14949 + Interview Questions in Maths in Class 11 Page 52 InterviewSolution

2551.	cosx=(2cosy-1)/(2-cosy) , where x , y in (0,pi) then tan""x/2 cot""(y)/2 is equal to
Answer» `SQRT2` `SQRT3` `1/sqrt2` `1/sqrt3` ANSWER :B

Discussion

2552.	How many of them are divisible by 10 ?
Answer» ANSWER :` 20`

Discussion

2553.	Consider a triangle whose sides are along x+y = 2, 3x-4y = 6 and x-y = 0 Find the equation of the circum circle of the triangle
Answer» SOLUTION :`x^2+y^2+4x+6y-12 = 0`

Discussion

2554.	r+r_(3)+r_(1)-r_(2)=
Answer» `4R COSA` `4R COSB` `4R COSC` 4R Answer :B

Discussion

2555.	The periodof cosxcos (120^(0)- x) cos (120^(0)+ x)is
Answer» `(2PI)/(3)` `(PI)/(3)` `(pi)` `(2pi)` ANSWER :1

Discussion

2556.	If h_(1),h_(2),h_(3) are lengths of altitudes of a Delta^("le")ABC and r is the inradius then minimum value of (h_(1)+r)/(h_(1)-r)+(h_(2)+r)/(h_(2)-r)+(h_(3)+r)/(h_(3)-r) is
Answer» `GE6` `LE6` `gt6` `LT 6` ANSWER :A

Discussion

2557.	A manufacturer has 600 litres of a 12 percent solution of acid. How many litres of a 30 percent acid solution must be added to it so that the acid contect in the resulting mixture will be more than 15 percent but less than 18 percent?
Answer» Answer :the NUMBER of litres of the 30% solution of acid will have to be more than 120 litres but LESS than 300 litres.

Discussion

2558.	Find the odd one out of the following :
Answer» (0, 5), (0, 7) (-7, 0) (5, 0), (-9, 0) (11, 0) (1, 1), (-5, -5), (-11, -11) (0, -2), (-7, 0), (4, 4) Answer :D

Discussion

2559.	Find the parametric representation of the circle x^(2) +y^(2) - 2 x - 4 y - 4 = 0
Answer» ANSWER :`THETA`

Discussion

2560.	Which of the following lines lie on the plnae x + 2y - z + 4=0 ?
Answer» `(x-1)/(1 ) = (y)/(-1) = (z-5)/(-1)` `x-y + z= 2x + y - z=0` `VECR = 2 hati - HATJ + 4 hatk + LAMDA ( 3 hati + hatj + 5 hatk)` `(x-2)/(1) = y/2 = (z-5)/(3)` Answer :A::C

Discussion

2561.	Let f, g : R to R be defined, respectively byt f(x)=x+1, g(x)=2x-3. Find f+g, f-g and f/g.
Answer» ANSWER :`(X+1)/(2x-3), x NE (3)/(2)`

Discussion

2562.	Abinomialprobabilitydistributionis symmertrial.If theprobabilityp of success in a singletrialis
Answer» GREATERTHAN`1//2` LESSTHAN`1//2` LESS than`q=1-p` EQUALTO 1/2 Answer :D

Discussion

2563.	For each of the following statement determine which type of 'or ' is used ? (i) the rectangle is a four sided or a five sided polygon. (ii) two lines interest at a point or are parallel. (iii) sun rises or moon sets.
Answer» SOLUTION :(i) INCLUSIVE (II) inclusive (III) inclusive.

Discussion

2564.	Let O(0,0), P(3,4), Q(6,0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal. The coordinates of R are
Answer» `(4/3,3)` `(3,2/3)` `(3,4/3)` `(4/3,2/3)` ANSWER :C

Discussion

2565.	The range of f(x)=(x^(4))/(1+x^(8)) is
Answer» `[0, OO)` `[0, 1/2]` `[0,1]` `(-oo, oo)` ANSWER :B

Discussion

2566.	Obtain the equation of the ellipse whose latus rectum is 5 and whose eccentricity is 2/3, the axes of the ellipse being the axes of coordinates.
Answer» ANSWER :`(4X^(2))/81+(4Y^(2))/45=1`

Discussion

2567.	Find (dy)/(dx)if x =a ( cos t + t sin t ), y = a ( sin t - t cos t).
Answer» ANSWER :TAN t

Discussion

2568.	Find the value of p, if the straight lines 3x+7y-1=0 and 7x-py+3=0 are mutually perpendicular.
Answer» ANSWER :3

Discussion

2569.	The two statements are given : p: 40 is multiple of5. q : 40 is a multiple of 6. check the validity of the compound statements by connecting the words ' and' and 'or'.
Answer» <P> SOLUTION :p and Q' is FALSE . 'p or q' is TRUE.

