14949 + Interview Questions in Maths in Class 11 Page 47 InterviewSolution

2301.	The mid-point of the sides of a triangle are (1, 5, -1), (0, 4, -2) and (2, 3, 4). Find its vertices. Also find the centriod of the triangle.
Answer» ANSWER :`(1,4,1/3)`

Discussion

2302.	The remaninder obtained when 1!+2!+3!+……..+11! is divided by 12 is:
Answer» 9 8 7 6 Answer :A

Discussion

2303.	Let A(6,7), B(2,3), C(-2,1) vertices of a triangle. The point P in the interior of DeltaABC " such that " Delta PBC
Answer» `(-sqrt3,2+2sqrt3)` `(-sqrt3,2-2sqrt3)` `(sqrt3,2-2sqrt3)` `(sqrt3,2+2sqrt3)` ANSWER :A

Discussion

2304.	A and B are mutually exclusive events. P(A)=0.28, P(B)=0.38, then find (i) P(AuuB), (ii) P(AnnB), (iii) P(AnnB'), (iv) P(A'nnB')
Answer» ANSWER :(i) 0.60 (II) 0 (III) 0.28 (IV) 0.34

Discussion

2305.	State true of false for the following: For any complex number, z, the minimum value of \|z\|+\|z-1\| is 1.
Answer» ANSWER :1

Discussion

2306.	((a^(2) - b^(2) sin A sin B) /( 2 sin ( A- B)))
Answer» `(DELTA)/(2) ` ` (Delta)/(3)` ` ( Delta )/(4) ` ` Delta ` ANSWER :D

Discussion

2307.	Define hyperbola as a set of points derive its equation in the form(x^(2))/( a^(2))-( y^(2))/( b^(2)) =1
Answer» Answer :` PUT C^(2)-a^(2)=b^(2)therefore X^(2)/a^(2)-y^(2)/b^(2) =1`

Discussion

2308.	Find the equation of the circle which touches X - axis and whose centre is (1,2).
Answer» ANSWER :`therefore x^(2) + y^(2) - 2X - 4y + 1 = 0` is required equation of the CIRCLE.

Discussion

2309.	Write each of the following statements in the form ''if-then'' You get a job implies that your credentials are good.
Answer» ANSWER :If you GET a JOB, then your CREDENTIALS are GOOD

Discussion

2310.	Two equilateral triangles are constructed from a line segment of length L. If M and m are the maximum and minimum values of the sum of the areas of two plane figures, then the value of M/m is.
Answer» 2 3 `SQRT2` `SQRT3` ANSWER :A

Discussion

2311.	The plane is perpendicular to the line x/1 =y/1 = (z)/(r ^(2)) passes through the origin and the point (-4, 3, 1) if r is equal to
Answer» 1 5 `-4` 3 Answer :A::C

Discussion

2312.	If log(sqrt(5)+2)=sinh^(-1)(k) then k =
Answer» 1 5 3 2 Answer :D

Discussion

2313.	a^(2) sin 2B+ b^(2)sin 2A =
Answer» ` DELTA ` `2 Delta ` ` 3Delta` ` 4 Delta ` ANSWER :D

Discussion

2314.	Evaluate lim_(x rarr a) (cos x - cos a)/(sqrtx - sqrta)
Answer» SOLUTION :`-2sqrta SIN a`

Discussion

2315.	Iff (x) = ( x sin 5 x)/(tan 2x tan 7x), x in 0 , f (0) = 5/9then at x = 0f(x) is
Answer» CONTINUOUS discontinuous not DETERMINED none ANSWER :B

Discussion

2316.	Using Mathemtical induction, show that for any natural number n, (1)/(1.2)+(1)/(2.3)+(1)/(3.4)+...+(1)/(n(n+1))=(n)/(n+1)
Answer» ANSWER : `N/(n+1) `

