14949 + Interview Questions in Maths in Class 11 Page 12 InterviewSolution

551.	The profit function P(x) of a company selling x items per day is given by P(x) = (150-x)x - 1000. Find the number of items that the company should manufacture to get maximum profit. Also find the maximum profit.
Answer» ANSWER :No. of ITEMS = 75; MAXIMUM PROFIT = 4625

Discussion

552.	If in DeltaABC,A=(pi)/(7),B=(2pi)/(7),C=(4pi)/(7) y then a^(2)+b^(2)+c^(2) must be
Answer» `R^(2)` `3R^(2)` `4R^(2)` `7R^(2)` ANSWER :D

Discussion

553.	Reduce the following equations into slope intercept form and find their slopes and the y- intercepts. (i) x+7y=0
Answer» ANSWER :SLOPE `m= (1)/(7)`, u-intercept `C=0`.

Discussion

554.	Reduce the following equations into slope intercept form and find their slopes and the y- intercepts. (ii) 6x+3y-5=0
Answer» ANSWER :SLOPE `m=-2`, y-intercept `C= (5)/(3)`.

Discussion

555.	Reduce the following equations into slope intercept form and find their slopes and the y- intercepts. (iii) y=0
Answer» ANSWER :SLOPE `m=0`; y-intercept `C=0`.

Discussion

556.	AA t in R suppose [t] has value t of all integer value of less than t then, lim_(xto0+)x([(1)/(x)]+[(2)/(x)]+........+[(15)/(x)])
Answer» EQUAL to 0 Equal to 15 Equal to 120 Does not EXISTS in R Answer :C

Discussion

557.	Which of the following can not be valid assignment of probabilities for outcomes of sample Space S = {omega_(1), omega_(2), omega_(3), omega_(4), omega_(5), omega_(6), omega_(7)} Assignment omega_(1)" "omega_(2)" "omega_(3)" "omega_(4)" "omega_(5)" "omega_(6) (a) 0.1 0.01 0.05 0.03 0.01 0.2 0.6 (b) 1/7 1/7 1/7 1/7 1/7 1/7 1/7 (c) 0.1 0.2 0.3 0.4 0.5 - 0.6 - 0.7 (d) -0.1 0.2 0.3 0.4 -0.2 0.1 0.3 (e) 1/14 2/14 3/14 4/14 5/14 6/1415/14
Answer» ANSWER :(a) YES, (B) Yes, (C) No, (d) No, (E) No.

Discussion

558.	The set of points of discontinuily of thef(x) = (1)/(x^(2) + 4x + 5)
Answer» `PHI` R `R^(+)` `R^(-)` ANSWER :A

Discussion

559.	Find the point to whichthe origin is to be shifted so thatthe point (3, 0) may change to (2,-3)
Answer» ANSWER :(1, 3)

Discussion

560.	Write the values of x and y if (3-4i) (x + yi) =1 + i(0)
Answer» ANSWER :`X=(3)/(25), y= (4)/(25)`

Discussion

561.	If z=cos((pi)/(3))-isin((pi)/(3)) then z^(2)-z+1=....
Answer» `-2I` 2 0 `-2` ANSWER :C

Discussion

562.	Find deltay and dy for the following functions y=x^(2)+3x+6,x=10,deltax=0.01
Answer» ANSWER :0.2301,0.23

Discussion

563.	A particle moves on a line according to the law s = at^(2) + bt + c. If the displacement after one second is 16 cm, the velocity after 2 second is 24 cm/sec and the acceleration is 8cm//sec^(2). Then (a,b,c)
Answer» (4,8,6) (4,4,8) (8,4,4) (8,8,4) ANSWER :A

Discussion

564.	{:("Column -I","Column - II"),("A) If maximum and minimum values of" ( 7+6 tan theta - tan^(2) theta)/(( 1 + tan^(2) theta) ) "for all real values of" theta ne (2n+1) (pi)/(2) "are" lambda " and u respectively then","p)" lambda+ mu =2),("B) If maximum and minimum values of" 5 cos theta + 3 cos ( theta + (pi)/(3) +3)"for all real values of" theta "are" lambda "and u respectively then" ,"q)"lambda- mu =6),("C) If maximum and minimum values of" 1+ sin((pi)/(4) + theta) + 2cos ((pi)/(4) - theta) "for all real values of" theta "are" lambda and mu "respectively then","s)" lambda- mu = 10),(,"t)" lambda- mu =14):}
Answer» ANSWER :A-rs; B-rt; C-pq

Discussion

565.	Let a,b,c,d,e,f,g,h be distinct elements in the set {-7,-5,-3,-2,2,4,6,13} . The minimum value of (a+b+c+d)^(2)+(e+f+g+h)^(2) is
Answer» 30 32 34 40 Answer :B

