14949 + Interview Questions in Maths in Class 11 Page 43 InterviewSolution

2101.	From the employees of a company, 5 person are selected to represent them in the managing committee of the company. Particular of five persons are as follows: {:("S.No.","Name ","sex","age in years"),(1.,"harish ",M,30),(2. , "Rohon",M,33),(3.,"sheetal",F,46),(4.,"Alis",F,28),(5. ,"Salim",M,41):} A person is selected at random from this group to act as a spokespersons. What is the probability that the spokespersons will be either male or over 35 years?
Answer» ANSWER :`4/5`

Discussion

2102.	There are 8 points in a plane. Out of them, 3 points are collinear. Using them how many triangles are formed ? How many lines are there passing through them ? How many line segment we get ?
Answer» ANSWER :55 TRIANGLES, 26 LINES, 28 Line SEGMENTS

Discussion

2103.	Evaluate the following limits. Lt_(xto0)(sin(picos^(2)x))/x^(2)
Answer» ANSWER :`PI`

Discussion

2104.	Find all values of x which satisfy 5 sin x = 4 cos x, (0^(@)lt x lt 360^(@))
Answer» ANSWER :`218^(@) 39`

Discussion

2105.	The slope of a line is double of the slope of another line. If tangent of the angle between them is 1/3 , find the slopes of the lines.
Answer» ANSWER :1 and 2, or `1/2` and 1, or`-1 " and " -2`, or `- 1/2" and " -1`

Discussion

2106.	If 4a^(2)+9b^(2)-c^(2)+12ab=0, then the set of lines ax + by+c = 0 pass through the fixed point
Answer» `(1, 2), (-1, -2)` `(2,3), (-2, -3)` `(2, -3), (-2, 3)` `(1, -2), (-1, 2)` ANSWER :B

Discussion

2107.	A (4,3,5), B(0,-2,2) and C( 3,2,1) are three points. The coordinates of the point in which the bisector of angleABC " meets the side " bar(BC)is
Answer» `(15/8,4/8,11/8)` `(12/7,2/7,10/7)` `(9/5,2/5,7/5)` `(3/2,0,3/2)` ANSWER :A

Discussion

2108.	If sin theta=-4/5,180^(@)ltthetalt270^(@) then find "sin"theta/2, "cos"theta/2
Answer» ANSWER :i) `2/SQRT5 , (-1)/sqrt5` II) `56/33`

Discussion

2109.	If f: R rarr R is defined by f(x)= x-[x]- 1/2 for x in R, where [x] is the greatest integer not exceeding x, then {x in R : f(x) + 1/2}=
Answer» Z N `PHI` R Answer :C

Discussion

2110.	(i) Is the equation 2 cos^(2)theta + cos theta -6 =0 possible ? (ii) Is the equation 2 "sin"^(2)theta-costheta +4=0can never be less than2.
Answer» ANSWER :No

Discussion

2111.	Find the axes, vertices, foci, eccentricity, equations of the directrices, and length of the latus rectum of the hyperbola 9x ^(2) - 16 y ^(2) = 144.
Answer» ANSWER :`9/4 =9/2`

Discussion

2112.	If \|z_(1)\|=\|z_(2)\|=....\|z_(n)\|=1, then show that, \|z_(1)+z_(2)+z_(3)+....z_(n)\|= \|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))+...+(1)/(z_(n))\|
Answer» ANSWER :`\|(1)/(z_(1))+(1)/(z_(2))+...+(1)/(ZN)\|`

Discussion

2113.	The middle term in the expansion (x^(2)-1/(2x))^(20) is r than (r+3)^(th) term is ………
Answer» `20 C_(14)(x/(2^(14)))` `20C_(12)x^(2)2^(-12)` `-20C_(7)x.2^(-13)` NONE of these Answer :C

Discussion

2114.	If tantheta+sectheta=sqrt(3), then the principal value of (theta+(pi)/(6)) is
Answer» `(PI)/(3)` `(pi)/(4)` `(2PI)/(3)` `(pi)/(2)` ANSWER :A

Discussion

2115.	If y = e^(x) cos x and y_n + k_n y = 0 , where y_n = (d^n y)/(dx^n) and k_n are constant AA n in N, then
Answer» `k_4 = 4` `k_8 = -16` `k_12 = 20` `k_16 = -24` ANSWER :A::B

Discussion

2116.	Solve: (Find x) 1 + 6+ 11+ 16+ ….+x= 148
Answer» ANSWER :36

Discussion

2117.	If x= -5 + sqrt(-16), find the value of x^(4) + 9x^(3) + 35x^(2)-x + 4
Answer» ANSWER :`-160`

Discussion

2118.	Write the negation of the following statements: Every natural number is an integer
Answer» ANSWER :EVERY NATURAL NUMBER is not an INTEGER