Discussion

2317.	Solve tan2x=-cot(x+(pi)/(3)).
Answer» Answer :`X = N pi + (5pi)/(5)`

Discussion

2318.	Find deltay and dy for the following functions y=(1)/(x+2),x=8 and deltax=0.02
Answer» ANSWER :`-0.0001996, -0.0002`

Discussion

2319.	If y=1+x+(x^(2))/(2!)+(x^(2))/(3!)+……+(x^(n))/(n!) then (dy)/(dx)=…………
Answer» y y-X `y-(x^(N))/(n!)` `y-(x^(n))/((n-1)!)` ANSWER :C

Discussion

2320.	For the following, using median, calculate mean deviation and coefficient of mean deviation.
Answer» ANSWER :M.D = 0.75, COEFFT. of M.D = 0.063

Discussion

2321.	For the following, using median, calculate mean deviation and coefficient of mean deviation.
Answer» ANSWER :M.D = 4.99, COEFFT. of M.D = 0.384

Discussion

2322.	Solve : tan ((pi)/(4)+ theta) + tan ((pi)/(4) - theta) = 4
Answer» ANSWER :`theta = n PI pm (pi)/(6)`

Discussion

2323.	The number of values of x for which sin^(-1)(x^(2)-x^(4)/3+x^(6)/9…..)+cos^(-1)(x^(4)-x^(8)/3+x^(12)/9….)=pi/2," where "0 le abs(x) lt sqrt(3), is
Answer» ANSWER :3

Discussion

2324.	The value ofcos ( 35^(@) + A)cos ( 35^(@) - B) + sin ( 35^(@) +A)sin ( 35^(@) - B) is equal to(i) sin(A+ B)(ii) sin(A - B)(iii) cos (A+B)(iv) cos(A-B)
Answer» `SIN(A+ B) ` `sin(A - B)` `COS (A+B)` `cos(A-B)` ANSWER :C

Discussion

2325.	The slope of angular bisector of line (ax+by)^2=c(bx-ay)^2,(cgto) are
Answer» `-a/B,b/a` `a/b,(-b)/a` `a/C,(-c)/a` `c/a,(-a)/c` ANSWER :A

Discussion

2326.	Find the derivative of f (x) w.r.t. g(x) for the f (x) = Sec ^(-1) ((1)/( 2 x ^(2) - 1 )) , g (x) = sqrt(1- x ^(2))
Answer» ANSWER :`2/x`

Discussion

2327.	Coordinate planes divide the space into _____ octants.
Answer» ANSWER :8 (EIGHT)

Discussion

2328.	The smallest value of 'theta' satisfying there equation sqrt(3)(tan theta+cot theta)=4 is
Answer» `(2pi)/(3)` `(pi)/(3)` `(pi)/(6)` `(pi)/(12)` ANSWER :C

Discussion

2329.	IF alpha,beta,gamma are the lengths of the altitudes of Delta ABC, then 1/alpha+1/beta-1/gamma-(2ab)/((a+b+c)Delta)cos^2""C/2=
Answer» `0` ` 1` ` 2S ` `DELTA ` ANSWER :A

Discussion

2330.	Consider the points A (1,2) and B (2,3) Let P and Q be the points of trisection of the segment joining A and B Find the co-ordinates of P and Q
Answer» <P> SOLUTION :`p (4/3,7/3),Q (5/3,8/3)`

Discussion

2331.	Consider the points A (1,2) and B (2,3) Let P and Q be the points of trisection of the segment joining A and B Find the equation of the line passing through Q and perpendicular to AB
Answer» SOLUTION :3X + 3Y - 13 = 0

Discussion

2332.	Consider the points A (1,2) and B (2,3) Let P and Q be the points of trisection of the segment joining A and B Find the equation of the line passing through P and perpendicular to AB
Answer» SOLUTION :3X + 3Y - 11 = 0

