14949 + Interview Questions in Maths in Class 11 Page 34 InterviewSolution

1651.	Write each of the following statements in the form ''if-then'' A quadrilateral is a parallelogram if its diagonals bisect each other.
Answer» ANSWER :If DIAGONALS of a QUADRILATERAL BISECT each other, then it is a PARALLELOGRAM

Discussion

1652.	Find the orthocenter of the triangle formed by the points (2,1,5),(3,2,3),(4,0,4).
Answer» ANSWER :(3,1,4)

Discussion

1653.	~(~phArrq)=………
Answer» `~p^^~q` `~pvv~q` `(p^^~q)VV(~p^^q)` `(p^^~q)^^(~p^^q)` ANSWER :C

Discussion

1654.	Three of six vertices of a regular hexagon are chosen at random. What is the probability that the triangle with these vertices is equilateral ?
Answer» ANSWER :`(1)/(10)`

Discussion

1655.	Solve the system of equations 2/x+3/y+10/z=4,4/x-6/y+5/z=1,6/x+9/y-20/z=2 by Gauss Jordan method.
Answer» ANSWER :`x=2,y=3,z=5`

Discussion

1656.	The point on the curve y=x/(1+x^2) where the tangent to the curve has the greatest slope is
Answer» `(1,(1)/(2))` `(-1,(-1)/(2))` `(2,(2)/(5))` `(0,0)` ANSWER :D

Discussion

1657.	Find the value of k such that the line (k-2)x+(k+3)y-5=0 perpendicualr to 2x-y+7=0.
Answer» ANSWER :7

Discussion

1658.	Prove that an angle between the pair of the lines joining the origin to the points of interesection of the line lx+my=1 with the curve x^(2)+y^(2)=a^(2) is 2cos^(-1)((1)/(a sqrt(l^(2)+m^(2))))
Answer» ANSWER :1

Discussion

1659.	An equation of a plane parallel to the plane x – 2y + 2z - 5 = 0 and at a unit distance from the origin is
Answer» `X - 2Y + 2Z - 7=0` `x - 2y + 2z + 5=-0` `x - 2y + 2z - 3=0` `x - 2y + 2z + 1=0` ANSWER :C

Discussion

1660.	The smallest value of M such that 1x^(2)-3x+2\|leM for all x in [1,5/2] is
Answer» 1 `1//2` `1//4` `3//4` ANSWER :D

Discussion

1661.	Find the sum to n terms of the series3 xx 8 + 6 xx 11 + 9 xx 14 +. . . . . .
Answer» ANSWER :3N (N + 1) (n + 3)

Discussion

1662.	In Delta ABC, if sin^2""A/2, sin^2""B/2,sin^2""C/2 are in H.P, then a,b,c in
Answer» A.G.P. G.P. A.P. H.P. ANSWER :C

Discussion

1663.	Ifsin theta , cos thetaare ther roots of the equationax^(2)-bx+c=0 , then the relation among a,b,c is
Answer» `a^(2)-B^(2)+2ac=0` `a^(2)+b^(2)-2ac=0` `a^(2)-b^(2)-2ac=0` `a^(2)+b^(2)+2ac=0` ANSWER :A

Discussion

1664.	Area of the triangle formed by the lines x^(2)-3xy+y^(2)=0 and x+y+1=0
Answer» `5 SQRT(2)` `(1)/(2 sqrt(5))` `(2)/(sqrt(3))` `(sqrt(3))/(2)` ANSWER :B

Discussion

1665.	int(x^(4)-x^(2)+2)/(x+1)dx :
Answer» `(X^(4))/(4)+(x^(3))/(3)+LOG(x+1)+C` `(x^(4))/(4)-(x^(3))/(3)+log(x+1)+c` `(x^(4))/(4)+(x^(3))/(3)+2log(x+1)+c` `(x^(4))/(4)-(x^(3))/(3)+2log(x+1)+c` Answer :D

Discussion

1666.	If 3bar(i)+3bar(j)+sqrt(3)bar(k), bar(i)+bar(k), sqrt(3)bar(i)+sqrt(3)bar(j)+lambdabar(k) are coplanar then lambda=
Answer» 1 2 3 4 Answer :A

Discussion

1667.	Differentiate the following w.r.t. x : (cos x)/(log x), x gt 0.
Answer» ANSWER :`- ( (x SIN x, log x + cos x ))/( x(log x ) ^(2)) , x ge 0`

