14949 + Interview Questions in Maths in Class 11 Page 3 InterviewSolution

101.	If f(x) = cos x cos 2x cos 4x cos 8x cos 16 xthen f^1((pi)/(4)) equals
Answer» `SQRT(2)` `0` `1/(sqrt(2))` `"Cosec" pi/4` Answer :B

Discussion

102.	Find the perpendicular distance of the point bar(c ) from the straight line bar(r )= bar(a) + t bar(b) and hence deduce that the area of the triangle whose vertices are the points bar(a), bar(b) and bar(c )" is" (1)/(2)\|bar(b) xx bar(c ) + bar( c) xx bar(a) + bar(a) xx bar(b)\|.
Answer» ANSWER :`(1)/(2) \|bar(B) xx bar(c ) + bar(c ) xx bar(a) + bar(a) xx bar(b)\|`

Discussion

103.	If a^2+b^2-c^2-2ab, then the point of concurrency of family of straight lines ax+by+c=0 lies on line
Answer» y=x y=x+1 y=-x y+x=1 Answer :C

Discussion

104.	The vector in the direction of the vectorhati -2 hatj + 2hatkthathas magnitude 9 is
Answer» ` HATI - 2hatj + 2HATK ` `( hati - 2hatj + 2hatk)/3 ` `3( hati - 2hati + 2hatk)` `9(hati - 2hatj + 2hatk)` ANSWER :D

Discussion

105.	Let V = { a, e, i, o, u } and B = { a, i, k, u}. Find V – B and B – V
Answer» ANSWER :`V - B= {E, o}, B - B= {K}`

Discussion

106.	Show that the solution of cos theta - sin theta = -1 is 2npi pm (3pi)/(4) - (pi)/(4), n in Z
Answer» Answer :`2npi PM (3PI)/(4) - (pi)/(4)`

Discussion

107.	Construct a quadratic equation in x such that the A.M. of its roots is A and G.M. is G.
Answer» Answer :`x^(2)-2 Ax + G^(2) =0`

Discussion

108.	Let f(x)={{:(x^(2)+3x",",-1lexlt0),(-sinx",",0lexltpi//2),(-1-cosx",",(pi)/(2)lexlepi):}Then
Answer» f(X) has global minimum VALUE -2 global maximum value occurs at x=0 global maximum valueoccursat `x=pi` `x=pi//2` is point of local minima Answer :A::B::C::D

Discussion

109.	Express each of the following in the form b or bi, where b is a real number sqrt(-25)
Answer» ANSWER :5I

Discussion

110.	Consider a circle with centre (2,-1) and which passes through (3,6) Find the radius of the circle
Answer» SOLUTION :`SQRT(50)`

Discussion

111.	Ifsin A = (336)/(625) " where " 450^(@) lt A lt 540^(@) , " then " sin"(A)/(4)=
Answer» ANSWER :`4/5`

Discussion

112.	Using sybols sub" and " cancelsub fill in the following blanks : {x, y, z}………..{x, y, z}
Answer» ANSWER :`SUB`

Discussion

113.	Which of the following are sets ? Justify your answer. The collection of all even integers.
Answer» ANSWER :it is a SET

Discussion

114.	Find the points which divide the line segment joining (8,12) and (12,8 ) into four equal parts.
Answer» ANSWER :(9,11), (10,10), (11,9)

Discussion

115.	The negation of for all x,p, is …
Answer» <P>there EXISTS X, `~p` For all x,`~p` `~p` `p` ANSWER :A

Discussion

116.	The radius and height of a cone are measured as 6 cm and 12 cm respectively and there is an error of 0.06 cm in both the measurements. The approximate error in the volume of the cone is
Answer» ANSWER :`3.6 PI` CUBIC CM

Discussion

117.	If x,y,z are natural number such that cot^(-1)x+cot^(-1)y=cot^(-1)z then the number of ordered triplets (x,y,z) that satisfy the equation is
Answer» 0 1 2 infinite solutions Answer :D

