14949 + Interview Questions in Maths in Class 11 Page 251 InterviewSolution

12501.	Find the angle through which the axes be rotated to remove the xy term from the equation ax^(2)+2hxy+ay^(2) = 0
Answer» ANSWER :`pi/4`

Discussion

12502.	The side of a cube increases at a uniform rate of 0.05cm per sec. Find the rate of increase in (a) the volume (b) the surface area when the side is 10 cm.
Answer» ANSWER :(a) `15 cm^3 (B) 6 cm^2`

Discussion

12503.	cos. (3pi)/(19) + cos . (7pi)/(19) + cos. (12pi)/(19) + cos. (16pi)/(19) =
Answer» 0 1 -1 2 Answer :A

Discussion

12504.	A coin is tossed twice, what is the probability that etleast on tail occurs?
Answer» ANSWER :`3/4`

Discussion

12505.	The number of the solutions of the equation cos(pisqrt(x-4))cos(pisqrt(x))=1 is
Answer» `GT2` 2 1 0 Answer :C

Discussion

12506.	Find the specified term of the expression in each of the following binomials: (iv) Middle term of (x^(4) - (1)/( x^3) )^(11).
Answer» ANSWER :`-462x^(9), 462 x^2`

Discussion

12507.	The locus of a point which is at a distance of 5 unit from (2,1,-3) is
Answer» ANSWER :`X^(2)+y^(2)+Z^(2)-4x-2y+6z-11=0`

Discussion

12508.	If XZ plane divide the join of points (2,3,4) and (1,-1,5) in the ratio lambda:1 then the integer lambda should be equal to
Answer» ANSWER :3

Discussion

12509.	Prove that -(cot (180^(@) + theta) sin (90^(@) - theta) cos (-theta))/(sin (270^(@) + theta) tan(-theta) coses (360^(@) + theta)) = cos^(2) theta cot theta.
Answer» ANSWER :35

Discussion

12510.	If f(x)= \|x+100\| + x^(2), test whether f^()(-100) exist.
Answer» ANSWER :-199

Discussion

12511.	For an event, odds against is 6 : 5. The probability that event does not occur, is
Answer» `(5)/(6)` `(6)/(11)` `(5)/(11)` `(1)/(6)` Answer :B

Discussion

12512.	Assume that 3.52 denotes 3.52222. Express this as a rational fraction.
Answer» SOLUTION :`(317)/90`

Discussion

12513.	The minimum value of 2^(sin x)+2^(cos x) is
Answer» ANSWER :`[-1,0]`

Discussion

12514.	Which of the following statements is true If C = A - B = 60^(@) then the value of (a-b)/(c)= sqrt(3) II If 3tan((A)/(2))tan((C)/(2))=1, then a,b,c are in A.P
Answer» onlyI only II both I and II neither I nor II Answer :B

Discussion

12515.	2x - y gt 1,2y - x gt 1
Answer» SOLUTION :

Discussion

12516.	Obser the following lists {:("List -I","List -II"),((A)"Maximum value of xy subject to x+y =7 is",(1)2),((B)"If"l^(2)+m^(2)=1",""then the maximum value of 1+m is",(2)1),((C)"If"x+y=12",""then the minimum Value of"x^(2)+y^(2)"is",(3)sqrt(2)),((D)"Minimum value" x^(2)-8x+17 "is",(4)49//4),(,(5)0):}
Answer» ` {:(A,B,C,D),(4,3,1,2):}` ` {:(A,B,C,D),(4,3,2,1):}` ` {:(A,B,C,D),(2,3,5,4):}` ` {:(A,B,C,D),(2,3,1,4):}` ANSWER :A

Discussion

12517.	If \|z_(1)\|=\|z_(2)\|, is the necessary that z_(1)=z_(2)
Answer» ANSWER :`Z_(1)=z_(2)`

Discussion

12518.	Write the following sets in the roaster form. B= {x \|x^(2)= x, x in R}
Answer» ANSWER :`X= 0, 1`

Discussion

12519.	If f(x)={{:(\|x\|,"if", 0 lt \|x\| le2),(1,"if", x=0):} then at x=0 has
Answer» LOCAL maximum local minimum no EXTREME value not determined Answer :A

Discussion

12520.	sqrt(2+sqrt(2+2cos4theta))= …………
Answer» `COSTHETA` `SINTHETA` `2costheta` `2sintheta` ANSWER :C

Discussion

12521.	A book contains 100 pages . A page is chosen at random . Whatis thechance that the sum of digits on the page is equal to 9 ?
Answer» ANSWER :`(10)/(100),i.e,(1)/(10)`

