14949 + Interview Questions in Maths in Class 11 Page 40 InterviewSolution

1951.	Find the modulus and the argument of the complex number -sqrt3 + i
Answer» ANSWER :`2,(5PI)/6`

Discussion

1952.	Let N be the set of natural numbers. Define a real valued function f: N to n by f(x)=2x+1. Using this defination, complete the table given below,
Answer» ANSWER :`(##KPK_AIO_MAT_XI_C02_E07_018_A01##)`

Discussion

1953.	If sin(alpha+beta)=1 and sin(alpha-beta)=1/2 where alpha,beta in [0,pi/2], then tan(2alpha+beta)=
Answer» `-SQRT3` `-1/sqrt3` `sqrt3` `1/sqrt3` ANSWER :B

Discussion

1954.	Using first principles, prove that (d)/( dx) ((1)/( f(x))) = (-f' (x))/( {f (x) }^2).
Answer» ANSWER :`=(-F'(X))/( {f(x)}^2)`.

Discussion

1955.	Assertion (A) : "cosech"^(-1)(2)=log_(e )((1+sqrt(5))/(2)) Reason (R ) : "Cosech"^(-1)(x)=log_(e ) ((1+sqrt(1+x^(2)))/(2))
Answer» Both A and B are TRUE and R is correct EXPLANATION of A Both A and R are true and R is not correct explanation of A A is true both R is false A is false but R is true Answer :A

Discussion

1956.	The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 3x^(2)+ 36x + 5. The marginal revenue, when x = 15 is
Answer» ANSWER :66

Discussion

1957.	Find the area of the triangle formed by the line joining the points (1,7),(2,-5) and co -ordinates axes.
Answer» ANSWER :`361/24`

Discussion

1958.	Write the 5^(th) terms of the sequences whose n^(th) term isa_(n) = 2^(n) ?
Answer» ANSWER :2,4,8,16 and 32

Discussion

1959.	Find the values of the following : Tan((pi)/(4)+theta).Tan((pi)/(4)-theta)Sin1140^(@).cos40^(@)-cos780^(@).sin750^(@)
Answer» ANSWER :`(1)/(2)`

Discussion

1960.	Find the derivative of the function (px ^(2) + qx +r)
Answer» Answer :`(pax ^(2) + 2 PBX + bq-ra)/((AX + B ) ^(2))`

Discussion

1961.	Find themaximumminimumvaluesofsin^(3)theta +cos^(3)theta AAEE R.
Answer» ANSWER :`-(3)/(4),(3)/(4)`

Discussion

1962.	Find the distance of the point (3, - 5)from the line 3x - 4y - 26 = 0 .
Answer» ANSWER :`= 3/5`

Discussion

1963.	Write the negation of the following simple statements. Area of a circle is same as the perimeter of the circle.
Answer» ANSWER :PERIMETER are not same.

Discussion

1964.	If S_1,S_2 and S_3 are respectively the sums of n, 2n and 3n terms of an A.P, whose first term is a and common difference d, then find S_1,S_2 and S_3
Answer» SOLUTION :`S_1=n/2[2A+(n-1)d],S_2=n[2a+(2n-1)d],S_3=(3N)/2[2a+(3n-1)d]]

Discussion

1965.	Evaluate : (sqrt(3)+sqrt(2))^(6)-(sqrt(3)-sqrt(2))^(6)
Answer» ANSWER :`= 396 (SQRT(6))`

Discussion

1966.	Evaluate : 1/2 - sin ^(2) ""(7pi)/(12)
Answer» ANSWER :`(1)/(2 SQRT2)`

Discussion

1967.	If barA = bari+lambdabarj+bark , barB=bari+barj+bark " then for " abs(barA+barB) = absbarA+absbarB " to be true," lambda=
Answer» 2 -2 -1 1 Answer :D