Discussion

118.	Ifalpha, beta , gammaare the lengthsof the altitudes ofDelta ABC , " then "alpha ^(-2)+beta ^(-2)+gamma^(-2) =
Answer» ` DELTA ` ` COT A + cot B +cot C ` ` ( cot A + cot B + cot C)/( Delta ` `( Delta )/(cot A+ cot B +cot C) ` ANSWER :C

Discussion

119.	Show that the length of intercept cut by pair of lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 on (i) x-axis is (2 sqrt(g^(2)-ac))/(\|a\|) and (ii) y-axis is (2 sqrt(f^(2)-bc))/(\|b\|)
Answer» ANSWER :`(2 sqrt(f^(2)-bc))/(\|B\|)`

Discussion

120.	(barbxxbarc).(axxbard)+(barcxxbara).(barbxxbard)+(baraxxbarb).(barcxxbard)=
Answer» 0 1 2 `-1` ANSWER :A

Discussion

121.	Evaluate the following limits in Exercises lim_(xto4)(4x+3)/(x-2)
Answer» ANSWER :`(19)/(2)`

Discussion

122.	InDelta ABC ,(bc cos A + c a cos B + ab cos C) /( cot A + cot B + cot C )=
Answer» `Delta` `2DELTA` `(1)/(2)Delta` `Delta^(2)` ANSWER :B

Discussion

123.	( b- c)^(2)cos ^(2)( A//2)+ ( b+ c) ^(2) sin ^(2) ( A//2) =
Answer» `a ` ` a ^(2) ` ` 2A ^(2) ` ` a ^(2) //2` ANSWER :B

Discussion

124.	If A andB are mutually exclusive events, then
Answer» <P>`P(A)LEP(B')` `P(A)geP(B')` `P(A)LTP(B')` none of these ANSWER :A

Discussion

125.	32sin^(6) 15^@ -48 sin^(4) 15 ^(@) + 18 sin^2 15^@ =
Answer» 1 2 3 `-1` ANSWER :A

Discussion

126.	If f(x)=a^x/x^a then f'(a)=
Answer» `LOG a - 1` `log a - a ` `a log a - a ` `a log a + a` ANSWER :A

Discussion

127.	If y = sin^(4)x + cos^(4)xthen (y_(4)(0))/8 is equal to
Answer»

Discussion

128.	Given the vertices A(10, 4), B(-4, 9) and C(-2, -1) of DeltaABC, find the equation of the side AB
Answer» ANSWER : `5x+114y=106`

Discussion

129.	If sin^(3)theta=sin theta cos theta +cos^(3)theta=1 then theta =(n inz)
Answer» `2NPI` `2npi+(pi)/2` `2npi-(pi)/2` `NPI` ANSWER :A::B

Discussion

130.	State whether the following sets are finite or infinite.(iii) {x in Z :x is even and less than 10}.
Answer» ANSWER :FINITE.

Discussion

131.	Evaluate the following limits. Lt_(xto2)(2/(x+1)-3/x)
Answer» ANSWER :`-5//6`

Discussion

132.	IfI_1is the centreof the first escribedcircle , then the value of( AI_1)/( r_1)=
Answer» ` SIN ( A//2) ` ` COSEC (A//2) ` ` COS ( A//2) ` ` sec ( A//2) ` ANSWER :B

Discussion

133.	If ax^(2)+12xy+9y^(2)=0 epresents two coincident lines then a=
Answer» 1 2 3 4 Answer :D

Discussion

134.	Solve the general vlaue. tan theta + tan 2 theta + sqrt3 tan theta tan 2 theta = sqrt3
Answer» ANSWER :`(NPI )/(3) + (PI)/(9) `

Discussion

135.	Three coins are tossed . Describe Two events which are mutually exclusive but not exhaustive.
Answer» ANSWER :`:.` A and B are mutually EXCLUSIVE but not EXHAUSTIVE EVENTS.

Discussion

136.	If A+B = 135^(@) then (1-TanA) (1- TanB) =
Answer» 0 1 2 `(1)/(2)` ANSWER :C

Discussion

137.	x = a represent a plane parallel to ______ .
Answer» ANSWER :YZ PLANE

Discussion

138.	If the coefficients of (r-5)^(th) and (2r - 1)^(th) terms in the expansion of (1 + x)^34 are equal, find r.
Answer» ANSWER :r=14.