Discussion

12522.	Find the mean deviation about the mean for the following data.
Answer» ANSWER :10

Discussion

12523.	If a_(1),a_(2),a_(3),...a_(n) are in A.P. with common difference d, then tan[tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a_(2)a_(3)))+,....+tan^(-1)((d)/(1+a_(n-1)a_(n)))]=
Answer» `((N-1)d)/(a_(1)+a_(n))` `((n-1)d)/(1+a_(1)a_(n))` `(ND)/(1+a_(1)a_(n))` `(a_(n)-a_(1))/(a_(n)+a_(1))` ANSWER :B

Discussion

12524.	"Cosh"^(4)(x)-"Sinh"^(4)(x)=
Answer» COSH(X) cosh(2X) SINH(x) sinh(2x) ANSWER :B

Discussion

12525.	If arg (z) lt 0 then arg(-z)-arg(z)=.....
Answer» `PI` `-pi` `-(pi)/(2)` `(pi)/(2)` ANSWER :A

Discussion

12526.	Find distance between following pair of points : (2, -1, 3) and (-2, 1, 3)
Answer» ANSWER :`2SQRT5` UNIT

Discussion

12527.	Find the point of intersectoon of the lines vec(AB) and vec(CD) where A(7,-6,1), B(17,-18,-3), C(1,4,-5) and D=(3,-4,11).
Answer» ANSWER :(2,0,3)

Discussion

12528.	Find the equation fo the ellipse with its centre at (1, 2) focus at (6, 2) and containing the point (4, 6).
Answer» ANSWER :`(x-1)^(2)/45+(y-2)^(2)/20=1`

Discussion

12529.	The point on the line 3x+4y=5 which is equidistant from (1, 2) and (3, 4) is :
Answer» `(7,-4)` `(1//7,8//7)` `(0,5//4)` `(15,-10)` ANSWER :D

Discussion

12530.	Iff(x) = {{:(1 - sqrt(2 sinx)/(pi - 4r ) " if" x ne (pi)/(4)),(a "if" x = (pi)/(4)):} continuous at (pi)/(4) then a =
Answer» 4 2 1 `1//4` ANSWER :D

Discussion

12531.	Let h_(a),h_(b) be the lengths of altitude from A and B respectively. If a ge h_(a), b le h_(b) and c=4then area of Delta^("le")ABC is
Answer» 1 2 3 4 Answer :D

Discussion

12532.	A straight line L through the origin meet the lines x+y=1 and x+y=3 at P and Q, respectively. Lines L_1 and L_2 " are drawn , parallel to 2x-y=5 and 3x=y=5 respectively lines "L_1 and L_2 intersect at R.Then that the locus of R, as L varies, is a staright line.
Answer» x-3y+5=0 x+3y+5=0 x+3y-5=0 x-3y+-5=0 Answer :A

Discussion

12533.	A farmer buys a used tractor for Rs. 12,000. He pays Rs. 6000 cash and agrees to pay the balance in 12 annual instalments of Rs. 500 plus 12% interest on the unpaid amount. Write the annual instalments as an A.P
Answer» SOLUTION :1220,1160,1100,….

Discussion

12534.	A farmer buys a used tractor for Rs. 12,000. He pays Rs. 6000 cash and agrees to pay the balance in 12 annual instalments of Rs. 500 plus 12% interest on the unpaid amount How mush will the tracter cost the farmer?
Answer» SOLUTION :RS. 16,680]

Discussion

12535.	Find the multiplicative inverse of 4-3i.
Answer» ANSWER :`(4+3i)/(25)`

Discussion

12536.	The term of the termindependent of x inthe expansion of (sqrt(x/3)+3/(2x^(2)))^(10)" is " ..........
Answer» ANSWER :` :. " CONSTANT TERM " = 5/4`

Discussion

12537.	If the circlesx^(2)+y^(2)+2ax+c=0andx^(2)+y^(2)+aby+c=0 touch each other then show that (1)/(a^(2)),(1)/(2c),(1)/(b^(2)) are in A.P.
Answer»

Discussion

12538.	Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive X-axis. (i) x - sqrt 3y + 8 = 0, (ii) y - 2 = 0 ,(iii) 3t + 2 = 0 .
Answer» Answer :`(i)X cos 120^(@) + y sin 120^(@) = 4, 4 , 120^(@) (ii) x cos 90^(@) + y sin 90^(@) = 2,2, 90^(@) ; ` (iii) ` x cos 315^(@) + y sin 315^(@) = 2 SQRT2 , 2 sqrt2 , 315^(@)`.

