14949 + Interview Questions in Maths in Class 11 Page 253 InterviewSolution

12601.	If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term.
Answer» ANSWER :4

Discussion

12602.	If errors of 1% each are made in the base radius and height of a cylinder, the percentage error in its volume is
Answer» 1 2 3 4 Answer :C

Discussion

12603.	Answer the equation: int(1+cos2x)/(sin^(2)x)dx
Answer» ANSWER :`-2[cotx+x]+C`

Discussion

12604.	Observe the following statements. Assertion (A) : The value of tanh^(-1)(2) can be calculated Reason (R ): The domain of tanh^(-1)x is (-1, 1) Then true statement among the following is
Answer» A is true, R is false AIS false, R is true A is false, R is false A is true, R is true, `R rArr A` ANSWER :B

Discussion

12605.	f(x) = {(cos""(pix)/(2),",",x gt 0,),("x + a",",",x le 0,):}. Find the values of a if x = 0 is a point of maxima.
Answer» ANSWER :`a GE 1`

Discussion

12606.	A straightline passes through the fixed point [1/k,1/k]. The sum of the reciprocals of itsintercepts on the coordinate axes is
Answer» `2/K` `k/2` `k` `1/k` ANSWER :C

Discussion

12607.	P_(1) and P_(2) are planes passing through origin, L_(1) and L_(2) are two lines on P_(1) and P_(2) respectivelym such that their intersection is the origin. Show that there exist points, A, B and C , whose perpmutation, A, B' and C' respectively, can be chosen such that (i) A is on L_(1) 'B and P_(1) " put not on " L_(1) and C not on P_(1) , (ii) A is on L_(2) , B' on P_(2) " but not on " L_(2) and C' " not on" P_(2) .
Answer» Solution :Fig A 2.29 shows the possi9ble sitution for PLANES`P_(1) and P_(2)` and the lines `L_(1) and L_(2)` : Now if we choss points A,B and C as A on `L_(1)` B on th3e LINE of interection of ` P_(1) and P_(2)`but other than th3 origin and C on `L_(2)` again other than the origin. then we can consider. a correspondes to one A', B', C' B corresponds to one of the REMAINING of A' B' and C' C corresponds to THRID of A', B', and C',e.g. A'= C' B = , C' =A Hence one permutation of [ A B C ] is [ C B A] . hence proved.

Discussion

12608.	If f ((x + 2y)/(3)) = (f (x) + 2f (y))/( 3) AA x, y in R and f '(0) = 1, f (0) = 2, then find f (x).
Answer» ANSWER :`F (X) = x +2`

Discussion

12609.	Write the converse of the following statements: If two integers a and b are such that agtb, then a-b is always a positive integer.
Answer» ANSWER :If two intergers a and b are such that `a-b` is ALWAYS a positive integer, then `AGTB`.

Discussion

12610.	An ellipse is the set of all pointsin a plane the sun of whose distance fromtwo fixed pointsin the plane is a constant ?
Answer» ANSWER :` (X^(2))/a^(2)+(y^(2))/B^(2) =1`

Discussion

12611.	Cos (theta + 45^(@)) + Sin (theta - 45^(@))=
Answer» `SIN THETA` `COS theta` `TAN theta` 0 Answer :D

Discussion

12612.	List all the elements of the following sets : E = {x : x is a month of a year not having 31 days}
Answer» ANSWER :E = { February, APRIL, June, SEPTEMBER, NOVEMBER }

Discussion

12613.	From 25 tickets , marked with the first 25 numberals , one is drawn at random . Find the probalility that it is a multiple of 5 or 7
Answer» ANSWER :`(8)/(25)`

Discussion

12614.	If theta_(1), theta_(2), theta_(3), theta_(4),….., theta_(n) are in AP whose common difference is d, show that sec theta_(1) sec theta_(2) + sec theta_(2) sec theta_(3)+ ………+ sec theta_((n-1)) sec theta_(n)= (tan theta_(n)- tan theta_(1))/(sin d)
Answer» ANSWER :`TAN theta_(N)- tan theta_(1)`

Discussion

12615.	From 25 tickets , marked with the first 25 numberals , one is drawn at random . Find the probalility that it is a multiple of 3 or 7.
Answer» ANSWER :`(2)/(5)`

Discussion

12616.	Vector equation of the plane passing through the line barr =bara+ alphabarb and parallel to the line barr=barc+betabard is
Answer» `[barr-bara BARB BARD]=0` `[barr-barb BARC bard]=0` `[barr-bardbarabarb]=0` none Answer :A

