14949 + Interview Questions in Maths in Class 11 Page 266 InterviewSolution

13251.	Evaluate the following limits : Lim_(x to 0) (sqrt(1+x)-1)/x
Answer» ANSWER :`1/2 `

Discussion

13252.	If the diameter of any excircle of a triangle is equal to its perimeter, then the triangle is
Answer» EQUILATERAL ISOSCELES RIGHT angled scalene Answer :C

Discussion

13253.	If U=sqrt(a^(2)cos^(2) theta+ b^(2) sin^(2) theta)+ sqrt(b^(2)cos^(2) theta+ a^(2) sin^(2) theta) then the difference between the maximum and minimum values of U^(2) is given by
Answer» `2(a^(2) + B^(2))` `2sqrt(a^(2) + b^(2))` `(a+b)^(2)` `(a-b)^(2)` ANSWER :D

Discussion

13254.	[barb barc bard]bara-[bara barc bard]barb+[bara barb bard]barc-[bara barb barc]bard=
Answer» `BARA` `barb` `BAR0` `BARC` ANSWER :C

Discussion

13255.	Form the bicoditional statement phArrq. Where p: A triangle is an equilateral triangle. q: All three sides of a triangle are equal.
Answer» ANSWER :TRIANGLE are EQUAL.

Discussion

13256.	If the vectors abari+barj+bark,bari+bbarj+bark,barI+barj+cbarK are coplanar then the value of a+b+c-abc =
Answer» `-2` `-1` 2 1 Answer :C

Discussion

13257.	Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5repetitions not allowed?
Answer» ANSWER :399960

Discussion

13258.	If the function fix) is defined by f(x)={{:((x-1)/(sqrt(x-1)), if x gt 1),(5-3x, if -2 le x le 1 "then discuss the continuity of f"),((6)/(x-10), if x lt -2):}then discuss the continuity of ‘f .
Answer» ANSWER :x=-2

Discussion

13259.	Write the negation of the following statements: s: There exists a number x such that 0 < x < 1.
Answer» ANSWER :There does not EXIST a number x such that `0 < x < 1`

Discussion

13260.	Set AcupB has m elements and set AcapB has n elements . Then set ADeltaBhas ….. elements .
Answer» ANSWER :`m-n`

Discussion

13261.	The period of sin^(3) x + cos^(3) x is
Answer» `PI/3` `pi` `2PI` `2pi/3` ANSWER :C

Discussion

13262.	The vector equation to the line through the point (2, 3, 1) and parallel to the vector (4, -2, 3)
Answer» `BAR(R)=(4bar(i)-2bar(J)+3bar(k))+t(2bar(i)+3bar(j)+bar(k))` `bar(r)=(2bar(i)+3bar(j)+bar(k))+t(2bar(i)-5bar(j)+2bar(k))` `bar(r)=(2bar(i)+3bar(j)+bar(k))+t(4bar(i)-2bar(j)+3bar(k))` `bar(r)=(4bar(i)-2bar(j)+3bar(k))+t(6bar(i)+bar(j)+4bar(k))` Answer :C

Discussion

13263.	Rewrite each of the following statements in the form ''p if and only if q'' p: If you watch television, then your mind is free and if your mind is free, then you watch television.
Answer» ANSWER :You WATCH TELEVISION if and only if your MIND in FREE.

Discussion

13264.	Find unit vector parallel to the XOY-plane and perpendicular to the vector 4bar(i) - 3bar(j) + bar(k).
Answer» ANSWER :`pm1/5(3bari+4barj)`

Discussion

13265.	Express the following expression in the form of a+ib, ((3+isqrt(5))(3-isqrt(5)))/((sqrt(3)+sqrt(2)i)+(sqrt(3)-sqrt(2)i))
Answer» ANSWER :`0-I (7sqrt(2))/2`

Discussion

13266.	Find the r^th term from the end in the expansion of (x + a)^n.
Answer» ANSWER :`(n+1)-(r-1)=(n-r+2)`

Discussion

13267.	Express the following in the form a+ bi (5)/(2i-7i^(2))
Answer» ANSWER :`(35)/(53)-(10)/(53)i`

Discussion

13268.	If the length of a simple pendulum is decreased by 2%, find the percentage error in its period T.
Answer» ANSWER :-1

Discussion

13269.	Ifthe equation (x^(2))/( 3 - lambda) + (y^(2))/(lambda - 8) + 1 = 0represents anellipse, then (i) lambda lt 8 (ii) lambda gt 3 (iii)3 ltlambda lt 8 (iv) lambda lt 3" or "lambda gt 8
Answer» `LAMBDA LT 8` `lambda gt 3` ` 3 ltlambda lt 8` `lambda lt 3" or "lambda gt 8 ` ANSWER :C