Discussion

1668.	The middle term in the expansion of ( (10)/(x) + (x)/(10) )^10 is :
Answer» `""^10C_5` `""^10C_6` `""^10C_(5) (1)/(x^10) ` `""^10C_5 x^10` ANSWER :A

Discussion

1669.	Solve: (x + 2) (x + 3)^(2) lt0.
Answer» Answer :the INEQUALITY is SATISFIED in the interval `(-INFTY, -3) and (-3, 2)therefore "SOLUTION set is " ( - infty, -3) CUP (-3, 2)`

Discussion

1670.	Find the derivative of the function If f (x) = mx + c and if f (0) = f ^(1) (0) =1 then find f (2).
Answer» ANSWER :3

Discussion

1671.	If A is an obtuse angle whose sine is (5)/(13)and Bis an acute angle whose tangent is (3)/(4), without using tables find the values of (a) sin 2B, (b) tan (A-B).
Answer» ANSWER :`- (56)/(33)`

Discussion

1672.	Find the maximum and minimum values, if any, of the functions given by f(x) = – (x -1)^(2) + 10
Answer» ANSWER :MAXIMUM VALUE = 3, at X = 1

Discussion

1673.	Ify = "cos^(-1)((2x)/(1 + x^2)), then (dy)/(dx) is
Answer» `(-2)/(1 + X^2)` for all x `(-2)/(1 + x^2)` for all `\|x\| LT 1` `(2)/(1 + x^2)` for `\|x\| GT 1` none of these Answer :B::C

Discussion

1674.	An experiment consists of tossing a coin and then throwing it second time if a head occurs on the first toss, then a die is rolled once. Find the sample space.
Answer» ANSWER :{HH, HT, T1, T2, T3, T4, T5, T6}

Discussion

1675.	f(x) = Cot^(-1)((x^x-x^(-x))/(2)) then f^(1)(1)=
Answer» `- LOG2` `LOG 2` 1 `-1` ANSWER :D

Discussion

1676.	If 4sinalphasin(x+alpha)sin(x-alpha)=sin3alpha, then general value of x is:
Answer» `NPI+-pi/4` `npi+-pi/3` `2NPI` `npi` SOLUTION :N//A

Discussion

1677.	In what direction should a line be drawn through the point (1,2) so that its point of intersection with the line x+y = 4 is at a distance ( sqrt(6) )/( 3) from the given point ?
Answer» ANSWER :`THETA = 75^(@)` OR `theta = 15^(@)`

Discussion

1678.	Write the first four terms in the expansions of the following :(i)(1)/((2+x)^(4)) where \|x\|gt 2(ii)(1)/(root(3)(6-3x)) where \|x\|lt 2
Answer» Answer :(i)`(1)/(X^(5))[x-8+(40)/(x)-(160)/(x^(2))+………….]` (ii)`= (1)/(6^(1//3))[1+(x)/(6)+(x^(2))/(18)+(7)/(324)x^(3)+….]`

Discussion

1679.	Evaluate cosec (-1410^(@))
Answer» ANSWER :2

Discussion

1680.	(barbxxbarc)xx(barcxxbara)=
Answer» `[vecavecbvecc]VECC` `[vecavecbvecc]VECB` `[vecavecbvecc]VECA` `BAR0` ANSWER :A

Discussion

1681.	The shortest distance between the lines (x -2)/(3) = (y-3)/(4) = (z -4)/(5), (x -1)/(2) = (y-2)/(3) = (z-3)/(4) is
Answer» 2 1 3 0 Answer :D

Discussion

1682.	Iff^1(x)=sqrt(2x^(2)-1)and y=f(x^2)thendy/dx at x = 1 is
Answer» 2 1 -2 -1 Answer :A

Discussion

1683.	Matching the items of Column-I with the items Column-II {:("Column-I", "Column-II"), ("A) If "cos^(-1)lambda+cos^(-1)mu+cos^(-1)gamma=3pi" then "lambdamu+mugamma+gammalambda" is","p) "2n), ("B) If "sum_(i=1)^(10)cos^(-1)x=0" then "sum_(i=1)^(10)x_(i)" is", "q) "(sin^(-1)x-pi/6)), ("C) If "sum_(i=1)^(2n)sin^(-1)x_(i)=npi" then "sum_(i=1)^(2n)x_(i)" is", "r) "10),("D) The value of "sin^(-1){sqrt(3)/2x-1/2sqrt(1-x^(2))}"," (-1/2 le x le 1/2)" is", "s) "3):}
Answer» ANSWER :A-s, B-r, C-p, D-q