Discussion

139.	If \|overline(a)\|=3,\|overline(b)\|=4and the angle between overline(a) and overline (b) is 120^@, then \|4overline(a)+3overline(b)\| is equal to
Answer» 25 7 13 12 Answer :D

Discussion

140.	What is idea proposed by Aristotle and Galileo about force?
Answer» SOLUTION :(i) Aristotle said that `FORCE causes MOTION’.(II) Galileo said force is not REQUIRED to maintain motion.

Discussion

141.	The reflection of the point A (1,0,0)in the line (x-1)/(2) = (y+1)/(-3) = (z+10)/(8) is
Answer» `(3,-4,-2)` `(5, -8, -4)` `(1, -1, 10)` `(2, -3, 8)` ANSWER :B

Discussion

142.	With usual notation C_(0)+ C_(2)+ C_(4) + ... is:
Answer» `2^(N-1)` `2^(n)` `2^(n+1)` `2^(n+2)` ANSWER :a

Discussion

143.	Simiplify :sqrt(-(49)/(25)) sqrt(-(1)/(9))
Answer» ANSWER :`(-7)/(15)`

Discussion

144.	Find the domains of the following functions f(x) = ( 2x+3)/( x^(2) - x+ 1)
Answer» ANSWER :R

Discussion

145.	Find the derivatives of the function tan ^(-1) (cos sqrtx)
Answer» ANSWER :`(- SIN SQRTX)/( 2 sqrtx [1 + cos ^(2) sqrt(x)])`

Discussion

146.	If f(x)=x+sinx,g(x)=e^(-x),u=sqrt(x+1)-sqrt(c )v=sqrt(c )-sqrt(c-1)(cgt1) , then
Answer» `FOG(u)ltfog(V)` `gof(u)ltgof(v)` `gof(u)ltgof(v)` `fog(u)ltfog(v)` ANSWER :C

Discussion

147.	Prove that, through three given points which are not collinear, there is only one circle.
Answer» ANSWER :Hence, there is only ONE CIRCLE through THREE non-collinear points.

Discussion

148.	The point A(5,-1,1), B(7,-4,7), C(1,-6,10), D(-1,-3,4) form
Answer» A PARALLELOGRAM A rhombus A square A rectangle Answer :B

Discussion

149.	If the function f(x)=Kx^3-9x^2+6x+3 is increasing Aax in R then K in
Answer» `(-OO,0)` `(-oo,9/2)` `(9/2,oo)` `(3,4)` ANSWER :C

Discussion

150.	If sin^(2) x - 2 sin x - 1 = 0has exactly four differentsolutions in x in [0, n pi] , then value/ values of n is / are (n in Z)
Answer» 5 3 4 6 Answer :A::C

Discussion

Explore topic-wise InterviewSolutions in .

If f(x) = cos x cos 2x cos 4x cos 8x cos 16 xthen f^1((pi)/(4)) equals

Find the perpendicular distance of the point bar(c ) from the straight line bar(r )= bar(a) + t bar(b) and hence deduce that the area of the triangle whose vertices are the points bar(a), bar(b) and bar(c )" is" (1)/(2)|bar(b) xx bar(c ) + bar( c) xx bar(a) + bar(a) xx bar(b)|.

If a^2+b^2-c^2-2ab, then the point of concurrency of family of straight lines ax+by+c=0 lies on line

The vector in the direction of the vectorhati -2 hatj + 2hatkthathas magnitude 9 is

Let V = { a, e, i, o, u } and B = { a, i, k, u}. Find V – B and B – V

Show that the solution of cos theta - sin theta = -1 is 2npi pm (3pi)/(4) - (pi)/(4), n in Z

Construct a quadratic equation in x such that the A.M. of its roots is A and G.M. is G.

Let f(x)={{:(x^(2)+3x",",-1lexlt0),(-sinx",",0lexltpi//2),(-1-cosx",",(pi)/(2)lexlepi):}Then

Express each of the following in the form b or bi, where b is a real number sqrt(-25)

Consider a circle with centre (2,-1) and which passes through (3,6) Find the radius of the circle

Ifsin A = (336)/(625) " where " 450^(@) lt A lt 540^(@) , " then " sin"(A)/(4)=

Using sybols sub" and " cancelsub fill in the following blanks : {x, y, z}………..{x, y, z}

Which of the following are sets ? Justify your answer. The collection of all even integers.