Discussion

2119.	Locus of point of intersection of the lines x sin theta-y cos theta=0 and ax sec theta-by "cosec"theta=a^(2)-b^(2) is
Answer» `X^(2)+y^(2)=a^(2)` `x^(2)+y^(2)=B^(2)` `x^(2)+y^(2)=a^(2)+b^(2)` `x^(2)+y^(2)=(a+b)^(2)` ANSWER :D

Discussion

2120.	Cos 40^(@) + Cos80^(@) + Cos160^(@) + Cos240^(@) =
Answer» 0 1 `1//2` `-1//2` ANSWER :D

Discussion

2121.	If tanA.tanB=1/2, then (5-3cos2A) (5-3cos2B)=
Answer» 2 8 12 16 Answer :D

Discussion

2122.	Find equation of line passes from ( sqrt(3) ,-1) whose perpendicular distance is sqrt(2) from origin.
Answer» ANSWER :`( SQRT(3) +1) X + ( sqrt(3) -1)y=4` `( sqrt(3) -1) x + ( sqrt(3) + 1) y=4`

Discussion

2123.	Letg(x) = sqrt(x- 2K) , AA 2 K le x lt 2( k+1), " where"k ininteger . If g(x)is periodic then period of g(x) is
Answer» 1 2 3 not defined Answer :B

Discussion

2124.	Prove by using the distance formula that the points A (1,2,3), B (-1, -1, -1) and C (3,5,7) are collinear.
Answer» ANSWER :`sqrt29`

Discussion

2125.	Let f:Rto"be defined by"f(x)=1absx. Then the range of f is
Answer» R `(1,OO)` `(-1,oo)` `(-oo,1]` ANSWER :A

Discussion

2126.	Write contrapositive and converse of the following statements: If 30 divides n then 2 divides n.
Answer» ANSWER :Contrapositive: If 2 does not DIVIDE n 30 does not DIVIDEN. CONVERSE: If 2 divides n, 30 divides n.

Discussion

2127.	(1 - Tan 99^(@)) (1 - Tan36^(@)) =
Answer» 0 1 2 `1//2` ANSWER :C

Discussion

2128.	If tan^(-1)(a//x)+tan^(-1)(b//x)=pi//2 then x=
Answer» `AB` `SQRT(ab)` `sqrt(a^(2)+B^(2))` `a^(2)+b^(2)` ANSWER :B

Discussion

2129.	alpha and beta are the positive acute angles and satisfying equation 5 sin 2 beta = 3 sin 2alpha and tan beta = 3 tan alpha Simultaneously . Then the value of tan alpha = tan betais ................
Answer» ANSWER :4

Discussion

2130.	Find the equation of a line which passes through the point (2, 3, 4) and which has equal intercepts on the axes.
Answer» `X^(2) + y^(2) + 6x + 6Y + 3 = 0` `x^(2) + y^(2) - 6x - 6y - 9 = 0` `x^(2) + y^(2) - 6x - 6y + 9 = 0` NONE of these Answer :C

Discussion

2131.	A lot consists of 12 good pencils , 6 with minor defects and 2 with major defects .A pencil is chosen at random .Find the probability that this pencil is not defective.
Answer» ANSWER :`=(3)/(5)`

Discussion

2132.	Find the valuesof the trigonometric functions cot(-(15pi)/(4))
Answer» ANSWER :1

Discussion

2133.	Draw a quadrilateral in the Cartesian plane, whose vertices are (-4,5), (0,7), (5,-5) and (-4,-2). Also, find its area.
Answer» ANSWER :`(121)/2` SQUARE UNIT.

Discussion

2134.	How many terms of the A.P. 1,4,7.... are needed to give the sum 715?
Answer» ANSWER :22

Discussion

2135.	If Lim_( theta to 0) k theta cosec theta = Lim_( theta to 0) theta cosec k theta ,prove that k must bepm 1:
Answer» ANSWER :` :. K = 1/k or k^(2) = 1 RARR k = PM 1 `

Discussion

2136.	The quotations for four different commodities for the years 2000 and 2005 are given below. Calculate the index number for 2005, with 2000 as the base year, by using the weighted average of price relatives method.
Answer» ANSWER :`=164.05`.

Discussion

2137.	If alpha,beta are the roots of the equation x^(2)+px+q=0, find the value of (a) alpha^(3)beta+alphabeta^(3) (b) alpha^(4)+alpha^(2)beta^(2)+beta^(4).
Answer» <P> Answer :`q(p^(2)-2Q),p^(4)+3Q^(2)-4p^(2)q`.