Discussion

2570.	A straight line which makes equal intercepts on positive X and Y axes and which is at a distance 1 unit from the origin intersects the striaght line y=2x+3X+sqrt(2) at (x_(0),y_(0)). Then 2x_(0)+y_(0)=
Answer» `3+SQRT(2)` `sqrt(2-1` `1` `0` ANSWER :B

Discussion

2571.	Differentiate the following functions w.r.t. x: sec ((x)/(2) -1)
Answer» ANSWER :`(1)/(2) SEC"" ((X)/(2) -1) tan((x)/(2) -1)`

Discussion

2572.	For what value of x the line joining A(4,1,2), B(5,x,0) is perpendicular to the line joining C(1,2,3), D(3,5,7).
Answer» ANSWER :X = 3

Discussion

2573.	Three cards are drawn fromadeck of 52 cards . Whatis the probability thatnone of them is a club ?
Answer» Answer :`(""^(39)C_(3))/(^(52)C_(3))=(703)/(1700)`

Discussion

2574.	Find the value of f(0) so thatf(x) = (1 + 5x)^(1//x)is continuous at x = 0 .
Answer» `E^(2)` `e^(3)` `e^(5)` `e^(7)` Answer :C

Discussion

2575.	The number of values of alphain [0,2 pi] for which 2 sin^(3) alpha - 7 sin^(2) alpha + 7 sin alpha = 2 is
Answer» 6 4 3 1 Answer :C

Discussion

2576.	If in a triangle ABC,(1+cosA)/(a)+(1+cosB)/(b)+(1+cosC)/(c)=(k^(2)(1+cosA)(1+cosB)(1+cosC))/(abc)then k is equal to
Answer» `(1)/(2 SQRT(2)R` 2R `(2)/(R)` None of these Answer :B

Discussion

2577.	Foot of the perpendicular from (-2,3) on x-axis is
Answer» (2,3) (-2,0) (0,3) (-2,-3) ANSWER :B

Discussion

2578.	Orthocentre of triangle of which two sides are formed by lines 6x^(2)-5xy-6y^(2)+x+5y-1=0is
Answer» `(-(1)/(13),(5)/(13))` `((1)/(13),(5)/(13))` `((1)/(13),(-5)/(13))` `((-1)/(13),(-5)/(13))` ANSWER :B

Discussion

2579.	Choose the correctoption for the following lim_(xrarrinfty)[(x^2 +5x +6)/(x^2 +2x +1)]^x is :
Answer» `e^4` `e^6` `e^2` `1/(e^2)` ANSWER :C

Discussion

2580.	Let O(0,0), P(3,4), Q(6,0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal. The coordinates of Rare
Answer» `(4/3,3)` `(3,2/3)` `(3,4/3)` `(4/3,2/3)` ANSWER :C

Discussion

2581.	If bara = xbari + ybari + zbark, then what are the value of x, y and z ?
Answer» ANSWER :`X =bara.bari ; y = bara.barj ; Z = bara.bark`

Discussion

2582.	If Sin^(-1)x+Sin^(-1)y=2pi//3,"then "Cos^(-1)x+Cos^(-1)y=
Answer» (0, 1) (1/2, 1) (1, 1/2) `(sqrt(3)//2, 1)` Answer :B

Discussion

2583.	Find the vector equation of the line passing through the points 2bar(i) + bar(j)+3bar(k), -bar(i)+3bar(j)-bar(k).
Answer» `bar(R)=(3BAR(i)+2BAR(j)-4bar(k))+t(2bar(i)+2bar(j)-2bar(k))` `bar(r)=(3bar(i)+2bar(j)-4bar(k))+t(2bar(i)-2bar(j)+2bar(k))` `bar(r)=(3bar(i)+2bar(j)-4bar(k))+t(-2bar(i)+2bar(j)-2bar(k))` `bar(r)=(5bar(i)+4bar(j)-6bar(k))+t(3bar(i)+2bar(j)-4bar(k))` ANSWER :A

Discussion

2584.	Find the co-ordinates of the points on the curve y= (x)/( 1-x^(2))" for which " (dy)/( dx)= 1
Answer» ANSWER :`(0,0) ( SQRT(3) , (- SQRT3)/( 2) ), (- sqrt3,(sqrt3)/(2))`