Discussion

1968.	Match the trigonometric equations from List I to solutions in List II {:(ul"List I",ul"List II"),("I) "Cosx=-1//2,"a) "x=7pi//3),("II) "Sinx=(sqrt(3))/(2),"b) "x=(7pi)/(6)),("III) "Tanx=(1)/(sqrt(3)),"c) "x=(8pi)/(3)),("iv) "Cotx=1,"d) "x=3pi//4),(,"e) "x=5pi//4):}
Answer» b,d,a,C c,a,E,b b,c,a,d d,a,b,c Answer :C

Discussion

1969.	Calculate the mean deviation from the mean for the following frequency distributions.
Answer» ANSWER :7.09

Discussion

1970.	Calculate the mean deviation from the mean for the following frequency distributions.
Answer» ANSWER :9.44 MARKS

Discussion

1971.	Calculate the mean deviation from the mean for the following frequency distributions.
Answer» ANSWER :0.75

Discussion

1972.	Calculate the mean deviation from the mean for the following frequency distributions.
Answer» ANSWER :M.D = 13.15, COEFFT. of M.D = 0.26

Discussion

1973.	Calculate the mean deviation from the mean for the following frequency distributions.
Answer» ANSWER :10.56

Discussion

1974.	If sin "" (pi)/(18) sin "" (5pi)/(18) sin "" (7pi)/(18) =
Answer» 8 `1/8` `1//7` 6 Answer :B

Discussion

1975.	(d)/(dx) {x ^(x)}=
Answer» `(x^x)^x {x(1 + log x)}` `(x^x)^x.x(1 - 2LOG x)` `(x^x)^x (1 + 2 log x)x` `(x^x)^x .x^2 (1 - 2log x)` ANSWER :C

Discussion

1976.	If f(x) = 3x + 1 if x
Answer» 1 5 3 -1 Answer :C

Discussion

1977.	Statement- I : Periodof cos^(3) x + cos^(3) (120^(0)- x)+ cos^(3) (120^(0)+ x )is (pi)/(3) Statement-II : Periodofcos((2pi x)/ 3 ) + sin((pix)/2) - tan ((pi x )/ 4)is12 Whichof the abovestatementis correct.
Answer» only I only II bothI & II NEITHERI nor II Answer :2

Discussion

1978.	Let A be any point on the x-axis and B=(2,3). The perpendicular at A to the line AB meets the y-axis at C. Then the locus of midpoint of segment AC as A moves is given by
Answer» `2X^(2)-2x+3y=0` `3X^(2)-3x+2y=0` `3x^(2)-3x-2y=0` `2x-2x^(2)+3y=0` ANSWER :A

Discussion

1979.	Four digit numbers are formed by using the digits 1,2,3,4 and 5 without repeating the digit. Find the probability that a number , chosen at random , is an odd number.
Answer» <P> Answer :`(3xx^(4)P_(3))/(""^(5)P_(4))=(3)/(5)or0.6`

Discussion

1980.	The value of cos^(-1)((sqrt(5)-1)/4)=
Answer» `(3PI)/10` `(2pi)/5` `(PI)/5` `(pi)/15` ANSWER :B

Discussion

1981.	Find the equation of line Passing through (0, 0) with slope m.
Answer» ANSWER :`y = MX`

Discussion

1982.	The value of(3 + cot 76 ^(@) cot 16 ^(@))/( cot 76^(@) + cot 16 ^(@))is
Answer» `TAN 44 ^(@)` `cot 46 ^(@)` `tan 2 ^(@)` `tan 46 ^(@)` ANSWER :D

Discussion

1983.	Find the complex number z satisfying the equation \|(z-12)/(z-8i)\|= (5)/(3), \|(z-4)/(z-8)\|=1
Answer» ANSWER :`6+8i, 6+17i`

Discussion

1984.	Find the eccentricity of the ellipse of minor axis is 2b, if the line segment joining the foci subtends an angle 2alpha at the upper vertex. Also, find the equation of the ellipse if the major axis is 2√2
Answer» ANSWER :Eccentricity `=sinalpha`. EQN. of the ELLIPSE is `x^(2)cos^(2)alpha+y^(2)=B^(2)`.