Discussion

2333.	Delta ABC is not a right angled and is inscribed in a fixed circle. If a,A,b,B be slightly varied keeping c,C fixed then (deltaa)/(cosA)+(deltab)/(cosB)=
Answer» 2 1 0 5 Answer :C

Discussion

2334.	If 2/(1!9!)+2/(3!7!)+2/(5!5!)=2^m/(n!), then orthocentre of the triangle have having sides x-y+=0,x+y+3 and 2x+5y-2=0 is
Answer» (2m-2n,m-n) (2m-2n,m-n) (2m-n,m+n) (2m-n,m-n) ANSWER :A

Discussion

2335.	Statement I: The points (a,0),(0,b) and (1,1) will be collinear if 1/a+1/b=1 Statement II: If 4a^(2)+9b^(2)-c^(2)+12ab=0, then the family of lines ax+by+c=0 is either concurrent at (2,3) or at (-2,-3). Then which of the followng is true
Answer» only I onlyII both I and Ii neither I nor II Answer :C

Discussion

2336.	A tree stands vertically on the slant of the hills From a point A on the ground 35 meters. Down the hill from the base of the tree , the angle of elevation of the top of the tree is 60 ^(@) . If the angle of elevation of the foot of the tree A is 15 ^(@) , then the height of the tree.
Answer» ANSWER :` 35 SQRT2 m `

Discussion

2337.	Let a,b,c and d be non-zero numbers. If the point of intersection of the lines 4ax+2ay+c=0 and 5bx+2by+d=0 lies in the fourth quadrant and is equidistant from the two axes then
Answer» `2bc-3ad=0` `2bc+3ad=0` `3bc-2ad=0` `3bc+2ad=0` ANSWER :C

Discussion

2338.	P is a point on the line y=2x+1, and Q and R are tow points on the line 3y+6x=6 such that triangle PQR is an equailateral triangle. The length of the side of the triangle is
Answer» `2//sqrt15` `3//sqrt5` `4//sqrt5` `1/sqrt5` ANSWER :A

Discussion

2339.	One root of theequation ax^(2)-3x+1=0 is (2+i).Find the value of 'a' when a is not real.
Answer» SOLUTION :`a=(27-11i)/(25)`

Discussion

2340.	If x,y,z , t gt 0 and xyzt=81 then minimum value of x+2y+z+8t is
Answer» 2 24 36 36 Answer :B

Discussion

2341.	If (1+tan alpha)(1+tan 4alpha)=2, alpha epsilon(0,(pi)/(6)), then alpha=.
Answer» `(pi)/(10)` `(pi)/(30)` `(pi)/(40)` `(pi)/(60)` ANSWER :A

Discussion

2342.	Evaluate the following limits. If f(x)=-sqrt(25-x^(2)) then find Lt_(xto1)(f(x)-f(1))/(x-1)
Answer» ANSWER :`1/sqrt24`

Discussion

2343.	If f(x) and g(x) are periodic functions with periods 7 and 11, respectively, then the period of F(x)=f(x)g(x/5)-g(x)f(x/3) is
Answer» 177 222 433 1155 Answer :D

Discussion

2344.	Find bcos ^(2) ""( C ) /(2)+ ccos ^(2)"" ( B ) /(2 )
Answer» ANSWER :` s`

Discussion

2345.	Find the derivative of the w.r.t.x (x cos x )/( sqrt (1+ x ^(2)))
Answer» Answer :`(cos X - x(1+ x ^(2)) SIN x )/( (1 + x ^(2) ) ^(3//2))`

Discussion

2346.	If the sum of distances of a moving point from the points (ae, 0) and (-ae, 0) is 2a, then find the locus of the point. It is given than b^(2)=a^(2)(1-e^(2)).
Answer» ANSWER :`(X^(2))/(a^(2))+(y^(2))/(B^(2))=1`