Discussion

1684.	PQ is the perpendicular bisector of AD.AB bot^("lar") BC " and " DC bot^("lar") BC. IfAB = 9BC = 8 " and " CD = 7. Then the area of quadrilateral APQB.
Answer» 26 27 25 24 Answer :a

Discussion

1685.	Evaluate the following limits : Lim_( xto 2) (7x^(2)-11x - 6)/(3x^(2)-x-10)
Answer» ANSWER :`17/11`

Discussion

1686.	If [Cot^(-1)x]+[Cos^(-1)x]=0 where x is non negative real number and [.] denotes the greatest integer function then complete set of values of x is
Answer» (COS1,1] (cos1,cot1) (cot1,1] (0,cos1) ANSWER :C

Discussion

1687.	construct truthtable for~(~p ^^ ~q)
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C27_E04_023_A01##)`

Discussion

1688.	construct truthtable for(~p)^^ (~q)
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C27_E04_019_A01##)`

Discussion

1689.	construct truthtable for(~p)^^ q
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C27_E04_018_A01##)`

Discussion

1690.	construct truthtable for~(p ^^ q)
Answer» ANSWER :`(##SCH_OPM_ISC_MAT_XI_C27_E04_020_A01##)`

Discussion

1691.	Do the limit of the function (sin (x - [x]))/(x - [x]) exist as x to 0 ? State the resons for your answer.
Answer» ANSWER :So, the LIMIT does not EXIST.

Discussion

1692.	A (1,3) and C (-2/5,-2/5) are the vertices of a triangle ABC and the equation of the internal angular bisector of angleABCis x+y -2=0 Coordinates of vertex B
Answer» `(3/10,17/10)` `(17/10,3/10)` `(-5/2,9/2)` (1,1) ANSWER :C

Discussion

1693.	A (1,3) and C (-2/5,-2/5) are the vertices of a triangle ABC and the equation of the internal angle bisector of angleABC is x+y =2 Equation of BC is
Answer» 7x+3y+4=0 3x+7y+4 13x+7y+8=0 x+9y+4=0 Answer :A

Discussion

1694.	A (1,3) and C (-2/5,-2/5) are the vertices of a triangle ABC and the equation of the angle bisector of angleABCis x+y =2 Equation of side AB is
Answer» `13x-7y+8=0` `13x+7y-34=0` `3x+7y-24=0` `3x+7y+24=0` ANSWER :C

Discussion

1695.	If two lines represented by x^4+x^3y+cx^2y^2-xy^3+y^4=0 bisect the angle between the other two then the value of 'c' is
Answer» 0 -1 1 -6 Answer :D

Discussion

1696.	There exists a positive real number x satisfying cos(tan^(-1)x)=x. Then the value of "cos"^(-1)((x^(2))/2) is
Answer» `(PI)/10` `(pi)/5` `(2PI)/5` `(4PI)/5` Answer :C

Discussion

1697.	Write the negation of the following simple statements. (i) The number 17 is prime.
Answer» ANSWER :PRIME NUMBER.

Discussion

1698.	Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Equation of the line whose X- intercept is 4 and slope (1)/(2).
Answer» ANSWER :`X - 2Y - 4 = 0`

Discussion

1699.	If x is a negative real number the the value of cos^(-1)x+sec^(-1)x is
Answer» RATIONAL number irrational number integer imaginary Answer :B

Discussion

1700.	Find the sum of 7 terms of the sequence 2, 6, 18,……
Answer» ANSWER :2186

Discussion

Explore topic-wise InterviewSolutions in .

Write each of the following statements in the form ''if-then'' A quadrilateral is a parallelogram if its diagonals bisect each other.

Find the orthocenter of the triangle formed by the points (2,1,5),(3,2,3),(4,0,4).

~(~phArrq)=………

Three of six vertices of a regular hexagon are chosen at random. What is the probability that the triangle with these vertices is equilateral ?

Solve the system of equations 2/x+3/y+10/z=4,4/x-6/y+5/z=1,6/x+9/y-20/z=2 by Gauss Jordan method.

The point on the curve y=x/(1+x^2) where the tangent to the curve has the greatest slope is

Find the value of k such that the line (k-2)x+(k+3)y-5=0 perpendicualr to 2x-y+7=0.

Prove that an angle between the pair of the lines joining the origin to the points of interesection of the line lx+my=1 with the curve x^(2)+y^(2)=a^(2) is 2cos^(-1)((1)/(a sqrt(l^(2)+m^(2))))

An equation of a plane parallel to the plane x – 2y + 2z - 5 = 0 and at a unit distance from the origin is

The smallest value of M such that 1x^(2)-3x+2|leM for all x in [1,5/2] is

Find the sum to n terms of the series3 xx 8 + 6 xx 11 + 9 xx 14 +. . . . . .