Find the points which divide the line segment joining (8,12) and (12,8 ) into four equal parts.

The negation of for all x,p, is …

The radius and height of a cone are measured as 6 cm and 12 cm respectively and there is an error of 0.06 cm in both the measurements. The approximate error in the volume of the cone is

If x,y,z are natural number such that cot^(-1)x+cot^(-1)y=cot^(-1)z then the number of ordered triplets (x,y,z) that satisfy the equation is

Ifalpha, beta , gammaare the lengthsof the altitudes ofDelta ABC , " then "alpha ^(-2)+beta ^(-2)+gamma^(-2) =

Show that the length of intercept cut by pair of lines ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 on (i) x-axis is (2 sqrt(g^(2)-ac))/(|a|) and (ii) y-axis is (2 sqrt(f^(2)-bc))/(|b|)

(barbxxbarc).(axxbard)+(barcxxbara).(barbxxbard)+(baraxxbarb).(barcxxbard)=

Evaluate the following limits in Exercises lim_(xto4)(4x+3)/(x-2)

InDelta ABC ,(bc cos A + c a cos B + ab cos C) /( cot A + cot B + cot C )=

( b- c)^(2)cos ^(2)( A//2)+ ( b+ c) ^(2) sin ^(2) ( A//2) =

If A andB are mutually exclusive events, then

32sin^(6) 15^@ -48 sin^(4) 15 ^(@) + 18 sin^2 15^@ =

If f(x)=a^x/x^a then f'(a)=

If y = sin^(4)x + cos^(4)xthen (y_(4)(0))/8 is equal to

Given the vertices A(10, 4), B(-4, 9) and C(-2, -1) of DeltaABC, find the equation of the side AB

If sin^(3)theta=sin theta cos theta +cos^(3)theta=1 then theta =(n inz)

State whether the following sets are finite or infinite.(iii) {x in Z :x is even and less than 10}.

Evaluate the following limits. Lt_(xto2)(2/(x+1)-3/x)

IfI_1is the centreof the first escribedcircle , then the value of( AI_1)/( r_1)=

If ax^(2)+12xy+9y^(2)=0 epresents two coincident lines then a=

Solve the general vlaue. tan theta + tan 2 theta + sqrt3 tan theta tan 2 theta = sqrt3

Three coins are tossed . Describe Two events which are mutually exclusive but not exhaustive.

If A+B = 135^(@) then (1-TanA) (1- TanB) =

x = a represent a plane parallel to ______ .

If the coefficients of (r-5)^(th) and (2r - 1)^(th) terms in the expansion of (1 + x)^34 are equal, find r.

If |overline(a)|=3,|overline(b)|=4and the angle between overline(a) and overline (b) is 120^@, then |4overline(a)+3overline(b)| is equal to

What is idea proposed by Aristotle and Galileo about force?

The reflection of the point A (1,0,0)in the line (x-1)/(2) = (y+1)/(-3) = (z+10)/(8) is

With usual notation C_(0)+ C_(2)+ C_(4) + ... is:

Simiplify :sqrt(-(49)/(25)) sqrt(-(1)/(9))

Find the domains of the following functions f(x) = ( 2x+3)/( x^(2) - x+ 1)

Find the derivatives of the function tan ^(-1) (cos sqrtx)

If f(x)=x+sinx,g(x)=e^(-x),u=sqrt(x+1)-sqrt(c )v=sqrt(c )-sqrt(c-1)(cgt1) , then

Prove that, through three given points which are not collinear, there is only one circle.

The point A(5,-1,1), B(7,-4,7), C(1,-6,10), D(-1,-3,4) form

If the function f(x)=Kx^3-9x^2+6x+3 is increasing Aax in R then K in

If sin^(2) x - 2 sin x - 1 = 0has exactly four differentsolutions in x in [0, n pi] , then value/ values of n is / are (n in Z)