Discussion

566.	Find the transformed equation of 4xy-3x^(2) = a^(2) when the axes are rotated through an angle Tan^(-1)2.
Answer» ANSWER :`RARR X^(2) - 4Y^(2) = a^(2)`

Discussion

567.	If n is an odd positive integer, prove that the coefficients of the middle terms in the expansion of (x+y)^(n) are equal.
Answer» ANSWER :`=2_(n+1)C_(n+1)`

Discussion

568.	Match of the following
Answer» C,b,E,a b,c,d,e c,d,e,a e,a,d,b Answer :A

Discussion

569.	Evaluate cos^2(pi/8)+cos^2((3pi)/8)
Answer» SOLUTION :`(sqrt2+1)/2SQRT2`

Discussion

570.	Show that (a^(2))/( 4) sin 2c +(c^(2))/( 4) sin 2A = Delta
Answer» ANSWER :` = ( ABC)/( 4R)= DELTA ( THEREFORE abc = 4R Delta ) `

Discussion

571.	State whether word or is used in following statement is Exclusive or Inclusive. Proof at identity is Pancard or Bank passbook.
Answer» ANSWER :INCLUSIVE SENSE

Discussion

572.	Writethe negation of the statement .'The sum of 3 and 4 is 9' ?
Answer» ANSWER :1

Discussion

573.	If oneof lines in ax^(2)+2hxy+by^(2)=0 bisects the angle between the coordinates axes then (a+b)^(2)=
Answer» `2H^(2)` `H^(2)` `3h^(2)` `4h^(2)` ANSWER :D

Discussion

574.	Letf(x)=(2x(sin x + tanx))/(2[(x+21pi)/(pi)]-41),x != n pi,then f is ( where [.] represents greatest integer function)
Answer» an ODD function an EVEN function both odd and even neither odd nor even Answer :A

Discussion

575.	If the sum of n terms of G.P. 3, 6, 12,…….is 381 then find n
Answer» ANSWER :10

Discussion

576.	From4 red balls, 2 white balls and 4 blackhalls , four halls are selected . The probabilityof getting 2 red balls is
Answer» `(7)/(21)` `(8)/(21)` `(9)/(21)` `(10)/(21)` ANSWER :C

Discussion

577.	I: The system of equations x+y+z=6,x-y+z=2, 2x-y+3z=9 has unique solution. II: The system of equations x+y+z=3, 2x+2y-z=3,x+y-z=1 has infinitely many solutions
Answer» only I is TRUE only II is true Both I, II are true NEITHER I nor II are true ANSWER :C

Discussion

578.	The point of concurrence of the lines (a+2b)x+(a-b)y+(a+5b)=0 is
Answer» (-1,2) (2,-1) (-2,1) (1,-2) ANSWER :C

Discussion

579.	Solve the equation 2z= \|z\| + 2i is complex numbers
Answer» ANSWER :`Z= (1)/(SQRT3) +i`

Discussion

580.	Evaluate the following limits. Lt_(xto pi)(x-22/7)
Answer» ANSWER :`pi-22/7`

Discussion

581.	If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that (A ∪ B)′ = A′ ∩ B′
Answer» ANSWER :`(A CUP B)' = A' CAP B'`

Discussion

582.	y = tan^(-1)sqrt((1-cosx)/(1+cosx)) dy/dx is:
Answer» 2 `1/2` `-1/2` -2 Answer :B

Discussion

583.	If 2S=a+b+c, prove that \|{:(a^(2),(S-a)^(2),(S-a)^(2)),((S-b)^(2),b^(2),(S-b)^(2)),((S-c)^(2),(S-c)^(2),c^(2)):}\|=2S^(3)(S-a)(S-b)(S-c).
Answer» ANSWER :S

Discussion

584.	\|{:(a-b-c,2b,2c),(2a,b-c-a,2c),(2a,2b,c-a-b):}\|=
Answer» `(a+b+c)^(3)` `2(a+b+c)^(3)` `(a+b+c)^(2)` `2(a+b+c)^(2)` ANSWER :A

Discussion

585.	If tantheta+tan2theta+sqrt(3)tanthetatan2theta=sqrt(3), then theta=(npi)/(3)+(pi)/(9).
Answer» ANSWER :TRUE

Discussion

586.	If y is an implicit funtiion of x given by the relation, find (dy)/(dx). x ^(2) + y ^(2) + 2x + 3y -4 =0.
Answer» ANSWER :`- (2 (X +1 ))/( 2y + 3 )`

Discussion

587.	Find the co-ordinates of the point of intersection of the straight lines 2x-3y-7=0 , 3x-4y-13=0
Answer» ANSWER : `(11, 5)`

Discussion

588.	Find the term independent of x in the expansion of (root(3)(x)+1/(2root(3)(x)))^18,x > 0.
Answer» ANSWER :The REQUIRED TERM is `^18`Cunderset9 `1/2^9`.