Discussion

13270.	Let f: { - pi/3, (2pi)/(3)} rarr [0, 4] be a function defined as f(x)=sqrt(3) sin x - cos x + 2. Then f^(-1)(x) is given by
Answer» `sin^(-1)((x-2)/(2))- pi/6` `sin^(-1)((x-2)/(2))+pi/6` `(2PI)/(3) + COS^(-1)((x-2)/(2))` none of these Answer :B

Discussion

13271.	If bar(a), bar(b), bar(c) are non coplanar then the vectors bar(a)-2bar(b)+3bar(c), -2bar(a)+3bar(b)-4bar(c), bar(a)-3bar(b)+5bar(c) are
Answer» Collinear Coplanar but NON collinear non coplanar cannot be determined Answer :C

Discussion

13272.	The sides of a Delta^("le") ABC " are " a = 4, b = 5, c = 6 The length of the internal angular bisector of C is
Answer» 3 `7/2` `10/3` `15/4` ANSWER :C

Discussion

13273.	If weights are not given, but p_(0) and q_(0) respectively the price and quantity of a commodity in the base year is given, then weight is given by . . . . . . . . . .
Answer» <P> ANSWER :`p_(0)q_(0)`

Discussion

13274.	Graph of constant function is line parallel to Y - axis (means graph is vertical line)
Answer» ANSWER :FALSE STATEMENT

Discussion

13275.	If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find B ∩ C
Answer» Answer :`={7, 9, 11, 13} CAP {11, 13, 15}= {11, 13}`

Discussion

13276.	The value of natural number 'a' for which sum_(k=1)^(n)f(a+k)=16(2^(n)-1), where the function satisfies the relation f(x+y)=f(x).f(y) for all natural numbers x, y and further f(1)=2 is
Answer» 3 0 2 1 Answer :A

Discussion

13277.	Find themodulus of (1+i)/(1-i) - (1-i)/(1+i)
Answer» ANSWER :2

Discussion

13278.	Find the dimensions and the volume of the greatest cylinder that can be inscribed in a sphere of radius a.
Answer» Answer :height `= (2a)/(sqrt(3))`; RADIUS `= (sqrt(2)a)/(sqrt(3))`; volume `= (4pi a^(3))/(3sqrt(3))` CUBIC UNITS

Discussion

13279.	Number of common points for the curves y=sin^(-1)(2x)+tan^(-1)(1/([2x]))+2 and y=cos^(-1)(2x+5)+1 is (where [.] denotes greatest integer function)
Answer» 0 1 3 4 Answer :A

Discussion

13280.	If tan(pi cos theta)=cot(pi sin theta), 0 lt theta lt (3pi)/(4) then sin(theta+(pi)/(4))=
Answer» `(1)/(SQRT(2))` `-(1)/(sqrt(2))` `(1)/(2sqrt(2))` `-(1)/(2sqrt(2))` ANSWER :C

Discussion

13281.	Write down the slopes of the following lines: 3x+4y-2(x+x_(1))-5(y+y_(1))+2=0
Answer» ANSWER :1

Discussion

13282.	If side of a cube is 10 cm and error in it is 0.05 cm then match the following and choose correct answer.
Answer» B,D,E,A A,C,E,D A,C,B,E B,E,A,C Answer :D

Discussion

13283.	Evaluate the following limits in lim_(xrarr2)((1)/(x)+(1)/(2))/(x+2)
Answer» ANSWER :`-(1)/(4)`

Discussion

13284.	The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below: sum_(i=1)^(50)x_(i)=212, sum_(i=1)^(50)x_(i)^(2)=902.8, sum_(i=1)^(50)y_(i)=261, sum_(i=1)^(50)y_(i)^(2)=1457.6 Which is more varying, the length or weight?
Answer» ANSWER :26.43

Discussion

13285.	Area of circle with centre (1,2) and passes from (4,6) is ..........
Answer» ANSWER :`25pi`SQUARE UNIT

Discussion

13286.	The period of the function f(x) = p\|sin x\| + p^(2)\|cos x\| + g(p) is (pi)/(2), if p is
Answer» 1 2 3 `1//2` ANSWER :A

Discussion

13287.	Find the equation of locus of P, if A=(4,0),B=(-4,0) and \|PA-PB\|=4
Answer» Answer :`(X^(2))/(4)-(y^(2))/(12)=1`

Discussion

13288.	Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n) = (n^(3)+1)/(2)
Answer» Answer :`1, (9)/(2), 14, (65)/(2), 63`

Discussion

13289.	If y = (x^4 - x^2 + 1)/(x^2 + sqrt(3)x + 1) and (dy)/(dx) = ax + b , then the value of a - b is
Answer» `"cot" pi/8` `"cot" (5PI)/12` `"TAN" (5pi)/12` `"tan"(5pi)/(8` ANSWER :B

Discussion

13290.	The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is ………….
Answer» ANSWER :2,52,500

Discussion

13291.	Find deltay and dy for the following functions y=x^(2)+x,x=10,deltax=0.1
Answer» ANSWER :2.11, 2.1

Discussion

13292.	The negation of the statement Rajesh or Rajni lived in Bangalore is………….
Answer» Rajesth did not the in BANGALORE or RAJNI LIVES in Bangalore. Rajesth lives in Bangalore and Rajni did not LIVE in Bangalore. Rajesh did not live in Bangalore and Rajni did not live in Bangalore Rajesh did not live in Bangalore or Rajni did not live in Bangalore. Answer :C

