14949 + Interview Questions in Maths in Class 11 Page 82 InterviewSolution

4051.	underset(x to oo)(Lt)(""^(7)sqrt(x^(7)-1)+""^(5)sqrt(x^(5)+2)+""^(9)sqrt(x^(9)-2))/(""^(6)sqrt(x^(6)+1)+""^(7)sqrt(x^(7)+1)-""^(4)sqrt(x^(4)+2))=
Answer» 3 `-3` `(1)/(3)` `(-1)/(3)` ANSWER :A

Discussion

4052.	The value of arg(x), when x lt 0 is
Answer» 0 `(PI)/(2)` `pi` None of these Answer :C

Discussion

4053.	If xy+yz+zx=1, " then " (x)/( 1+x^(2))+(y)/(1+y^2)+(z)/(1+z^(2))=
Answer» `(2)/(sqrt ((1 + X ^(2)) (1- y ^(2)) (1-z ^(2))))` `(2)/(sqrt ((1 - x ^(2)) (1+y ^(2)) (1-z ^(2))))` `(2)/(sqrt ((1 + x ^(2)) (1+ y ^(2)) (1+z ^(2))))` `(2)/(sqrt ((1 - x ^(2)) (1+ y ^(2)) (1+z ^(2))))` ANSWER :C

Discussion

4054.	State the equation of the line which has the y-intercept -3 and slope -4
Answer» ANSWER : `y=-4x-3`

Discussion

4055.	A question papers has 12 questions consistingPart A having 8 questions and the rest inPart B. A student has to answer the questions from each Part. In how many ways one canselect the questions.
Answer» ANSWER :84

Discussion

4056.	State the conditions under which the equation lx^(2)+2mxy+2px+2qy+r=0 represents a pair of lines
Answer» ANSWER :`2pqm-lq^(2)-RM^(2)=0 & p^(2) ge rl`

Discussion

4057.	If a sin b= cos x =(2c tan x)/(1-tan^(2) x) "then" ((a^(2)-b^(2))^(2))/(a^(2)+b^(2))=
Answer» `C^(2)` `2c^(2)` `4C^(2)` `8C^(2)` ANSWER :C

Discussion

4058.	The longest distance of the point (a,0) from the curve 2x^(2)+y2-2x=0 , is given by
Answer» `SQRT(1-2a+a^(2))` `sqrt(1+2a+2a^(2))` `sqrt(1+2a-a^(2))` `sqrt(1-2a+2a^(2))` ANSWER :D

Discussion

4059.	The transformed equation of x^(2) - y^(2) + 2x + 4y = 0 when the origin is shifted to the point (-1, 2) is
Answer» `X^(2) + Y^(2) = 1` `X^(2) + 3Y^(2) = 1` `X^(2) - Y^(2) + 3 = 0` `4X^(2) + 9Y^(2) = 36` Answer :C

Discussion

4060.	f(x) and g(x) are two differentiable functions on [0,2], such that f^('')(x) - g^('') (x) = 0,f' (1) = 4,g'(1) = 2, f(2) = 9, g(2) = 3, then f(x) = g(x) at x = 3//2 is
Answer» `0` `2` `10` `5` ANSWER :D

Discussion

4061.	If A be a matrix of rank r. Then rank of A^(T) is
Answer» R `r-1` `r+1` 0 Answer :A

Discussion

4062.	Find the sum 1+ (1^(3) + 2^(3))/(2) + (1^(3) + 2^(3) + 3^(3))/(3) + …….(1^(3) + 2^(3) + 3^(3) + …..+ 20^(3))/(20)
Answer» ANSWER :`(25025)/(2)`

Discussion

4063.	Evaluate Lt_(x to 3) (x^4 - 81)/(2x^2 - 5x - 3)
Answer» ANSWER :`108/7`

Discussion

4064.	A person standing at the junction (crossing) of two straight paths represented by the equations 2x-3y+4=0 and 3x + 4y-5=0 wants to reach the path whose equation is 6x-7y+8=0 in the least time. Find equation of the path that he should follow.
Answer» ANSWER :Hence equation of path FOLLOWS by person is `119x + 102y = 125`.