Discussion

589.	The sum and product of three consecutive terms of an A.P. are 24 and 312 respectively. Find these terms.
Answer» ANSWER :3,8,13

Discussion

590.	Find the mean deviation by short cut method.
Answer» SOLUTION : Let `a=45, h=10` Arithmetic MEAN `BARX=a+(sumf_(i)(u_(i)))/(sumf_(i))xxh` `=45+0/40xx10=45` Mean deviation `=(sumf_(i)\|x_(i)-barx\|)/(sumf_(i))` `=400/40=10`

Discussion

591.	Form the bicoditional statement phArrq. Where p: Natural number n is odd. q: Natural number n is not divisible by 2.
Answer» ANSWER :DIVISIBLE by 2.

Discussion

592.	If A(1, -1, -3), B(2, 1, -2), C(-5, 2, -6) are the vertices of a DeltaABC, then the length of internal bisector of angle A is
Answer» `3/4sqrt(10)` `1/2sqrt(10)` `1/4sqrt(10)` `SQRT(10)` ANSWER :A

Discussion

593.	(sqrt(2)-sin alpha - cos alpha)/(sin alpha - cos alpha) is equal to
Answer» `SEC((alpha)/(2)-(pi)/(8))` `cos((pi)/(8)-(alpha)/(2))` `TAN((alpha)/(2)-(pi)/(8))` `cot((alpha)/(2)-(pi)/(2))` Answer :C

Discussion

594.	Solve the following equations: x^(2)-sqrt(2)ix+12=0
Answer» ANSWER :`-2 SQRT(2)I 3 sqrt(2)i`

Discussion

595.	Statement-1 : Condition of Lagrange's mean value theorem fail in f(x) = \| x-1 \| (x-1). Statement-2 : \|x-1\| is not differentiableat x=1 .
Answer» If both the statement are TRUE and STATEMENT 2 is the correct EXPLANATION of STATMEMENT -1 If both the statement are TRUE and STATEMENT2 is NOT the correctexplanation of STATEMENT-1 If STATEMENT -1 is TRUE and STATEMENT 2 is FALSE If STATEMENT-1 is FALSE and STATEMENT 2 is TRUE Answer :D

Discussion

596.	Equilateral triangle DEF is inscribed in equilateral triangle ABC as shown with DE bot^("lar")B Cthen ratio of Area of triangle DEF to the Area of Delta^("le") ABC is then
Answer» `(1)/(3)` 3 `(2)/(3)` `(3)/(2)` ANSWER :A

Discussion

597.	Separate the intervals of monotonicity of the following functions : f(x) = -sin^(3)x + 3 sin^(2)x + 5, x in [-pi//2, pi//2]
Answer» ANSWER :`(-pi//2, 0)`

Discussion

598.	If the distance between the pair of parallel lines x^(2)+2xy+y^(2)-8ax-8ay-9a^(2)=0 is 25sqrt2, then \|a\|=
Answer» 1 2 3 5 Answer :D

Discussion

599.	If (5,-2),(-2,1) and (9,6) are collinear find alpha.
Answer» ANSWER :a=-23

Discussion

600.	Express sin "" (5pi)/(2) in terms ofcos 5pi ,
Answer» Answer :`PM SQRT (( 1- cos 5 THETA)/(2))`

Discussion

Explore topic-wise InterviewSolutions in .

The profit function P(x) of a company selling x items per day is given by P(x) = (150-x)x - 1000. Find the number of items that the company should manufacture to get maximum profit. Also find the maximum profit.

If in DeltaABC,A=(pi)/(7),B=(2pi)/(7),C=(4pi)/(7) y then a^(2)+b^(2)+c^(2) must be

Reduce the following equations into slope intercept form and find their slopes and the y- intercepts. (i) x+7y=0

Reduce the following equations into slope intercept form and find their slopes and the y- intercepts. (ii) 6x+3y-5=0

Reduce the following equations into slope intercept form and find their slopes and the y- intercepts. (iii) y=0

AA t in R suppose [t] has value t of all integer value of less than t then, lim_(xto0+)x([(1)/(x)]+[(2)/(x)]+........+[(15)/(x)])

The set of points of discontinuily of thef(x) = (1)/(x^(2) + 4x + 5)

Find the point to whichthe origin is to be shifted so thatthe point (3, 0) may change to (2,-3)

Write the values of x and y if (3-4i) (x + yi) =1 + i(0)

If z=cos((pi)/(3))-isin((pi)/(3)) then z^(2)-z+1=....

