n, then t_(n)^(1) = sum_(1)^(n) t_(n) =
Answer» `(N(n+1) )/(2)` `(n (n+3))/(2)` `(n (n+1)(n+2) )/( 6)` `(n (n+4))/(3)` Answer :C

Discussion

1823.	If \|a\| = 5, \|b\| = 6, \|a.b\| = 24 then \|a xx b\| =
Answer» `sqrt224` 18 `sqrt300` `sqrt254` ANSWER :B

Discussion

1824.	If 0 lt x lt pi and cos x + sin x=1/(2), then tanx =
Answer» `((4-sqrt7))/3` `-((4+sqrt7))/3` `-((1+sqrt7))/4` `((1-sqrt7))/4` ANSWER :B

Discussion

1825.	If x^3+3x^2-9x+c is the form (x-alpha)^2(x - beta), then the positive value of c is .........
Answer»

Discussion

1826.	(Sin^(2) A + SinA+1)/( Sin A)ge Kthen k=
Answer» 2 1 4 3 Answer :4

Discussion

1827.	Evaluate the following limits. Lt_(xto0)(sin5x+sin3x)/(sin6x-sin4x)
Answer» ANSWER :4

Discussion

1828.	Find the derivative of f(x) from the first principle where f(x) is x sin x
Answer» ANSWER :X COS x+sinx

Discussion

1829.	The range of f(x)=cos^(-1)((sqrt(2x^(2)+1))/(x^(2)+1)) is
Answer» `[ - PI/2, pi/2]` `[0, pi]` `[0, pi/2)` `(0, pi)` ANSWER :C

Discussion

1830.	If the line 2x+y=k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2, then k equals
Answer» `29/5` `5` `6` `11/5` ANSWER :C

Discussion

1831.	Find the value of: "sin"75^(@) "tan"15^(@)
Answer» ANSWER :`2-sqrt(3)`

Discussion

1832.	Find the equation of that focal chord of the parabola y^(2)=8x whose mid-point is (2,0).
Answer» Solution :Equation of parabola `y^(2)=8X`. . .(1) Comparing with `y^(2)=4AX` 4a=8 `rArr""a=2` Co-ordinates of ends of focal chord of parabola (1) `=(at^(2),2at)and((a)/(t^(2)),(-2A)/(t))` `=(2t^(2),4T)and((2)/(t^(2)),(-4)/(t))` The mid-point of this chord is (2,0). `:.""(2t^(2)+(2)/(t^(2)))/(2)=2and(4t-(4)/(t))/(2)=0` `rArr""t^(2)+(1)/(t^(2))=andt-(1)/(t)=0` `rArr""t=1` Therefore, the co-ordinates of the ends of latus RECTUM=(2,4) and (2,-4) `:.` Equation of latus rectum `y-4=(-4-4)/(2-2)(x-2)` `rArr""x-2=0`.

Discussion

1833.	A(1, 4), B(2, -3) and C(-1, -2)are the verticies at Delta ABC then find, (1) Equation of median from A. (2) Equation of perpendicular from A. (3) Equation of perpendicular bisector of bar(BC).
Answer» ANSWER :`13x-y-9=0; 3X - y + 1 = 0; 3x - y - 4 = 0`

Discussion

1834.	Evaluate the following limits : Lim_(h to 0 ) 1/h ( 1/sqrt(x+h)-1/(sqrt(x)))
Answer» ANSWER :`(-1)/(2xsqrt(X))`

Discussion

1835.	Find k such that the equation 12x^(2)+7xy-12y^(2)-x+7y+k=0 represents a pair of straight lines. Find the separate equations of the straight lines and also the angle between the lines.
Answer» ANSWER :`90^(@)`

Discussion

1836.	Find the derivative of f(x) from the first principle where f(x) is sin x+ cos x
Answer» ANSWER :COS X-sin x

Discussion

1837.	Descibe the sample space :A coin is tossed . If it results in a head , a die is thrown . If the die is shown up an even number the die is thrown again.
Answer» Answer :`S={T,H1,H3,H5,H21,H22,H23,H24,H25,H26,H41,H42,H43,H44,H45,H46,H61,H62,H63,H64,H65,H66}`

Discussion

1838.	d/(dx)(sqrt(sinsqrtx))
Answer» `(cossqrtx)/(4sqrt(X sinsqrtx))` `(sinsqrtx)/(4sqrt(x cossqrtx))` `(-cossqrtx)/(4sqrt(x sinsqrtx))` `(-tansqrtx)/(4sqrt(x cossqrtx))` ANSWER :A