In Delta ABC, if sin^2""A/2, sin^2""B/2,sin^2""C/2 are in H.P, then a,b,c in

Ifsin theta , cos thetaare ther roots of the equationax^(2)-bx+c=0 , then the relation among a,b,c is

Area of the triangle formed by the lines x^(2)-3xy+y^(2)=0 and x+y+1=0

int(x^(4)-x^(2)+2)/(x+1)dx :

If 3bar(i)+3bar(j)+sqrt(3)bar(k), bar(i)+bar(k), sqrt(3)bar(i)+sqrt(3)bar(j)+lambdabar(k) are coplanar then lambda=

Differentiate the following w.r.t. x : (cos x)/(log x), x gt 0.

The middle term in the expansion of ( (10)/(x) + (x)/(10) )^10 is :

Solve: (x + 2) (x + 3)^(2) lt0.

Find the derivative of the function If f (x) = mx + c and if f (0) = f ^(1) (0) =1 then find f (2).

If A is an obtuse angle whose sine is (5)/(13)and Bis an acute angle whose tangent is (3)/(4), without using tables find the values of (a) sin 2B, (b) tan (A-B).

Find the maximum and minimum values, if any, of the functions given by f(x) = – (x -1)^(2) + 10

Ify = "cos^(-1)((2x)/(1 + x^2)), then (dy)/(dx) is

An experiment consists of tossing a coin and then throwing it second time if a head occurs on the first toss, then a die is rolled once. Find the sample space.

f(x) = Cot^(-1)((x^x-x^(-x))/(2)) then f^(1)(1)=

If 4sinalphasin(x+alpha)sin(x-alpha)=sin3alpha, then general value of x is:

In what direction should a line be drawn through the point (1,2) so that its point of intersection with the line x+y = 4 is at a distance ( sqrt(6) )/( 3) from the given point ?

Write the first four terms in the expansions of the following :(i)(1)/((2+x)^(4)) where |x|gt 2(ii)(1)/(root(3)(6-3x)) where |x|lt 2

Evaluate cosec (-1410^(@))

(barbxxbarc)xx(barcxxbara)=

The shortest distance between the lines (x -2)/(3) = (y-3)/(4) = (z -4)/(5), (x -1)/(2) = (y-2)/(3) = (z-3)/(4) is

Iff^1(x)=sqrt(2x^(2)-1)and y=f(x^2)thendy/dx at x = 1 is

PQ is the perpendicular bisector of AD.AB bot^("lar") BC " and " DC bot^("lar") BC. IfAB = 9BC = 8 " and " CD = 7. Then the area of quadrilateral APQB.

Evaluate the following limits : Lim_( xto 2) (7x^(2)-11x - 6)/(3x^(2)-x-10)

If [Cot^(-1)x]+[Cos^(-1)x]=0 where x is non negative real number and [.] denotes the greatest integer function then complete set of values of x is

construct truthtable for~(~p ^^ ~q)

construct truthtable for(~p)^^ (~q)

construct truthtable for(~p)^^ q

construct truthtable for~(p ^^ q)

Do the limit of the function (sin (x - [x]))/(x - [x]) exist as x to 0 ? State the resons for your answer.

A (1,3) and C (-2/5,-2/5) are the vertices of a triangle ABC and the equation of the internal angular bisector of angleABCis x+y -2=0 Coordinates of vertex B

A (1,3) and C (-2/5,-2/5) are the vertices of a triangle ABC and the equation of the internal angle bisector of angleABC is x+y =2 Equation of BC is

A (1,3) and C (-2/5,-2/5) are the vertices of a triangle ABC and the equation of the angle bisector of angleABCis x+y =2 Equation of side AB is

If two lines represented by x^4+x^3y+cx^2y^2-xy^3+y^4=0 bisect the angle between the other two then the value of 'c' is

There exists a positive real number x satisfying cos(tan^(-1)x)=x. Then the value of "cos"^(-1)((x^(2))/2) is

Write the negation of the following simple statements. (i) The number 17 is prime.

Obtain the equation at the line in Ex. (1) to (10) satisfying given condition : Equation of the line whose X- intercept is 4 and slope (1)/(2).

If x is a negative real number the the value of cos^(-1)x+sec^(-1)x is

Find the sum of 7 terms of the sequence 2, 6, 18,……