Discussion

12539.	Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : {x : x is an even natural number} . . .{x : x is an integer}
Answer» ANSWER :`⊂`

Discussion

12540.	4 cards are drawn from a well - shuffled deck of 52 cards. What is the probability of obtaining 3 dimonds and one speak?
Answer» Answer :`(""^(13)C_(3).""^(13)C_(1))/(""^(52)C_(4))`

Discussion

12541.	L : 3x + 2y-7 =0 (1) Reduce the above equation in slope intercept from. Find their slope and y -intercept. (2) Reduce the equation into intercept from. Find their intercepts on axis. (3) Reduce the equation in normal form and find perpendicular distance from origin and measure of an angle made by perpendicular with positive side of X -axis.
Answer» Answer :`y=-(3)/(2) x + (7)/(2) , - (3)/(2) ,(7)/(2). ""(x)/( (7)/(3) )+ ( y)/( (7)/(2) ) =1, (7)/(3) , (7)/(2) "" (3)/( sqrt(13))x + (2)/( sqrt(13) ) y = ( 7)/( sqrt(13) ) , ( 7)/( sqrt(13) ) TAN^(-1) ""((2)/(3))`

Discussion

12542.	Show that the point whose distance from Y-axis in thrice its distance from (1,2,-1) satisfies the equation 8x^(2)+9y^(2)+8z^(2)-18x-36y+18z+54=0.
Answer» 54 45 24 42 Answer :A

Discussion

12543.	What is the probability that there are 53 Sunday in a leap year ?
Answer» ANSWER :`=(2)/(7)`.

Discussion

12544.	The volume of the triangular pyramid with vertices A(2, 2, 2), B(4, 3, 3), C(4, 5, 4), D(5, 5, 6) is .... (in cu. units)
Answer» 7 `7/2` `7/3` `7/6` ANSWER :D

Discussion

12545.	The normal to the curve x^(2)+2xy-3y^2=0 at (1,1)
Answer» Does not meet the curve again MEETS the curve again in the SECOND quadrant Meets the curve again in the THIRD quadrant Meets the curve again in the foruth quadrant Answer :D

Discussion

12546.	A box contains 25 tickets numbered 1 to 25 Two tickets are drawn at random . Whatis the probability that the product of the numbers is even ?
Answer» ANSWER :`(37)/(50)`

Discussion

12547.	The Stationary points of8x^(2)-x^(4)-4are
Answer» `(0,-4),(2,12),(-2,12)` `(1,2)` `(1,12)` `(1,1)` ANSWER :A

Discussion

12548.	Thevalueof aforwhichthe sumof thesquaresof therootsof theequationx^2 -(a-2)x-a-1=0assumetheleastvalueis
Answer» 1 0 3 2 Answer :A

Discussion

12549.	Find the range of the following functions given by f(x)= 1 + 3 cos 2x
Answer» ANSWER :`[-2, 4]`

Discussion

12550.	Find the domain and range of the following function f(x)= (x^(2)-1)/(x-1)
Answer» ANSWER :Domain `R- {1}` RANGE `R- {2}`

Discussion

Explore topic-wise InterviewSolutions in .

Find the angle through which the axes be rotated to remove the xy term from the equation ax^(2)+2hxy+ay^(2) = 0

The side of a cube increases at a uniform rate of 0.05cm per sec. Find the rate of increase in (a) the volume (b) the surface area when the side is 10 cm.

cos. (3pi)/(19) + cos . (7pi)/(19) + cos. (12pi)/(19) + cos. (16pi)/(19) =

A coin is tossed twice, what is the probability that etleast on tail occurs?

The number of the solutions of the equation cos(pisqrt(x-4))cos(pisqrt(x))=1 is

Find the specified term of the expression in each of the following binomials: (iv) Middle term of (x^(4) - (1)/( x^3) )^(11).

The locus of a point which is at a distance of 5 unit from (2,1,-3) is

If XZ plane divide the join of points (2,3,4) and (1,-1,5) in the ratio lambda:1 then the integer lambda should be equal to

Prove that -(cot (180^(@) + theta) sin (90^(@) - theta) cos (-theta))/(sin (270^(@) + theta) tan(-theta) coses (360^(@) + theta)) = cos^(2) theta cot theta.

If f(x)= |x+100| + x^(2), test whether f^()(-100) exist.

For an event, odds against is 6 : 5. The probability that event does not occur, is

Assume that 3.52 denotes 3.52222. Express this as a rational fraction.