Discussion

12617.	If \|2 sin theta - cos ec theta\| ge 1 and theta ne (n pi)/(2), n in Z , then
Answer» `COS 2 THETA GE 1//2` `cos 2 theta ge 1//4` `cos 2 theta LE 1//2` `cos 2 theta le 1//4` Answer :A

Discussion

12618.	If g is the inverse function of f and f^1(x) = sin x then g^1(x) is
Answer» `"cosec"(g(x))` `SIN(g(x))` `-1/(sin(g(x))` `COS (g(x))` Answer :A

Discussion

12619.	If sets A and B are defined as A= {(x, y)\|y = (1)/(x), x ne 0 in R}, B= {(x, y)\| y= -x, x in R}. Then,
Answer» `A CAP B = A` `A cap B = B` `A cap B = phi` `A CUP B = A` ANSWER :C

Discussion

12620.	The upper 3//4th portion of a vertical pole subteds pole subteds an angle Tan^(-1)(3//5) at a point in the horizontal plane through its foot and at a distance 40m from the foot. A possible height of the vertical pole is
Answer» `20M` `40M` `60m` `80m` Answer :B

Discussion

12621.	Transform the following equations into a. Slope intercpetform b. Intercept form c. Normal form x+y-2=0
Answer» ANSWER :a. `y=-x+2;` B. `x/2+y/2=1`

Discussion

12622.	Transform the following equations into a. Slope intercpetform b. Intercept form c. Normal form x+y+2=0
Answer» ANSWER :a. `y=-x-2;` B. `x/(-2)+y/(-2)=1` C.`x "cos"(5pi)/4+y"sin"(5pi)/4=sqrt(2)`

Discussion

12623.	Find the conine of the angle between the lines whose direction cosines are ((1)/(sqrt(3)),(1)/(sqrt(3)),(1)/(sqrt(3)))and((1)/(sqrt(2)),(1)/(sqrt(2)),0).
Answer» ANSWER :`SQRT((2)/(3))`

Discussion

12624.	How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?
Answer» ANSWER :More than 562.5 LITRES but LESS than 900 litres.

Discussion

12625.	State the equation of the line which has the y-intercept equal to 4/(3) and is perpendicular to 3x-4y+11=0
Answer» ANSWER :4

Discussion

12626.	If4 sin(60^(@) + theta ) sin (60^(@) - theta )-1=k cos 2 theta, the value of k is
Answer» 1 2 3 `1/2` ANSWER :B

Discussion

12627.	A die has faces each with number '1' three faces each with number'2'and one face with number '3' .If die is rolled once,determine (i) P(2) (ii) P(1 or 3) (iii)P(not 3) ?
Answer» ANSWER :(i) `1/2`, (II) `1/2`, (III) `5/6`

Discussion

12628.	Express each of the complex number given in the form of a+ib (-2-1/3 i)^(3)
Answer» ANSWER :`-22/3 -I 107/27`

Discussion

12629.	In triangle ABC, AD and BE are the medians drawn through the angular points A and B respectively. lfloorDAB= 2lfloorABE = 36^(@)" and " AD = 6units then circumradius of the triangle is equal to
Answer» `(3 - sqrt5) Co sec C ` `(3 + sqrt5) Co sec C` `2(3 - sqrt5) Co SECC ` `2(3 + sqrt5) Co sec C ` Answer :B

Discussion

12630.	Range of tan^(-1)((2x)/(1+x^(2))) is
Answer» `[-(PI)/4,(pi)/4]` `(-(pi)/2,(pi)/2)` `(-(pi)/2,(pi)/4]` `[(pi)/4,(pi)/2]` ANSWER :A

Discussion

12631.	Find the distance of the point (3,-5) from the line 3x -4y -26 =0
Answer» ANSWER :`= 3/5`

Discussion

12632.	A firm manufactures PVC pipes in three plants viz, X ,Y and Z . The deily production velumes from the three firms X,Y and Z are respectively 2000 units , 3000 units and 5000 units . It is known from the past experience that3%of the output from plant X,4%from plant Y and 2% from plant Z are defective A pipe is selected at random from a day's total production ,if the selected pipe is a defective , then what is the probability that it was produced by plant Y ?
Answer» <P> ANSWER : ` P (B//A_(3)) = (2)/(100)` ` therefore P(A_(2)//B) = 3/7`

Discussion

12633.	If both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 are less than 5, then k lies in the interval.
Answer» (5,6] (6,`OO`) `(-oo,4)` `[4,5]` ANSWER :C

Discussion

12634.	A circle in first quadrant has a pair of tangents having equation 2xy - y^2 = 0. If one point of contact is (1, 0) then find radious of the circle.
Answer» ANSWER :`(sqrt5-1)/(2)`

Discussion

12635.	The sum of the first 7 terms of an A.P is 10 and that of next 7 terms is 17. Find the progression.
Answer» ANSWER :`1,(8)/(7), (9)/(7)`,…..