Discussion

2138.	If ABCD is a cydic quadrilateral such that 12 tanA - 5 = 0and 5 cos B + 3 = 0, then cos C tan D =
Answer» `(-16)/(13)` `(16)/(13)` `(-13)/(16)` `(23)/(16)` ANSWER :A

Discussion

2139.	Check the continuity of the functionn 'f' defined by fx={{:((sin2x)/(x),if, x ne0),(x,if,x=0):}at x=0
Answer» ANSWER :DISCONTINUOUS

Discussion

2140.	If (sin (theta+ alpha))/(cos (theta- alpha))=(1-M)/(1+M) then Tan ((pi)/(4)- theta). Tan ((pi)/(4)- alpha)=
Answer» `(1)/(M)` M `-(1)/(M)` 2M Answer :B

Discussion

2141.	Assertion If G is the centroid of thetriangle ABC then vecGA+vecGB+vecGC=0.Reason: If veca,vecb, vecc are two p.vof A ,B ,Cof /_\ABC then the p.vof its centroid is (veca+vecb+vecc)/(3).Also vecAB=vecb-veca
Answer» Both ASSERTION and REASON are not CORRECT. Reason is correct, but Assertion is not correct. Using Reason, Assertion can be proved. Using Reason, Assertion cannot be proved. Answer :C

Discussion

2142.	A tetrahedron has vertices at O(0,0,0), A(1,2,1), B(2,1,3) and C(-1,1,2). Then the angle between the faces OAB and ABC will be
Answer» `cos ^(-1) ((19)/(35))` `cos ^(-1) ((17)/(31))` `30^(@)` `90^(@)` ANSWER :A

Discussion

2143.	Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Equation of perpendicular bisector of bar(AB) joining A(-2, 3) and B(4, 5).
Answer» ANSWER :`3X + y - 7 = 0`

Discussion

2144.	A hyperbola passes through (3, 3) and the length of its conjugate axis is 8. Find the length of the latus rectum.
Answer» SOLUTION :N/A

Discussion

2145.	Given the relations R_2 = {(x,y): x,y in N and x^2 + y^2 le 10}.
Answer» SOLUTION :DOM `(R_2) = {1,2,3,}, RANGE (R_2) = {1,2,3}`

Discussion

2146.	How many natural numbers less than 1,000 can be formed with digits 1,2,3,4 and 5 if(i) no digit is repeated(ii)repetition of digits is allowed ?
Answer» ANSWER :(i) 85 (II)155

Discussion

2147.	A,B,C are three points OX,OY,OZ respectively, at distance a,b,c from the origin 'O'. Find the coordinates of the point which is equidistant from A,B,C and 'O'.
Answer» ANSWER :`(a/2,b/2,c/2)`

Discussion

2148.	The probability of A,B,C hitting a target are (4)/(5),(3)/(4),(2)/(3) respectively. Find the probability that (i)the target is damaged by excatly one hit(ii)the target is damaged by exactly two hits.
Answer» ANSWER :`(3)/(10),(13)/(10`

Discussion

2149.	The ratio of the area of a regular polygon of n sides inscribed in a circle to that of the polygon of same number of sides circumscribing the same circle is 3:4. Then the value of n is
Answer» 6 4 8 12 Answer :A

Discussion

2150.	Range of the function f(x)= (x+2)/(\|x+2\|), x ne -2 is……
Answer» `{-1, 1}` `{-1, 0, 1}` {1} `(0, OO)` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

There are 8 points in a plane. Out of them, 3 points are collinear. Using them how many triangles are formed ? How many lines are there passing through them ? How many line segment we get ?

Evaluate the following limits. Lt_(xto0)(sin(picos^(2)x))/x^(2)

Find all values of x which satisfy 5 sin x = 4 cos x, (0^(@)lt x lt 360^(@))

The slope of a line is double of the slope of another line. If tangent of the angle between them is 1/3 , find the slopes of the lines.

If 4a^(2)+9b^(2)-c^(2)+12ab=0, then the set of lines ax + by+c = 0 pass through the fixed point

A (4,3,5), B(0,-2,2) and C( 3,2,1) are three points. The coordinates of the point in which the bisector of angleABC " meets the side " bar(BC)is

If sin theta=-4/5,180^(@)ltthetalt270^(@) then find "sin"theta/2, "cos"theta/2

If f: R rarr R is defined by f(x)= x-[x]- 1/2 for x in R, where [x] is the greatest integer not exceeding x, then {x in R : f(x) + 1/2}=

(i) Is the equation 2 cos^(2)theta + cos theta -6 =0 possible ? (ii) Is the equation 2 "sin"^(2)theta-costheta +4=0can never be less than2.

Find the axes, vertices, foci, eccentricity, equations of the directrices, and length of the latus rectum of the hyperbola 9x ^(2) - 16 y ^(2) = 144.