Discussion

1985.	Find the vector equation of the plane which passes through the points 2bar(i)+4bar(j)+2bar(k), 2bar(i)+3bar(j)+5bar(k) and parallel to the vector 3bar(i)-2bar(j)+bar(k). Also find the point where this plane meets the line joining the points 2bar(i)+bar(j)+3bar(k) and 4bar(i)-2bar(j)+3bar(k).
Answer» ANSWER :`bar(R)=(2+3s)bar(i)+(4-t-2s)bar(J)+(2+3t+s)bar(k) and (-14/17, 89/17, 3),s, t in R`

Discussion

1986.	Let bara ,barb,barc be non coplanar vectors and bara^(1)=(barbxxbarc)/([barabarbbarc]),barb^(1)=(barcxxbara)/([barabarbbarc]) and barc^(1)=(baraxxbarb)/([barabarbbarc]) then prove that (bara+barb).bara^(1)+(barb+barc).barb^(1)+(barc+bara).barc^(1)=3
Answer» `BAR0` 1 2 3 Answer :D

Discussion

1987.	A plumber can be paid according to the following schemes, In the first scheme he will be paid rupees 500 plus rupees 70 per hour, and in the second scheme he will paid 120 rupees perhour. If he works x hours. Then for what value of x does the first scheme give better wages?
Answer» ANSWER :` rArr 10 gt x rArr x lt 10 ` ` therefore ` Number of hours should be LESS then TEN hours .

Discussion

1988.	Let f(x) be a polynomical function in x satisfyingthe conditionf(x) f(1//x)=f(x) +f(x) and f(3) = 28x ne 0 If the centroid of a triangle ABC having vertices A(3, 4, 2) and B(1, 3, 2) is (2, 4, 3). Then the remaining vertex 'C' of the triangle where f(3) = 10 is
Answer» (f(1).f(2).(f(3)) (f(1),f(-2).f(2)) (f(2).f(3).f(1)) (f(1).f(3).f(5)) ANSWER :B

Discussion

1989.	Fill in the blanks so as to make each of the following statements true : If the sum of first n terms of an AP is 2n^2+5n,then its nth term is .........
Answer» `4n-3` `3n-4` `4n+3` `3n+4` ANSWER :C

Discussion

1990.	If f(x)={{:(\|x\|+1","xlt0),(0","x=0),(\|x\|-1","xgt0):} For what value (s) of a does lim_(xtoa)f(x) exist?
Answer» ANSWER :`lim_(xrarra)f(X)` EXISTS for all `ANE0`.

Discussion

1991.	Identify the Quantifiers in the following statements: for all real number x and y,x.y=y.x
Answer» ANSWER :UNIVERSAL QUANTIFIER is USED

Discussion

1992.	If z=3+5iand then z^(3)+barz+198=0....
Answer» `-3-5i` `-3+5i` `3+5i` `3-5i` ANSWER :C

Discussion

1993.	Let x_1,x_2,x_3,………,x_n be n observations . Let W_i = lx_i + k for i=1,2,……,n, where l and k are constants. If the mean of x_i'sis 48 and their standard deviation is 12, the mean of w_i's is 55 and standard deviation of w_i's is 15, the values of l and k should be ..........
Answer» L = 1.25 and K = -5 l = -1.25 and k = 5 l = 2.5 and k = -5 l = 2.5 andk = 5 ANSWER :A

Discussion

1994.	A (x_(1),y_(1),z_(1)), B(x_(2),y_(2),z_(2)) are two points. Then the lenghts of projection on
Answer» `{:(A,B,C),(1,2,3):}` `{:(A,B,C),(3,5,9):}` `{:(A,B,C),(5,9,6):}` `{:(A,B,C),(4,2,3):}` ANSWER :A

Discussion

1995.	If A and B are two sets having 3 elements is common. If n(A)= 5, n(B)= 4. find n(A xx B) and n[(A xx B) nn (B xx A)]
Answer» ANSWER :20, 9