Discussion

1839.	Let f(theta) = sintheta(sintheta + sin 3theta) . Then f(theta) is
Answer» ` ge 0 ` ONLYWHEN ` THETA ge 0` ` ge 0 ` for all REAL `theta` `gt0` for all real `theta` `LE 0 ` only when `theta le 0` Answer :C

Discussion

1840.	The second term of a G.P. is 2 and the sum of infinite terms is 8. Find the first term.
Answer» ANSWER :4

Discussion

1841.	If the hypotenuse of a rightangledtriangle is 2sqrt2times the lengthof the perpendiculardrawnfrom the opposite vertex, to itthen the diffrenceof twoacuteangles is
Answer» `30 ^(@) ` ` 45 ^(@) ` ` 60 ^(@) ` ` 75 ^(@) ` Answer :B

Discussion

1842.	InDelta ABCProve that cos A + cos B+ cos C =1 +( r ) / ( R )
Answer» ` 1 - ( R )/( r ) ` ` 1- ( r )/( R ) ` ` 1+ ( R )/( r ) ` ` 1 + ( r )/( R )` ANSWER :D

Discussion

1843.	Solve the general vlaue. 2cos ^(2) theta - 5 cos theta + 2 = 0
Answer» ANSWER :`2M PM (PI)/(3)`

Discussion

1844.	Ifb=3 , c =2 , A = 120 ^(@)then lengthof bisector of angle A is
Answer» ` (5)/(6) ` ` (4)/(3)` ` (5)/(4) ` ` (6)/(5) ` ANSWER :D

Discussion

1845.	x = cos^(-1)((1)/(sqrt(1+t^(2)))),y = sin^(-1)((t)/(sqrt(1+t^(2))))rArr(dy)/(dx) is equal to
Answer» 0 1 `-1` 2 Answer :B

Discussion

1846.	The value of sin^(2) 46^(0) + sin^(2) 14^(0) + sin 46^(0) sin 14^(0) =
Answer» `1/4` `3/4` `5/4` `1/2` ANSWER :B

Discussion

1847.	Statement - 1 : The sum of the series 1+ ( 1+2+4) + ( 4+6+9) + ( 9+ 12+ 16) + ... + ( 361 + 380 + 400) is 8000 Statement-2: sum_(k=1)^(n) [ k^(3) - (k-1)^(3) ]= n^(3), for any natural number 'n'
Answer» Statement-1 is TRUE, Staternent-2 is true, Statement-2 is not a CORRECT EXPLANATION for Statement-1 Statement-1 is true, Statement-2 is FALSE. Statement-1 is false, Statement-2 is true. Statement-1 is true, Statement-2 is true, Statement-2 is correct explanation for Statement-1. Answer :D

Discussion

1848.	Find a rational number which when expressed as a decimal will have 1.2bar(56) as its expansion.
Answer» ANSWER :`(622)/(495)`

Discussion

1849.	Solve the equations: 10x^(-2)-9-x^(-4)=0.
Answer» ANSWER :`pm1,PM(1)/(3)`.

Discussion

1850.	Two cards are drawn from a well-shuffled deck of 52 cards. Find the probability thateither both are red or both are kings .
Answer» ANSWER :`(55)/(21)`

Discussion

Explore topic-wise InterviewSolutions in .

Letf (x) = { tan "" ((pi)/(4) + x)}^(1/x) , x ne 0 " and " f(0) = k .For what value of k, f(x) is

Find the n^(th) term of the series 2+(5)/(9)+(7)/(27) +…… . Hence find sum to n terms.

Ifcos A =-3//5 , sin B=7//25 and 90^(@) lt A lt 180^@,0^(@) lt B lt 90^(@) , "then " tan (A+B)=

Find the values of each of the following : tan225^(@),sin315^(@),tan(-1742^(@)),cos(-1760^(@)).

Let H be the ortho centre of Delta^("le") ABC,then angle subtended by the side BC at the centre of in circle of Delta^("le') BHCis

Let f(x)=x(2-x), 0 le x le 2. If the definition of 'f' is extended over the set R-[0, 2] by f(x+1)=f(x) then f is a periodic function with period.

Find the equation of the line passing through the points (-1, 1) " and " (2, - 4).

The coefficient of x^(m) and x^n in the expansion of (1+x)^(m+n) are ...........