Find deltay and dy for the following functions y=x^(2)+3x+6,x=10,deltax=0.01

A particle moves on a line according to the law s = at^(2) + bt + c. If the displacement after one second is 16 cm, the velocity after 2 second is 24 cm/sec and the acceleration is 8cm//sec^(2). Then (a,b,c)

Let a,b,c,d,e,f,g,h be distinct elements in the set {-7,-5,-3,-2,2,4,6,13} . The minimum value of (a+b+c+d)^(2)+(e+f+g+h)^(2) is

Find the transformed equation of 4xy-3x^(2) = a^(2) when the axes are rotated through an angle Tan^(-1)2.

If n is an odd positive integer, prove that the coefficients of the middle terms in the expansion of (x+y)^(n) are equal.

Match of the following

Evaluate cos^2(pi/8)+cos^2((3pi)/8)

Show that (a^(2))/( 4) sin 2c +(c^(2))/( 4) sin 2A = Delta

State whether word or is used in following statement is Exclusive or Inclusive. Proof at identity is Pancard or Bank passbook.

Writethe negation of the statement .'The sum of 3 and 4 is 9' ?

If oneof lines in ax^(2)+2hxy+by^(2)=0 bisects the angle between the coordinates axes then (a+b)^(2)=

Letf(x)=(2x(sin x + tanx))/(2[(x+21pi)/(pi)]-41),x != n pi,then f is ( where [.] represents greatest integer function)

If the sum of n terms of G.P. 3, 6, 12,…….is 381 then find n

From4 red balls, 2 white balls and 4 blackhalls , four halls are selected . The probabilityof getting 2 red balls is

I: The system of equations x+y+z=6,x-y+z=2, 2x-y+3z=9 has unique solution. II: The system of equations x+y+z=3, 2x+2y-z=3,x+y-z=1 has infinitely many solutions

The point of concurrence of the lines (a+2b)x+(a-b)y+(a+5b)=0 is

Solve the equation 2z= |z| + 2i is complex numbers

Evaluate the following limits. Lt_(xto pi)(x-22/7)

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that (A ∪ B)′ = A′ ∩ B′

y = tan^(-1)sqrt((1-cosx)/(1+cosx)) dy/dx is:

If 2S=a+b+c, prove that |{:(a^(2),(S-a)^(2),(S-a)^(2)),((S-b)^(2),b^(2),(S-b)^(2)),((S-c)^(2),(S-c)^(2),c^(2)):}|=2S^(3)(S-a)(S-b)(S-c).

|{:(a-b-c,2b,2c),(2a,b-c-a,2c),(2a,2b,c-a-b):}|=

If tantheta+tan2theta+sqrt(3)tanthetatan2theta=sqrt(3), then theta=(npi)/(3)+(pi)/(9).

If y is an implicit funtiion of x given by the relation, find (dy)/(dx). x ^(2) + y ^(2) + 2x + 3y -4 =0.

Find the co-ordinates of the point of intersection of the straight lines 2x-3y-7=0 , 3x-4y-13=0

Find the term independent of x in the expansion of (root(3)(x)+1/(2root(3)(x)))^18,x > 0.

The sum and product of three consecutive terms of an A.P. are 24 and 312 respectively. Find these terms.

Find the mean deviation by short cut method.

Form the bicoditional statement phArrq. Where p: Natural number n is odd. q: Natural number n is not divisible by 2.

If A(1, -1, -3), B(2, 1, -2), C(-5, 2, -6) are the vertices of a DeltaABC, then the length of internal bisector of angle A is

(sqrt(2)-sin alpha - cos alpha)/(sin alpha - cos alpha) is equal to

Solve the following equations: x^(2)-sqrt(2)ix+12=0

Statement-1 : Condition of Lagrange's mean value theorem fail in f(x) = | x-1 | (x-1). Statement-2 : |x-1| is not differentiableat x=1 .

Equilateral triangle DEF is inscribed in equilateral triangle ABC as shown with DE bot^("lar")B Cthen ratio of Area of triangle DEF to the Area of Delta^("le") ABC is then

Separate the intervals of monotonicity of the following functions : f(x) = -sin^(3)x + 3 sin^(2)x + 5, x in [-pi//2, pi//2]

If the distance between the pair of parallel lines x^(2)+2xy+y^(2)-8ax-8ay-9a^(2)=0 is 25sqrt2, then |a|=

If (5,-2),(-2,1) and (9,6) are collinear find alpha.

Express sin "" (5pi)/(2) in terms ofcos 5pi ,