Discussion

2347.	Prove thatcos ^(2) x + cos ^(2) (x + (pi)/(3) + cos ^(2) (x - (pi)/(3)) = 3/2.
Answer» ANSWER :`3/2=R.H.S.`

Discussion

2348.	If a: b: c = 2 :sqrt 6 : ( sqrt3+ 1 )" then "angle C =
Answer» `45 ^(@) ` ` 60 ^(@) ` ` 75 ^(@) ` ` 90 ^(@) ` ANSWER :C

Discussion

2349.	A geometrical progression of positive terms and an arithmetical progression have the same first term. The sum of their first terms is 1 , the sum of their second terms is (1)/(2) and the sum of their third terms is 2. Calculate the sum of their fourth terms.
Answer» ANSWER :`9 (1)/(2)`

Discussion

2350.	If ((1-i)/(1-i))^(3)-((1-i)/(1+i^(3)))=x+iy, then (x,y).
Answer» ANSWER :`(0,-2)`

Discussion

Explore topic-wise InterviewSolutions in .

The mid-point of the sides of a triangle are (1, 5, -1), (0, 4, -2) and (2, 3, 4). Find its vertices. Also find the centriod of the triangle.

The remaninder obtained when 1!+2!+3!+……..+11! is divided by 12 is:

Let A(6,7), B(2,3), C(-2,1) vertices of a triangle. The point P in the interior of DeltaABC " such that " Delta PBC

A and B are mutually exclusive events. P(A)=0.28, P(B)=0.38, then find (i) P(AuuB), (ii) P(AnnB), (iii) P(AnnB'), (iv) P(A'nnB')

State true of false for the following: For any complex number, z, the minimum value of |z|+|z-1| is 1.

((a^(2) - b^(2) sin A sin B) /( 2 sin ( A- B)))

Define hyperbola as a set of points derive its equation in the form(x^(2))/( a^(2))-( y^(2))/( b^(2)) =1

Find the equation of the circle which touches X - axis and whose centre is (1,2).

Write each of the following statements in the form ''if-then'' You get a job implies that your credentials are good.

Two equilateral triangles are constructed from a line segment of length L. If M and m are the maximum and minimum values of the sum of the areas of two plane figures, then the value of M/m is.

The plane is perpendicular to the line x/1 =y/1 = (z)/(r ^(2)) passes through the origin and the point (-4, 3, 1) if r is equal to

If log(sqrt(5)+2)=sinh^(-1)(k) then k =

a^(2) sin 2B+ b^(2)sin 2A =

Evaluate lim_(x rarr a) (cos x - cos a)/(sqrtx - sqrta)

Iff (x) = ( x sin 5 x)/(tan 2x tan 7x), x in 0 , f (0) = 5/9then at x = 0f(x) is

Using Mathemtical induction, show that for any natural number n, (1)/(1.2)+(1)/(2.3)+(1)/(3.4)+...+(1)/(n(n+1))=(n)/(n+1)

Solve tan2x=-cot(x+(pi)/(3)).

Find deltay and dy for the following functions y=(1)/(x+2),x=8 and deltax=0.02

If y=1+x+(x^(2))/(2!)+(x^(2))/(3!)+……+(x^(n))/(n!) then (dy)/(dx)=…………

For the following, using median, calculate mean deviation and coefficient of mean deviation.

For the following, using median, calculate mean deviation and coefficient of mean deviation.

Solve : tan ((pi)/(4)+ theta) + tan ((pi)/(4) - theta) = 4

The number of values of x for which sin^(-1)(x^(2)-x^(4)/3+x^(6)/9…..)+cos^(-1)(x^(4)-x^(8)/3+x^(12)/9….)=pi/2," where "0 le abs(x) lt sqrt(3), is

The value ofcos ( 35^(@) + A)cos ( 35^(@) - B) + sin ( 35^(@) +A)sin ( 35^(@) - B) is equal to(i) sin(A+ B)(ii) sin(A - B)(iii) cos (A+B)(iv) cos(A-B)

The slope of angular bisector of line (ax+by)^2=c(bx-ay)^2,(cgto) are

Find the derivative of f (x) w.r.t. g(x) for the f (x) = Sec ^(-1) ((1)/( 2 x ^(2) - 1 )) , g (x) = sqrt(1- x ^(2))

Coordinate planes divide the space into _____ octants.