Discussion

12636.	If cos25^(@)+sin25^(@)=p, then cos 50^(@) is
Answer» <P>`SQRT(2-p^(2))` `-sqrt(2-p^(2))` `p sqrt(2-p^(2))` `-p sqrt(2-p^(2))` ANSWER :C

Discussion

12637.	If the line y=sqrt3x " cuts the curve " x^3+y^3+3xy+5x^2+3y^2+4x+5y-1=0 at the points A,B,C then OA.OB.OC is
Answer» `4/13(3sqrt3-1)` `3sqrt3+1` `2/sqrt3+7` `3sqrt3-1` ANSWER :A

Discussion

12638.	Find the mean deviation from the mean for the following data: 38, 70, 48, 40, 42, 55, 63, 46, 54, 44
Answer» ANSWER :8.4

Discussion

12639.	In Delta ABC, (r_1-r)(r_2-r)(r_3-r)=
Answer» ANSWER :` 4 R r^(2) `

Discussion

12640.	If (a,b) be an end of a diagonal of a squae and the other diagonal has the equation x-y=a then another vertex of the square can be
Answer» (a-B,a) (a,0) (0,-a) (a+b,b) ANSWER :B::D

Discussion

12641.	If the points (5, 4, 2), (8, k, -7) and (6, 2, -1) and collinear, then k =
Answer» `-2` 2 10 1 Answer :a

Discussion

12642.	If y = "Cos"^(-1) ((x - x^-1)/(x + x^-1)) then (dy)/(dx) =
Answer» `(-2)/(1 + x^2)` `2/(1 +x^2)` `1/(1 + x^2)` `(-1)/(1 + x^2)` ANSWER :A

Discussion

12643.	If alpha is an integer satisfying \|a\|le4-\|[x]\|, where x is a real number for which2xtan^(-1)x is greater than or equal to In (1+x^(2)) , then the number of maximum possible values of a (where[.] represents the greatest integer function) is
Answer» ANSWER :9

Discussion

12644.	If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets : A = {a, b, c}
Answer» Answer :`={1, 3, 4, 5, 6, 7, 9}`

Discussion

12645.	If R be the set of points inside a rectangle of sides a and b (a, b gt 1) with two sides along the positive direction of X-axis and Y-axis. Then,
Answer» `R= {(x, y) : 0 le x le a, 0 le y le B}` `R= {(x, y) : 0 le x LT a, 0 le y lt b}` `R= {(x, y) : 0 le x le a, 0 lt y lt b}` `R= {(x, y) : 0 lt x lt a, 0 lt y lt b}` ANSWER :D

Discussion

12646.	Illustrate in the complex plane the following set of points and explain your answer \|Z\|=3
Answer» ANSWER :9

Discussion

12647.	The range of value of alpha " such that " (0,alpha) lie on or inside the triangle formed by the liney+3x+2 =0, 3y-2x-5=0, 4y+x-14=0 is
Answer» `5ltalphale7` `1/2le alphale1` `5/3lealphale7/2` `1/3le alphale1/2` ANSWER :C

Discussion

12648.	.........are the 9 digit numbers formed from the number with all digits different.
Answer» 10! 9! `9 XX 9!` `10 xx 10!`

Discussion

12649.	If cos^(-1)x=3cos^(-1)(3a-2) has a solution, then
Answer» `5/6leale1` `5/6geage1` `5/6geage1` `5/6age1` ANSWER :A

Discussion

12650.	Number of straight lines passing through (1,3),(7,-3),(5-1),(6,-2) is
Answer» 1 2 3 4 Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term.

If errors of 1% each are made in the base radius and height of a cylinder, the percentage error in its volume is

Answer the equation: int(1+cos2x)/(sin^(2)x)dx

Observe the following statements. Assertion (A) : The value of tanh^(-1)(2) can be calculated Reason (R ): The domain of tanh^(-1)x is (-1, 1) Then true statement among the following is

f(x) = {(cos""(pix)/(2),",",x gt 0,),("x + a",",",x le 0,):}. Find the values of a if x = 0 is a point of maxima.

A straightline passes through the fixed point [1/k,1/k]. The sum of the reciprocals of itsintercepts on the coordinate axes is

If f ((x + 2y)/(3)) = (f (x) + 2f (y))/( 3) AA x, y in R and f '(0) = 1, f (0) = 2, then find f (x).

Write the converse of the following statements: If two integers a and b are such that agtb, then a-b is always a positive integer.