If |z_(1)|=|z_(2)|=....|z_(n)|=1, then show that, |z_(1)+z_(2)+z_(3)+....z_(n)|= |(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))+...+(1)/(z_(n))|

The middle term in the expansion (x^(2)-1/(2x))^(20) is r than (r+3)^(th) term is ………

If tantheta+sectheta=sqrt(3), then the principal value of (theta+(pi)/(6)) is

If y = e^(x) cos x and y_n + k_n y = 0 , where y_n = (d^n y)/(dx^n) and k_n are constant AA n in N, then

Solve: (Find x) 1 + 6+ 11+ 16+ ….+x= 148

If x= -5 + sqrt(-16), find the value of x^(4) + 9x^(3) + 35x^(2)-x + 4

Write the negation of the following statements: Every natural number is an integer

Locus of point of intersection of the lines x sin theta-y cos theta=0 and ax sec theta-by "cosec"theta=a^(2)-b^(2) is

Cos 40^(@) + Cos80^(@) + Cos160^(@) + Cos240^(@) =

If tanA.tanB=1/2, then (5-3cos2A) (5-3cos2B)=

Find equation of line passes from ( sqrt(3) ,-1) whose perpendicular distance is sqrt(2) from origin.

Letg(x) = sqrt(x- 2K) , AA 2 K le x lt 2( k+1), " where"k ininteger . If g(x)is periodic then period of g(x) is

Prove by using the distance formula that the points A (1,2,3), B (-1, -1, -1) and C (3,5,7) are collinear.

Let f:Rto"be defined by"f(x)=1absx. Then the range of f is

Write contrapositive and converse of the following statements: If 30 divides n then 2 divides n.

(1 - Tan 99^(@)) (1 - Tan36^(@)) =

If tan^(-1)(a//x)+tan^(-1)(b//x)=pi//2 then x=

alpha and beta are the positive acute angles and satisfying equation 5 sin 2 beta = 3 sin 2alpha and tan beta = 3 tan alpha Simultaneously . Then the value of tan alpha = tan betais ................

Find the equation of a line which passes through the point (2, 3, 4) and which has equal intercepts on the axes.

A lot consists of 12 good pencils , 6 with minor defects and 2 with major defects .A pencil is chosen at random .Find the probability that this pencil is not defective.

Find the valuesof the trigonometric functions cot(-(15pi)/(4))

Draw a quadrilateral in the Cartesian plane, whose vertices are (-4,5), (0,7), (5,-5) and (-4,-2). Also, find its area.

How many terms of the A.P. 1,4,7.... are needed to give the sum 715?

If Lim_( theta to 0) k theta cosec theta = Lim_( theta to 0) theta cosec k theta ,prove that k must bepm 1:

The quotations for four different commodities for the years 2000 and 2005 are given below. Calculate the index number for 2005, with 2000 as the base year, by using the weighted average of price relatives method.

If alpha,beta are the roots of the equation x^(2)+px+q=0, find the value of (a) alpha^(3)beta+alphabeta^(3) (b) alpha^(4)+alpha^(2)beta^(2)+beta^(4).

If ABCD is a cydic quadrilateral such that 12 tanA - 5 = 0and 5 cos B + 3 = 0, then cos C tan D =

Check the continuity of the functionn 'f' defined by fx={{:((sin2x)/(x),if, x ne0),(x,if,x=0):}at x=0

If (sin (theta+ alpha))/(cos (theta- alpha))=(1-M)/(1+M) then Tan ((pi)/(4)- theta). Tan ((pi)/(4)- alpha)=

Assertion If G is the centroid of thetriangle ABC then vecGA+vecGB+vecGC=0.Reason: If veca,vecb, vecc are two p.vof A ,B ,Cof /_\ABC then the p.vof its centroid is (veca+vecb+vecc)/(3).Also vecAB=vecb-veca

A tetrahedron has vertices at O(0,0,0), A(1,2,1), B(2,1,3) and C(-1,1,2). Then the angle between the faces OAB and ABC will be

Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Equation of perpendicular bisector of bar(AB) joining A(-2, 3) and B(4, 5).

A hyperbola passes through (3, 3) and the length of its conjugate axis is 8. Find the length of the latus rectum.

Given the relations R_2 = {(x,y): x,y in N and x^2 + y^2 le 10}.

How many natural numbers less than 1,000 can be formed with digits 1,2,3,4 and 5 if(i) no digit is repeated(ii)repetition of digits is allowed ?

A,B,C are three points OX,OY,OZ respectively, at distance a,b,c from the origin 'O'. Find the coordinates of the point which is equidistant from A,B,C and 'O'.

The probability of A,B,C hitting a target are (4)/(5),(3)/(4),(2)/(3) respectively. Find the probability that (i)the target is damaged by excatly one hit(ii)the target is damaged by exactly two hits.

The ratio of the area of a regular polygon of n sides inscribed in a circle to that of the polygon of same number of sides circumscribing the same circle is 3:4. Then the value of n is

Range of the function f(x)= (x+2)/(|x+2|), x ne -2 is……