The smallest value of 'theta' satisfying there equation sqrt(3)(tan theta+cot theta)=4 is

IF alpha,beta,gamma are the lengths of the altitudes of Delta ABC, then 1/alpha+1/beta-1/gamma-(2ab)/((a+b+c)Delta)cos^2""C/2=

Consider the points A (1,2) and B (2,3) Let P and Q be the points of trisection of the segment joining A and B Find the co-ordinates of P and Q

Consider the points A (1,2) and B (2,3) Let P and Q be the points of trisection of the segment joining A and B Find the equation of the line passing through Q and perpendicular to AB

Consider the points A (1,2) and B (2,3) Let P and Q be the points of trisection of the segment joining A and B Find the equation of the line passing through P and perpendicular to AB

Delta ABC is not a right angled and is inscribed in a fixed circle. If a,A,b,B be slightly varied keeping c,C fixed then (deltaa)/(cosA)+(deltab)/(cosB)=

If 2/(1!9!)+2/(3!7!)+2/(5!5!)=2^m/(n!), then orthocentre of the triangle have having sides x-y+=0,x+y+3 and 2x+5y-2=0 is

Statement I: The points (a,0),(0,b) and (1,1) will be collinear if 1/a+1/b=1 Statement II: If 4a^(2)+9b^(2)-c^(2)+12ab=0, then the family of lines ax+by+c=0 is either concurrent at (2,3) or at (-2,-3). Then which of the followng is true

A tree stands vertically on the slant of the hills From a point A on the ground 35 meters. Down the hill from the base of the tree , the angle of elevation of the top of the tree is 60 ^(@) . If the angle of elevation of the foot of the tree A is 15 ^(@) , then the height of the tree.

Let a,b,c and d be non-zero numbers. If the point of intersection of the lines 4ax+2ay+c=0 and 5bx+2by+d=0 lies in the fourth quadrant and is equidistant from the two axes then

P is a point on the line y=2x+1, and Q and R are tow points on the line 3y+6x=6 such that triangle PQR is an equailateral triangle. The length of the side of the triangle is

One root of theequation ax^(2)-3x+1=0 is (2+i).Find the value of 'a' when a is not real.

If x,y,z , t gt 0 and xyzt=81 then minimum value of x+2y+z+8t is

If (1+tan alpha)(1+tan 4alpha)=2, alpha epsilon(0,(pi)/(6)), then alpha=.

Evaluate the following limits. If f(x)=-sqrt(25-x^(2)) then find Lt_(xto1)(f(x)-f(1))/(x-1)

If f(x) and g(x) are periodic functions with periods 7 and 11, respectively, then the period of F(x)=f(x)g(x/5)-g(x)f(x/3) is

Find bcos ^(2) ""( C ) /(2)+ ccos ^(2)"" ( B ) /(2 )

Find the derivative of the w.r.t.x (x cos x )/( sqrt (1+ x ^(2)))

If the sum of distances of a moving point from the points (ae, 0) and (-ae, 0) is 2a, then find the locus of the point. It is given than b^(2)=a^(2)(1-e^(2)).

Prove thatcos ^(2) x + cos ^(2) (x + (pi)/(3) + cos ^(2) (x - (pi)/(3)) = 3/2.

If a: b: c = 2 :sqrt 6 : ( sqrt3+ 1 )" then "angle C =

A geometrical progression of positive terms and an arithmetical progression have the same first term. The sum of their first terms is 1 , the sum of their second terms is (1)/(2) and the sum of their third terms is 2. Calculate the sum of their fourth terms.

If ((1-i)/(1-i))^(3)-((1-i)/(1+i^(3)))=x+iy, then (x,y).