Discussion

2585.	If absbara =3, absbarb = 4, and (bara-barb) = 5, " then "abs(bara+barb)=
Answer» 6 5 4 3 Answer :B

Discussion

2586.	If in two cirlces arcs of the same length subtend angles 60^(@) and 75^(@) at the centre, find the ratio of their radii.
Answer» ANSWER :`5:4`

Discussion

2587.	Find the ratio in which the point P(5,4,-6) divides the line segment joining the points A(3,2,-4) and B(9,8,-10) . Also find the harmonic conjugate of P.
Answer» ANSWER :1 : 2,(-3,-4,2)

Discussion

2588.	The side of a square is increased from 3cm to 3.01cm. Find the approximate increase in the area of the square.
Answer» ANSWER :0.06

Discussion

2589.	The orthocentre of the triangle formed by (1,-3),(6,1),(4,-1) is
Answer» `(3//2, 3//2)` `(-3,2)` `(4,8//3)` `(24,-26)` ANSWER :D

Discussion

2590.	How many 3-digit even numbers that can be formed using the digit 2,4,6,8 ?
Answer» ANSWER :64, 24

Discussion

2591.	Find the derivative of the function sqrt x + 2x ^(3//4)+ 3. x ^(5//6)
Answer» ANSWER :` (1)/( 2 SQRTX) + 3/2 X ^(-1//4) + 5/2 x ^(-1//6) `

Discussion

2592.	If (3-"tan"^(2)(pi)/(7))/(1-"tan"^(2)(pi)/(7))="k cos" (pi)/(7) then the value of k is
Answer» 1 2 3 4 Answer :D

Discussion

2593.	Find the eccentricity of the hyperbola 9y^(2) - 4x^(2) = 36.
Answer» ANSWER :`(SQRT(13))/(2)`

Discussion

2594.	Write down the converse of following statements: If x is zero then x is neither positive nor negative.
Answer» ANSWER :X is ZERO.

Discussion

2595.	If C=60 ^(@) " then "( a) /( b+ c) + ( b) /( c+a) =
Answer» `2` `4` `3` `1` ANSWER :D

Discussion

2596.	Simplify : (cos(-theta))/(sin (90^(@)+theta))
Answer» ANSWER :1

Discussion

2597.	Calculate the possible values of x, if the standard deviation of the numbers 2, 3, 2x and 11 is 3.5.
Answer» ANSWER :X = 3 or `7/3`

Discussion

2598.	-3 le 4 - (3x)/(-5) le 2
Answer» ANSWER :`[-4,2]`

Discussion

2599.	Let 'O' be the origin and A, B be two points. bar(p), bar(q) are vectors represented by bar(OA), bar(OB) and their magnitudes are p, q respectively. Unit vector bisecting angleAOB is
Answer» <P>`(BAR(p)/p+bar(Q)/q)/ABS(bar(p)/p+bar(q)/q)` `(bar(p)/p-bar(q)/q)/abs(bar(p)/p-bar(q)/q)` `bar(p)/p+bar(q)/q` `bar(p)/p-bar(q)/q` ANSWER :A

Discussion

2600.	If two lines, whose equations are (x -3)/(2) = (y -2)/(3) = (z-1)/(lamda) and (x-2)/(3) = (y-3)/(3) = (z-2)/(3) lie in the same plane. Then the value of sin ^(-1) sin lamda is
Answer» 3 `PI -3` 4 `pi -4` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

cosx=(2cosy-1)/(2-cosy) , where x , y in (0,pi) then tan""x/2 cot""(y)/2 is equal to

How many of them are divisible by 10 ?

Consider a triangle whose sides are along x+y = 2, 3x-4y = 6 and x-y = 0 Find the equation of the circum circle of the triangle

r+r_(3)+r_(1)-r_(2)=

The periodof cosxcos (120^(0)- x) cos (120^(0)+ x)is

If h_(1),h_(2),h_(3) are lengths of altitudes of a Delta^("le")ABC and r is the inradius then minimum value of (h_(1)+r)/(h_(1)-r)+(h_(2)+r)/(h_(2)-r)+(h_(3)+r)/(h_(3)-r) is

A manufacturer has 600 litres of a 12 percent solution of acid. How many litres of a 30 percent acid solution must be added to it so that the acid contect in the resulting mixture will be more than 15 percent but less than 18 percent?

Find the odd one out of the following :

Find the parametric representation of the circle x^(2) +y^(2) - 2 x - 4 y - 4 = 0

Which of the following lines lie on the plnae x + 2y - z + 4=0 ?

Let f, g : R to R be defined, respectively byt f(x)=x+1, g(x)=2x-3. Find f+g, f-g and f/g.