An ellipse is the set of all pointsin a plane the sun of whose distance fromtwo fixed pointsin the plane is a constant ?

Cos (theta + 45^(@)) + Sin (theta - 45^(@))=

List all the elements of the following sets : E = {x : x is a month of a year not having 31 days}

From 25 tickets , marked with the first 25 numberals , one is drawn at random . Find the probalility that it is a multiple of 5 or 7

If theta_(1), theta_(2), theta_(3), theta_(4),….., theta_(n) are in AP whose common difference is d, show that sec theta_(1) sec theta_(2) + sec theta_(2) sec theta_(3)+ ………+ sec theta_((n-1)) sec theta_(n)= (tan theta_(n)- tan theta_(1))/(sin d)

From 25 tickets , marked with the first 25 numberals , one is drawn at random . Find the probalility that it is a multiple of 3 or 7.

Vector equation of the plane passing through the line barr =bara+ alphabarb and parallel to the line barr=barc+betabard is

If |2 sin theta - cos ec theta| ge 1 and theta ne (n pi)/(2), n in Z , then

If g is the inverse function of f and f^1(x) = sin x then g^1(x) is

If sets A and B are defined as A= {(x, y)|y = (1)/(x), x ne 0 in R}, B= {(x, y)| y= -x, x in R}. Then,

The upper 3//4th portion of a vertical pole subteds pole subteds an angle Tan^(-1)(3//5) at a point in the horizontal plane through its foot and at a distance 40m from the foot. A possible height of the vertical pole is

Transform the following equations into a. Slope intercpetform b. Intercept form c. Normal form x+y-2=0

Transform the following equations into a. Slope intercpetform b. Intercept form c. Normal form x+y+2=0

Find the conine of the angle between the lines whose direction cosines are ((1)/(sqrt(3)),(1)/(sqrt(3)),(1)/(sqrt(3)))and((1)/(sqrt(2)),(1)/(sqrt(2)),0).

How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

State the equation of the line which has the y-intercept equal to 4/(3) and is perpendicular to 3x-4y+11=0

If4 sin(60^(@) + theta ) sin (60^(@) - theta )-1=k cos 2 theta, the value of k is

A die has faces each with number '1' three faces each with number'2'and one face with number '3' .If die is rolled once,determine (i) P(2) (ii) P(1 or 3) (iii)P(not 3) ?

Express each of the complex number given in the form of a+ib (-2-1/3 i)^(3)

In triangle ABC, AD and BE are the medians drawn through the angular points A and B respectively. lfloorDAB= 2lfloorABE = 36^(@)" and " AD = 6units then circumradius of the triangle is equal to

Range of tan^(-1)((2x)/(1+x^(2))) is

Find the distance of the point (3,-5) from the line 3x -4y -26 =0

If both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 are less than 5, then k lies in the interval.

A circle in first quadrant has a pair of tangents having equation 2xy - y^2 = 0. If one point of contact is (1, 0) then find radious of the circle.

The sum of the first 7 terms of an A.P is 10 and that of next 7 terms is 17. Find the progression.

If cos25^(@)+sin25^(@)=p, then cos 50^(@) is

If the line y=sqrt3x " cuts the curve " x^3+y^3+3xy+5x^2+3y^2+4x+5y-1=0 at the points A,B,C then OA.OB.OC is

Find the mean deviation from the mean for the following data: 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

In Delta ABC, (r_1-r)(r_2-r)(r_3-r)=

If (a,b) be an end of a diagonal of a squae and the other diagonal has the equation x-y=a then another vertex of the square can be

If the points (5, 4, 2), (8, k, -7) and (6, 2, -1) and collinear, then k =

If y = "Cos"^(-1) ((x - x^-1)/(x + x^-1)) then (dy)/(dx) =

If alpha is an integer satisfying |a|le4-|[x]|, where x is a real number for which2xtan^(-1)x is greater than or equal to In (1+x^(2)) , then the number of maximum possible values of a (where[.] represents the greatest integer function) is

If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets : A = {a, b, c}

If R be the set of points inside a rectangle of sides a and b (a, b gt 1) with two sides along the positive direction of X-axis and Y-axis. Then,

Illustrate in the complex plane the following set of points and explain your answer |Z|=3

The range of value of alpha " such that " (0,alpha) lie on or inside the triangle formed by the liney+3x+2 =0, 3y-2x-5=0, 4y+x-14=0 is

.........are the 9 digit numbers formed from the number with all digits different.

If cos^(-1)x=3cos^(-1)(3a-2) has a solution, then

Number of straight lines passing through (1,3),(7,-3),(5-1),(6,-2) is