Discussion

1996.	4^(3) + 5^(3) + 6^(3) + … + 10^(3)
Answer» 1905 2358 2447 2989 Answer :D

Discussion

1997.	Express the following in the form a+ bi (2+i)/((3-i)(1+2i))
Answer» ANSWER :`(3)/(10)-(1)/(10)i`

Discussion

1998.	Ifx= tan15^(@) , y="cosec"75^@ and z= 4 sin18^(@) , then
Answer» `yltzltx` `zltxlty` `xltzlty` `xltyltz` ANSWER :D

Discussion

1999.	Find the domain and range of the following function f(x)= (1)/(sqrt(x-5))
Answer» ANSWER :`R^(+)`

Discussion

2000.	Find the eccentricity of the hyperbola with centre at origin, the length of transverse axis 6 and one focus at (0, 4)
Answer» ANSWER :`(4)/(3)`

Discussion

Explore topic-wise InterviewSolutions in .

Find the modulus and the argument of the complex number -sqrt3 + i

Let N be the set of natural numbers. Define a real valued function f: N to n by f(x)=2x+1. Using this defination, complete the table given below,

If sin(alpha+beta)=1 and sin(alpha-beta)=1/2 where alpha,beta in [0,pi/2], then tan(2alpha+beta)=

Using first principles, prove that (d)/( dx) ((1)/( f(x))) = (-f' (x))/( {f (x) }^2).

Assertion (A) : "cosech"^(-1)(2)=log_(e )((1+sqrt(5))/(2)) Reason (R ) : "Cosech"^(-1)(x)=log_(e ) ((1+sqrt(1+x^(2)))/(2))

The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 3x^(2)+ 36x + 5. The marginal revenue, when x = 15 is

Find the area of the triangle formed by the line joining the points (1,7),(2,-5) and co -ordinates axes.

Write the 5^(th) terms of the sequences whose n^(th) term isa_(n) = 2^(n) ?

Find the values of the following : Tan((pi)/(4)+theta).Tan((pi)/(4)-theta)Sin1140^(@).cos40^(@)-cos780^(@).sin750^(@)

Find the derivative of the function (px ^(2) + qx +r)

Find themaximumminimumvaluesofsin^(3)theta +cos^(3)theta AAEE R.

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

Write the negation of the following simple statements. Area of a circle is same as the perimeter of the circle.

If S_1,S_2 and S_3 are respectively the sums of n, 2n and 3n terms of an A.P, whose first term is a and common difference d, then find S_1,S_2 and S_3

Evaluate : (sqrt(3)+sqrt(2))^(6)-(sqrt(3)-sqrt(2))^(6)

Evaluate : 1/2 - sin ^(2) ""(7pi)/(12)

If barA = bari+lambdabarj+bark , barB=bari+barj+bark " then for " abs(barA+barB) = absbarA+absbarB " to be true," lambda=

Match the trigonometric equations from List I to solutions in List II {:(ul"List I",ul"List II"),("I) "Cosx=-1//2,"a) "x=7pi//3),("II) "Sinx=(sqrt(3))/(2),"b) "x=(7pi)/(6)),("III) "Tanx=(1)/(sqrt(3)),"c) "x=(8pi)/(3)),("iv) "Cotx=1,"d) "x=3pi//4),(,"e) "x=5pi//4):}

Calculate the mean deviation from the mean for the following frequency distributions.

Calculate the mean deviation from the mean for the following frequency distributions.

Calculate the mean deviation from the mean for the following frequency distributions.

Calculate the mean deviation from the mean for the following frequency distributions.

Calculate the mean deviation from the mean for the following frequency distributions.