The minimum value of 2^(sin x)+2^(cos x) is

Which of the following statements is true If C = A - B = 60^(@) then the value of (a-b)/(c)= sqrt(3) II If 3tan((A)/(2))tan((C)/(2))=1, then a,b,c are in A.P

2x - y gt 1,2y - x gt 1

Obser the following lists {:("List -I","List -II"),((A)"Maximum value of xy subject to x+y =7 is",(1)2),((B)"If"l^(2)+m^(2)=1",""then the maximum value of 1+m is",(2)1),((C)"If"x+y=12",""then the minimum Value of"x^(2)+y^(2)"is",(3)sqrt(2)),((D)"Minimum value" x^(2)-8x+17 "is",(4)49//4),(,(5)0):}

If |z_(1)|=|z_(2)|, is the necessary that z_(1)=z_(2)

Write the following sets in the roaster form. B= {x |x^(2)= x, x in R}

If f(x)={{:(|x|,"if", 0 lt |x| le2),(1,"if", x=0):} then at x=0 has

sqrt(2+sqrt(2+2cos4theta))= …………

A book contains 100 pages . A page is chosen at random . Whatis thechance that the sum of digits on the page is equal to 9 ?

Find the mean deviation about the mean for the following data.

If a_(1),a_(2),a_(3),...a_(n) are in A.P. with common difference d, then tan[tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a_(2)a_(3)))+,....+tan^(-1)((d)/(1+a_(n-1)a_(n)))]=

"Cosh"^(4)(x)-"Sinh"^(4)(x)=

If arg (z) lt 0 then arg(-z)-arg(z)=.....

Find distance between following pair of points : (2, -1, 3) and (-2, 1, 3)

Find the point of intersectoon of the lines vec(AB) and vec(CD) where A(7,-6,1), B(17,-18,-3), C(1,4,-5) and D=(3,-4,11).

Find the equation fo the ellipse with its centre at (1, 2) focus at (6, 2) and containing the point (4, 6).

The point on the line 3x+4y=5 which is equidistant from (1, 2) and (3, 4) is :

Iff(x) = {{:(1 - sqrt(2 sinx)/(pi - 4r ) " if" x ne (pi)/(4)),(a "if" x = (pi)/(4)):} continuous at (pi)/(4) then a =

Let h_(a),h_(b) be the lengths of altitude from A and B respectively. If a ge h_(a), b le h_(b) and c=4then area of Delta^("le")ABC is

A straight line L through the origin meet the lines x+y=1 and x+y=3 at P and Q, respectively. Lines L_1 and L_2 " are drawn , parallel to 2x-y=5 and 3x=y=5 respectively lines "L_1 and L_2 intersect at R.Then that the locus of R, as L varies, is a staright line.

A farmer buys a used tractor for Rs. 12,000. He pays Rs. 6000 cash and agrees to pay the balance in 12 annual instalments of Rs. 500 plus 12% interest on the unpaid amount. Write the annual instalments as an A.P

A farmer buys a used tractor for Rs. 12,000. He pays Rs. 6000 cash and agrees to pay the balance in 12 annual instalments of Rs. 500 plus 12% interest on the unpaid amount How mush will the tracter cost the farmer?

Find the multiplicative inverse of 4-3i.

The term of the termindependent of x inthe expansion of (sqrt(x/3)+3/(2x^(2)))^(10)" is " ..........

If the circlesx^(2)+y^(2)+2ax+c=0andx^(2)+y^(2)+aby+c=0 touch each other then show that (1)/(a^(2)),(1)/(2c),(1)/(b^(2)) are in A.P.

Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive X-axis. (i) x - sqrt 3y + 8 = 0, (ii) y - 2 = 0 ,(iii) 3t + 2 = 0 .

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : {x : x is an even natural number} . . .{x : x is an integer}

4 cards are drawn from a well - shuffled deck of 52 cards. What is the probability of obtaining 3 dimonds and one speak?

Show that the point whose distance from Y-axis in thrice its distance from (1,2,-1) satisfies the equation 8x^(2)+9y^(2)+8z^(2)-18x-36y+18z+54=0.

What is the probability that there are 53 Sunday in a leap year ?

The volume of the triangular pyramid with vertices A(2, 2, 2), B(4, 3, 3), C(4, 5, 4), D(5, 5, 6) is .... (in cu. units)

The normal to the curve x^(2)+2xy-3y^2=0 at (1,1)

A box contains 25 tickets numbered 1 to 25 Two tickets are drawn at random . Whatis the probability that the product of the numbers is even ?

The Stationary points of8x^(2)-x^(4)-4are

Thevalueof aforwhichthe sumof thesquaresof therootsof theequationx^2 -(a-2)x-a-1=0assumetheleastvalueis

Find the range of the following functions given by f(x)= 1 + 3 cos 2x

Find the domain and range of the following function f(x)= (x^(2)-1)/(x-1)