Discussion

4065.	Evaluate Lim_(xto0) ((1+x)^(6)-1)/((1+x)^(2)-1)
Answer» ANSWER :3

Discussion

4066.	If the locus of a point which is equidistant form (2,3,-1) and (-3,4,-3) is ax+by+cz=d and agt 0 then a+b+c+d =
Answer» -4 4 16 -2 Answer :A

Discussion

4067.	If y = sqrt(cos x^2 + sqrt(cos x^2 + sqrt(cos x^2 + ....oo))), then (dy)/(dx) is equal to
Answer» `(- SIN X)/(2y - 1)` `(-2 x sin x^2)/(2y - 1)` `(-sin x^2)/(x(2y - 1))` `(COS x^2)/(2y)` Answer :B

Discussion

4068.	Ifx = log [ cot (pi/4 + theta )] then sinh x =
Answer» `tan 2 THETA` `COT 2 theta` `- tan 2 theta` `-cot 2 theta` Answer :C

Discussion

4069.	Evaluate Lt_(x to pi/4)cotx.
Answer» ANSWER :1

Discussion

4070.	Observe the following Columns.
Answer» ANSWER :A::B::C::D

Discussion

4071.	A particle 'p' moves along a straight line away from a point 'O' obeying the relation S = 16 + 48t - t^(3). The direction of 'P' after t = 4 is
Answer» `VEC(OP)` `vec(PO)` Rest at the INSTANT Perpendicular to `vec(OP)`. Answer :B

Discussion

4072.	The weight of the commodity milk given that Price in base year = Rs. 1.50 Price is current year = Rs. 1.75, Quantity consumed in base year = 10 litres
Answer» 40 15 17.5 11.5 Answer :B

Discussion

4073.	A line OA length r starts from its initial position OX and traces an angle AOB = alpha in the anticlockwise direction. It then traces back in the clockwise direction an angle BOC = 3 theta ( where alpha gt 3 theta ) . L is the foot of the the perpendicular from C on OA. (sin^3 theta)/(CL) = (cos^3 theta)/(OL ) = 1 (2rsin alpha)/(1+2rcos alpha)is equal to
Answer» `TAN^2 THETA` `COT^2 theta` `cot 2 theta` `tan 2 theta` ANSWER :D

Discussion

4074.	Express (2x+1)! in terms of(2x-1)!,(x+2)! in terms of(x-1)!.Hence, solve the equation ((2x+1)!)/((x+2)!)xx((x-1)!)/((2x-1)!)=3/5
Answer» SOLUTION :`(X+1)!=(2X+1)(2x)(2x-1)!,(x+2)! =(x+2)(x+1)x(x-1)!,x=4`

Discussion

4075.	If sin theta + cos theta = sqrt(2) cos A " then " theta =
Answer» `2 n pi + (pi)/(3) PM A, AA n in Z ` `2 n pi + (pi)/(2) pm A, AA n in Z ` `2 n pi + (pi)/(4) pm A, AA n in Z ` `2 n pi + (pi)/(6) pm A, AA n in Z ` ANSWER :C

Discussion

4076.	f(x) = {{:(a tan^(-1) ((1)/(x-4)) " if " 0 le x lt 4),(btan^(-1) ((2)/(x-4)) " if " 4 lt x lt 6),(sin^(-1) (7-x) + 0 (pi)/(4)" if " 6 le x le 8):}andf(4) = pi //2 is continuous on [0,8] then (a,b) =
Answer» (1,1) (1,-1) (-1,1) (-1,-1) ANSWER :C

Discussion

4077.	If A is the A.M. between a and b, then find (A-a)^(2)+(A-b)^(2).
Answer» ANSWER :`1/2(a-b)^(2)`

Discussion

4078.	Find the distance of a point (2,5,-3) from the planer r.(6i-3j+2k)=4
Answer» ANSWER :`(13)/7`

Discussion

4079.	The value of a third order determinant is 11 then the value of the square of the determinant formed by the cofactors is
Answer» 121 `(121)^(2)` `(121)^(3)` `(121)^(4)` ANSWER :B