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)

n points are given of which r points are collinear, then the number of straightlines that can be found =(a) ""^(n)C_(2)-""^(r)C_(2)(b) ""^(n)C_(2)-""^(r)C_(2)+1(c) ""^(n)C_(2)-""^(r)C_(2)-1(d) None of these

Evaluate the following limits : Lim_(x to 0) (sin ax)/(sin bx)

p vec(a) is a vector perpendicular to vec(i) and vec(j) whose magnitude is 2 where 'p' is a scalar, then

Evaluate the following limits : Lt_(xto7/2)(2x^(2)-9x+8)^(cot(2x-7))

Find the number of even positive integers which have three digits?

The price of six different commodities for years 2009 and year 2011 are as follows: The index number for the year 2011 taking 2009 as the base year for the above data was calculated to be 125. Find the values of x and y if the total price in 2009 is Rs. 360.

Find the modulus and the arguments of the following complex numbers : 1+i sqrt(3)

If f (x) ={{:( 3x+ 1,0le xle2"") ,( 1+ 9x ,2lt xlt3 "then "),( 3 0+ 2x ,xge 3"") :}

(4x+5sinx)/(3x+7cosx)

Check the continuity of the function f defined by f(x)={{:((x^(2)-9)/(x^(2)-2x-3),if 0 lt x lt 5 and x ne 3):} at the point x =3

Area of triangle ABC isa^(2) - (b-c)^(2)then tan A =

Let f'(sinx)lt0andf''(sinx)gt0AAx in(0,(pi)/(2))andg(x)=f(sinx)+f(cosx). Which of the following is true in (0,(pi)/(2))?

If t_(n)= sum_(1)^(n) n, then t_(n)^(1) = sum_(1)^(n) t_(n) =

If |a| = 5, |b| = 6, |a.b| = 24 then |a xx b| =

If 0 lt x lt pi and cos x + sin x=1/(2), then tanx =

If x^3+3x^2-9x+c is the form (x-alpha)^2(x - beta), then the positive value of c is .........

(Sin^(2) A + SinA+1)/( Sin A)ge Kthen k=

Evaluate the following limits. Lt_(xto0)(sin5x+sin3x)/(sin6x-sin4x)

Find the derivative of f(x) from the first principle where f(x) is x sin x

The range of f(x)=cos^(-1)((sqrt(2x^(2)+1))/(x^(2)+1)) is

If the line 2x+y=k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2, then k equals

Find the value of: "sin"75^(@) "tan"15^(@)

Find the equation of that focal chord of the parabola y^(2)=8x whose mid-point is (2,0).

A(1, 4), B(2, -3) and C(-1, -2)are the verticies at Delta ABC then find, (1) Equation of median from A. (2) Equation of perpendicular from A. (3) Equation of perpendicular bisector of bar(BC).

Evaluate the following limits : Lim_(h to 0 ) 1/h ( 1/sqrt(x+h)-1/(sqrt(x)))

Find k such that the equation 12x^(2)+7xy-12y^(2)-x+7y+k=0 represents a pair of straight lines. Find the separate equations of the straight lines and also the angle between the lines.

Find the derivative of f(x) from the first principle where f(x) is sin x+ cos x

Descibe the sample space :A coin is tossed . If it results in a head , a die is thrown . If the die is shown up an even number the die is thrown again.

d/(dx)(sqrt(sinsqrtx))

Let f(theta) = sintheta(sintheta + sin 3theta) . Then f(theta) is

The second term of a G.P. is 2 and the sum of infinite terms is 8. Find the first term.

If the hypotenuse of a rightangledtriangle is 2sqrt2times the lengthof the perpendiculardrawnfrom the opposite vertex, to itthen the diffrenceof twoacuteangles is

InDelta ABCProve that cos A + cos B+ cos C =1 +( r ) / ( R )

Solve the general vlaue. 2cos ^(2) theta - 5 cos theta + 2 = 0

Ifb=3 , c =2 , A = 120 ^(@)then lengthof bisector of angle A is

x = cos^(-1)((1)/(sqrt(1+t^(2)))),y = sin^(-1)((t)/(sqrt(1+t^(2))))rArr(dy)/(dx) is equal to

The value of sin^(2) 46^(0) + sin^(2) 14^(0) + sin 46^(0) sin 14^(0) =

Statement - 1 : The sum of the series 1+ ( 1+2+4) + ( 4+6+9) + ( 9+ 12+ 16) + ... + ( 361 + 380 + 400) is 8000 Statement-2: sum_(k=1)^(n) [ k^(3) - (k-1)^(3) ]= n^(3), for any natural number 'n'

Find a rational number which when expressed as a decimal will have 1.2bar(56) as its expansion.

Solve the equations: 10x^(-2)-9-x^(-4)=0.

Two cards are drawn from a well-shuffled deck of 52 cards. Find the probability thateither both are red or both are kings .