Abinomialprobabilitydistributionis symmertrial.If theprobabilityp of success in a singletrialis

For each of the following statement determine which type of 'or ' is used ? (i) the rectangle is a four sided or a five sided polygon. (ii) two lines interest at a point or are parallel. (iii) sun rises or moon sets.

Let O(0,0), P(3,4), Q(6,0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal. The coordinates of R are

The range of f(x)=(x^(4))/(1+x^(8)) is

Obtain the equation of the ellipse whose latus rectum is 5 and whose eccentricity is 2/3, the axes of the ellipse being the axes of coordinates.

Find (dy)/(dx)if x =a ( cos t + t sin t ), y = a ( sin t - t cos t).

Find the value of p, if the straight lines 3x+7y-1=0 and 7x-py+3=0 are mutually perpendicular.

The two statements are given : p: 40 is multiple of5. q : 40 is a multiple of 6. check the validity of the compound statements by connecting the words ' and' and 'or'.

A straight line which makes equal intercepts on positive X and Y axes and which is at a distance 1 unit from the origin intersects the striaght line y=2x+3X+sqrt(2) at (x_(0),y_(0)). Then 2x_(0)+y_(0)=

Differentiate the following functions w.r.t. x: sec ((x)/(2) -1)

For what value of x the line joining A(4,1,2), B(5,x,0) is perpendicular to the line joining C(1,2,3), D(3,5,7).

Three cards are drawn fromadeck of 52 cards . Whatis the probability thatnone of them is a club ?

Find the value of f(0) so thatf(x) = (1 + 5x)^(1//x)is continuous at x = 0 .

The number of values of alphain [0,2 pi] for which 2 sin^(3) alpha - 7 sin^(2) alpha + 7 sin alpha = 2 is

If in a triangle ABC,(1+cosA)/(a)+(1+cosB)/(b)+(1+cosC)/(c)=(k^(2)(1+cosA)(1+cosB)(1+cosC))/(abc)then k is equal to

Foot of the perpendicular from (-2,3) on x-axis is

Orthocentre of triangle of which two sides are formed by lines 6x^(2)-5xy-6y^(2)+x+5y-1=0is

Choose the correctoption for the following lim_(xrarrinfty)[(x^2 +5x +6)/(x^2 +2x +1)]^x is :

Let O(0,0), P(3,4), Q(6,0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal. The coordinates of Rare

If bara = xbari + ybari + zbark, then what are the value of x, y and z ?

If Sin^(-1)x+Sin^(-1)y=2pi//3,"then "Cos^(-1)x+Cos^(-1)y=

Find the vector equation of the line passing through the points 2bar(i) + bar(j)+3bar(k), -bar(i)+3bar(j)-bar(k).

Find the co-ordinates of the points on the curve y= (x)/( 1-x^(2))" for which " (dy)/( dx)= 1

If absbara =3, absbarb = 4, and (bara-barb) = 5, " then "abs(bara+barb)=

If in two cirlces arcs of the same length subtend angles 60^(@) and 75^(@) at the centre, find the ratio of their radii.

Find the ratio in which the point P(5,4,-6) divides the line segment joining the points A(3,2,-4) and B(9,8,-10) . Also find the harmonic conjugate of P.

The side of a square is increased from 3cm to 3.01cm. Find the approximate increase in the area of the square.

The orthocentre of the triangle formed by (1,-3),(6,1),(4,-1) is

How many 3-digit even numbers that can be formed using the digit 2,4,6,8 ?

Find the derivative of the function sqrt x + 2x ^(3//4)+ 3. x ^(5//6)

If (3-"tan"^(2)(pi)/(7))/(1-"tan"^(2)(pi)/(7))="k cos" (pi)/(7) then the value of k is

Find the eccentricity of the hyperbola 9y^(2) - 4x^(2) = 36.

Write down the converse of following statements: If x is zero then x is neither positive nor negative.

If C=60 ^(@) " then "( a) /( b+ c) + ( b) /( c+a) =

Simplify : (cos(-theta))/(sin (90^(@)+theta))

Calculate the possible values of x, if the standard deviation of the numbers 2, 3, 2x and 11 is 3.5.

-3 le 4 - (3x)/(-5) le 2

Let 'O' be the origin and A, B be two points. bar(p), bar(q) are vectors represented by bar(OA), bar(OB) and their magnitudes are p, q respectively. Unit vector bisecting angleAOB is

If two lines, whose equations are (x -3)/(2) = (y -2)/(3) = (z-1)/(lamda) and (x-2)/(3) = (y-3)/(3) = (z-2)/(3) lie in the same plane. Then the value of sin ^(-1) sin lamda is