If sin "" (pi)/(18) sin "" (5pi)/(18) sin "" (7pi)/(18) =

(d)/(dx) {x ^(x)}=

If f(x) = 3x + 1 if x

Statement- I : Periodof cos^(3) x + cos^(3) (120^(0)- x)+ cos^(3) (120^(0)+ x )is (pi)/(3) Statement-II : Periodofcos((2pi x)/ 3 ) + sin((pix)/2) - tan ((pi x )/ 4)is12 Whichof the abovestatementis correct.

Let A be any point on the x-axis and B=(2,3). The perpendicular at A to the line AB meets the y-axis at C. Then the locus of midpoint of segment AC as A moves is given by

Four digit numbers are formed by using the digits 1,2,3,4 and 5 without repeating the digit. Find the probability that a number , chosen at random , is an odd number.

The value of cos^(-1)((sqrt(5)-1)/4)=

Find the equation of line Passing through (0, 0) with slope m.

The value of(3 + cot 76 ^(@) cot 16 ^(@))/( cot 76^(@) + cot 16 ^(@))is

Find the complex number z satisfying the equation |(z-12)/(z-8i)|= (5)/(3), |(z-4)/(z-8)|=1

Find the eccentricity of the ellipse of minor axis is 2b, if the line segment joining the foci subtends an angle 2alpha at the upper vertex. Also, find the equation of the ellipse if the major axis is 2√2

Find the vector equation of the plane which passes through the points 2bar(i)+4bar(j)+2bar(k), 2bar(i)+3bar(j)+5bar(k) and parallel to the vector 3bar(i)-2bar(j)+bar(k). Also find the point where this plane meets the line joining the points 2bar(i)+bar(j)+3bar(k) and 4bar(i)-2bar(j)+3bar(k).

Let bara ,barb,barc be non coplanar vectors and bara^(1)=(barbxxbarc)/([barabarbbarc]),barb^(1)=(barcxxbara)/([barabarbbarc]) and barc^(1)=(baraxxbarb)/([barabarbbarc]) then prove that (bara+barb).bara^(1)+(barb+barc).barb^(1)+(barc+bara).barc^(1)=3

A plumber can be paid according to the following schemes, In the first scheme he will be paid rupees 500 plus rupees 70 per hour, and in the second scheme he will paid 120 rupees perhour. If he works x hours. Then for what value of x does the first scheme give better wages?

Let f(x) be a polynomical function in x satisfyingthe conditionf(x) f(1//x)=f(x) +f(x) and f(3) = 28x ne 0 If the centroid of a triangle ABC having vertices A(3, 4, 2) and B(1, 3, 2) is (2, 4, 3). Then the remaining vertex 'C' of the triangle where f(3) = 10 is

Fill in the blanks so as to make each of the following statements true : If the sum of first n terms of an AP is 2n^2+5n,then its nth term is .........

If f(x)={{:(|x|+1","xlt0),(0","x=0),(|x|-1","xgt0):} For what value (s) of a does lim_(xtoa)f(x) exist?

Identify the Quantifiers in the following statements: for all real number x and y,x.y=y.x

If z=3+5iand then z^(3)+barz+198=0....

Let x_1,x_2,x_3,………,x_n be n observations . Let W_i = lx_i + k for i=1,2,……,n, where l and k are constants. If the mean of x_i'sis 48 and their standard deviation is 12, the mean of w_i's is 55 and standard deviation of w_i's is 15, the values of l and k should be ..........

A (x_(1),y_(1),z_(1)), B(x_(2),y_(2),z_(2)) are two points. Then the lenghts of projection on

If A and B are two sets having 3 elements is common. If n(A)= 5, n(B)= 4. find n(A xx B) and n[(A xx B) nn (B xx A)]

4^(3) + 5^(3) + 6^(3) + … + 10^(3)

Express the following in the form a+ bi (2+i)/((3-i)(1+2i))

Ifx= tan15^(@) , y="cosec"75^@ and z= 4 sin18^(@) , then

Find the domain and range of the following function f(x)= (1)/(sqrt(x-5))

Find the eccentricity of the hyperbola with centre at origin, the length of transverse axis 6 and one focus at (0, 4)