Discussion

4080.	Let f:R rarr R is defined by f(x)=2x^(3)+2x^(2)+300x+5 sin x, then f is
Answer» ONE-one onto one-one into many one onto many one into Answer :A

Discussion

4081.	The periodof 3sin^(6) x + 5cos^(4) xis
Answer» `PI` `(pi)/(2 )` `(3pi)/(2)` `2PI` Answer :1

Discussion

4082.	If tan theta = 5 a - (1)/(20a)then sec theta + tan theta =
Answer» 10A (or) `(1)/(10a)` `(1)/(10a)` (or) -10a `- (1)/(10a)` (or) -10a 10a (or) `- (1)/(10a)` ANSWER :D

Discussion

4083.	Does Lim_(x to 0 ) f(x) exist if f(x) = {:{(x," when "x lt 0 ),(0 ," when " x = 0 ),(x^(2)," when " x gt 0):}
Answer» ANSWER :YES 0

Discussion

4084.	Three cards are drawn fromadeck of 52 cards . Whatis the probability thatall of them are aces ?
Answer» ANSWER :`(""^(4)C_(3))/(""^(52)C_(3))=(1)/(5525)`

Discussion

4085.	Assertion: If a and b are distinct integers then(a - b) is a factor of a^(n) - b^(n):Reason(R): a^(n)=[(a-b)+b]^(n)
Answer» ANSWER :B

Discussion

4086.	Find the constant term of (3x^(2)-1/(2x^(3)))^(10)
Answer» ANSWER :`(76545)/8`

Discussion

4087.	The angle of rotation of axes to remove xy terms in the equation 3x^(2) - 2 sqrt(3) xy + 9y^(2) = 10 is
Answer» ANSWER :`(PI)/(6)`

Discussion

4088.	If incircle of radius 4 of a triangle ABC touches the sides BC, CA, AB at D,E,F such thar BD, CE, AF are consecutive number then
Answer» `BC=15` `AC=14` `AB=13` Altitude from A to the BC is `(56)/(5)` ANSWER :A::B::C::D

Discussion

4089.	The ratio in which yz-plane divides the line segment joining (-3,4,2 ), (2,1,3 ) is
Answer» `-4:1` `3:2` `-2:3` `1:4` ANSWER :B

Discussion

4090.	If bar(a), bar(b), bar(c )respresents the vertices A, B, and C respectively of DeltaABC then prove that \|(bar(a) xx bar(b)) + (bar(b) xx bar(c ))+ (bar(c ) xx bar(a))\| is twice the area of DeltaABC.
Answer» ANSWER :1

Discussion

4091.	If sin 2 theta = cos 3 theta and theta is an acute angle, then sin theta equals
Answer» `(sqrt5-1)/4` `-((sqrt5-1)/4)` `(sqrt5+1)/4` `(-sqrt5+1)/4` ANSWER :A

Discussion

4092.	Solve the following equations and write general solutions 2 + sqrt(3) Sec x - 4 Cos x = 2sqrt(3)
Answer» Answer :`2npi pm (pi)/(3)` or `2npi pm(5PI)/(6), N in Z`

Discussion

4093.	Observe the following lists : Match List-I to List-II :
Answer» `{:(UL"A",ul"B",ul"C"),(3,2,1):}` `{:(ul"A",ul"B",ul"C"),(2,1,3):}` `{:(ul"A",ul"B",ul"C"),(2,3,1):}` `{:(ul"A",ul"B",ul"C"),(3,1,2):}` ANSWER :D

Discussion

4094.	Transform the following equations into a. Slope intercpetform b. Intercept form c. Normal form sqrt(3)x+y=4
Answer» ANSWER :a. `y=-sqrt(3)X+4;` B. `x/((4/(sqrt(3))))+y/4=1` c. `x cos pi //6+ysin pi//6=2`

Discussion

4095.	Find the number of points wheref(x) = [sin x + cos x] , x in [0,2 pi] is not continous . ([.] denotes the greatest integer function ).
Answer» Answer :6 points, `X=(pi)/(2),(3pi)/(4),pi(3pi)/(2),(7pi)/(4),2PI`.

Discussion

4096.	Transform the following equations into a. Slope intercpetform b. Intercept form c. Normal form sqrt(3)x+y+10=0
Answer» ANSWER :a. `y=-sqrt(3)x-10;` b. `x/((-10/(sqrt(3))))+y/(-10)=1` c. `x"COS"(7pi)/6+y"SIN"(7pi)/6=5`

Discussion

4097.	Find the principal solutions of the equation sin x = (sqrt3)/(2).
Answer» ANSWER :`X = PI /3 and (2PI)/(3).`

Discussion

4098.	Given that alpha and beta are the roots of the equation x^(2)-x+7=0, find (i) The numerical value of (alpha)/(beta+3)+(beta)/(alpha+3), (ii) an equation whose roots are (alpha)/(beta+3) and (beta)/(alpha+3).
Answer» ANSWER :(i) `(-10)/(19)` (II) `19x^(2)+10x+7=0`.

Discussion

4099.	(i) Find the equation of a circle which touches both the axes and whose centre is (2,2). (ii) Find the equation of a circle, touching the lines x=0, y=0 and x=6.
Answer» ANSWER :`X^(2)+y^(2)-4x-4y+4=0`

Discussion

4100.	The values of theta satisfying sin 5theta = sin 3theta-sin theta and 0 lt theta lt (pi)/(2) are
Answer» `pi//6, pi//3` `pi//6, pi//4` `pi//4, pi//3` `pi//4, pi//2` ANSWER :A

Discussion

Explore topic-wise InterviewSolutions in .

underset(x to oo)(Lt)(""^(7)sqrt(x^(7)-1)+""^(5)sqrt(x^(5)+2)+""^(9)sqrt(x^(9)-2))/(""^(6)sqrt(x^(6)+1)+""^(7)sqrt(x^(7)+1)-""^(4)sqrt(x^(4)+2))=

The value of arg(x), when x lt 0 is

If xy+yz+zx=1, " then " (x)/( 1+x^(2))+(y)/(1+y^2)+(z)/(1+z^(2))=

State the equation of the line which has the y-intercept -3 and slope -4

A question papers has 12 questions consistingPart A having 8 questions and the rest inPart B. A student has to answer the questions from each Part. In how many ways one canselect the questions.

State the conditions under which the equation lx^(2)+2mxy+2px+2qy+r=0 represents a pair of lines

If a sin b= cos x =(2c tan x)/(1-tan^(2) x) "then" ((a^(2)-b^(2))^(2))/(a^(2)+b^(2))=

The longest distance of the point (a,0) from the curve 2x^(2)+y2-2x=0 , is given by

The transformed equation of x^(2) - y^(2) + 2x + 4y = 0 when the origin is shifted to the point (-1, 2) is

f(x) and g(x) are two differentiable functions on [0,2], such that f^('')(x) - g^('') (x) = 0,f' (1) = 4,g'(1) = 2, f(2) = 9, g(2) = 3, then f(x) = g(x) at x = 3//2 is

If A be a matrix of rank r. Then rank of A^(T) is

Find the sum 1+ (1^(3) + 2^(3))/(2) + (1^(3) + 2^(3) + 3^(3))/(3) + …….(1^(3) + 2^(3) + 3^(3) + …..+ 20^(3))/(20)

Evaluate Lt_(x to 3) (x^4 - 81)/(2x^2 - 5x - 3)

A person standing at the junction (crossing) of two straight paths represented by the equations 2x-3y+4=0 and 3x + 4y-5=0 wants to reach the path whose equation is 6x-7y+8=0 in the least time. Find equation of the path that he should follow.

Evaluate Lim_(xto0) ((1+x)^(6)-1)/((1+x)^(2)-1)

If the locus of a point which is equidistant form (2,3,-1) and (-3,4,-3) is ax+by+cz=d and agt 0 then a+b+c+d =

If y = sqrt(cos x^2 + sqrt(cos x^2 + sqrt(cos x^2 + ....oo))), then (dy)/(dx) is equal to

Ifx = log [ cot (pi/4 + theta )] then sinh x =

Evaluate Lt_(x to pi/4)cotx.

Observe the following Columns.

A particle 'p' moves along a straight line away from a point 'O' obeying the relation S = 16 + 48t - t^(3). The direction of 'P' after t = 4 is

The weight of the commodity milk given that Price in base year = Rs. 1.50 Price is current year = Rs. 1.75, Quantity consumed in base year = 10 litres

Express (2x+1)! in terms of(2x-1)!,(x+2)! in terms of(x-1)!.Hence, solve the equation ((2x+1)!)/((x+2)!)xx((x-1)!)/((2x-1)!)=3/5

If sin theta + cos theta = sqrt(2) cos A " then " theta =

f(x) = {{:(a tan^(-1) ((1)/(x-4)) " if " 0 le x lt 4),(btan^(-1) ((2)/(x-4)) " if " 4 lt x lt 6),(sin^(-1) (7-x) + 0 (pi)/(4)" if " 6 le x le 8):}andf(4) = pi //2 is continuous on [0,8] then (a,b) =

If A is the A.M. between a and b, then find (A-a)^(2)+(A-b)^(2).

Find the distance of a point (2,5,-3) from the planer r.(6i-3j+2k)=4

The value of a third order determinant is 11 then the value of the square of the determinant formed by the cofactors is

Let f:R rarr R is defined by f(x)=2x^(3)+2x^(2)+300x+5 sin x, then f is

The periodof 3sin^(6) x + 5cos^(4) xis

If tan theta = 5 a - (1)/(20a)then sec theta + tan theta =

Does Lim_(x to 0 ) f(x) exist if f(x) = {:{(x," when "x lt 0 ),(0 ," when " x = 0 ),(x^(2)," when " x gt 0):}

Three cards are drawn fromadeck of 52 cards . Whatis the probability thatall of them are aces ?

Assertion: If a and b are distinct integers then(a - b) is a factor of a^(n) - b^(n):Reason(R): a^(n)=[(a-b)+b]^(n)

Find the constant term of (3x^(2)-1/(2x^(3)))^(10)

The angle of rotation of axes to remove xy terms in the equation 3x^(2) - 2 sqrt(3) xy + 9y^(2) = 10 is

If incircle of radius 4 of a triangle ABC touches the sides BC, CA, AB at D,E,F such thar BD, CE, AF are consecutive number then

The ratio in which yz-plane divides the line segment joining (-3,4,2 ), (2,1,3 ) is

If bar(a), bar(b), bar(c )respresents the vertices A, B, and C respectively of DeltaABC then prove that |(bar(a) xx bar(b)) + (bar(b) xx bar(c ))+ (bar(c ) xx bar(a))| is twice the area of DeltaABC.

If sin 2 theta = cos 3 theta and theta is an acute angle, then sin theta equals

Solve the following equations and write general solutions 2 + sqrt(3) Sec x - 4 Cos x = 2sqrt(3)

Observe the following lists : Match List-I to List-II :

Transform the following equations into a. Slope intercpetform b. Intercept form c. Normal form sqrt(3)x+y=4

Find the number of points wheref(x) = [sin x + cos x] , x in [0,2 pi] is not continous . ([.] denotes the greatest integer function ).

Transform the following equations into a. Slope intercpetform b. Intercept form c. Normal form sqrt(3)x+y+10=0

Find the principal solutions of the equation sin x = (sqrt3)/(2).

Given that alpha and beta are the roots of the equation x^(2)-x+7=0, find (i) The numerical value of (alpha)/(beta+3)+(beta)/(alpha+3), (ii) an equation whose roots are (alpha)/(beta+3) and (beta)/(alpha+3).

(i) Find the equation of a circle which touches both the axes and whose centre is (2,2). (ii) Find the equation of a circle, touching the lines x=0, y=0 and x=6.

The values of theta satisfying sin 5theta = sin 3theta-sin theta and 0 lt theta lt (pi)/(2) are