Discussion

13293.	Find the union of each of the following pairs of sets : X = {1, 3, 5} Y = {1, 2, 3}
Answer» Answer :`X ∪ Y = {1, 2, 3, 5 }`

Discussion

13294.	Express each of the following complex number in the form a+ib: (-i)(2i)(-(1)/(3)i)^(3)
Answer» ANSWER :`0+(2I)/(27)`

Discussion

13295.	Let P(n) denotes the statement 2^(n+3) le (n+3)! Are P(1) and P(2) true? Justify your answer.
Answer» SOLUTION :YES, Yes

Discussion

13296.	Solve the system of equations 2x+4y-z=0,x+2y+2z=5,3x+6y-7z=2 by Gauss Jordan Method.
Answer» ANSWER :HENCE the GIVEN SYSTEM has no SOLUTION.

Discussion

13297.	Find the principal solution of the equation tan x =- (1)/(sqrt3).
Answer» ANSWER :`N in Z`

Discussion

13298.	Ifcos alpha + cos beta = 1//2 and sin alpha + sin beta = 1//3, then
Answer» ANSWER :A::B::C::D

Discussion

13299.	What is the value of C_1+C_3+C_5+...?
Answer» SOLUTION :`2^(n-1]`

Discussion

13300.	Find the roots 2x^(2) + x+1=0
Answer» ANSWER :`(-1 +-SQRT(7)i)/4`

Discussion

Explore topic-wise InterviewSolutions in .

Evaluate the following limits : Lim_(x to 0) (sqrt(1+x)-1)/x

If the diameter of any excircle of a triangle is equal to its perimeter, then the triangle is

If U=sqrt(a^(2)cos^(2) theta+ b^(2) sin^(2) theta)+ sqrt(b^(2)cos^(2) theta+ a^(2) sin^(2) theta) then the difference between the maximum and minimum values of U^(2) is given by

[barb barc bard]bara-[bara barc bard]barb+[bara barb bard]barc-[bara barb barc]bard=

Form the bicoditional statement phArrq. Where p: A triangle is an equilateral triangle. q: All three sides of a triangle are equal.

If the vectors abari+barj+bark,bari+bbarj+bark,barI+barj+cbarK are coplanar then the value of a+b+c-abc =

Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5repetitions not allowed?

If the function fix) is defined by f(x)={{:((x-1)/(sqrt(x-1)), if x gt 1),(5-3x, if -2 le x le 1 "then discuss the continuity of f"),((6)/(x-10), if x lt -2):}then discuss the continuity of ‘f .

Write the negation of the following statements: s: There exists a number x such that 0 < x < 1.

Set AcupB has m elements and set AcapB has n elements . Then set ADeltaBhas ….. elements .

The period of sin^(3) x + cos^(3) x is

The vector equation to the line through the point (2, 3, 1) and parallel to the vector (4, -2, 3)

Rewrite each of the following statements in the form ''p if and only if q'' p: If you watch television, then your mind is free and if your mind is free, then you watch television.

Find unit vector parallel to the XOY-plane and perpendicular to the vector 4bar(i) - 3bar(j) + bar(k).

Express the following expression in the form of a+ib, ((3+isqrt(5))(3-isqrt(5)))/((sqrt(3)+sqrt(2)i)+(sqrt(3)-sqrt(2)i))

Find the r^th term from the end in the expansion of (x + a)^n.

Express the following in the form a+ bi (5)/(2i-7i^(2))

If the length of a simple pendulum is decreased by 2%, find the percentage error in its period T.

Ifthe equation (x^(2))/( 3 - lambda) + (y^(2))/(lambda - 8) + 1 = 0represents anellipse, then (i) lambda lt 8 (ii) lambda gt 3 (iii)3 ltlambda lt 8 (iv) lambda lt 3" or "lambda gt 8

Let f: { - pi/3, (2pi)/(3)} rarr [0, 4] be a function defined as f(x)=sqrt(3) sin x - cos x + 2. Then f^(-1)(x) is given by

If bar(a), bar(b), bar(c) are non coplanar then the vectors bar(a)-2bar(b)+3bar(c), -2bar(a)+3bar(b)-4bar(c), bar(a)-3bar(b)+5bar(c) are

The sides of a Delta^("le") ABC " are " a = 4, b = 5, c = 6 The length of the internal angular bisector of C is

If weights are not given, but p_(0) and q_(0) respectively the price and quantity of a commodity in the base year is given, then weight is given by . . . . . . . . . .

Graph of constant function is line parallel to Y - axis (means graph is vertical line)

If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, find B ∩ C

The value of natural number 'a' for which sum_(k=1)^(n)f(a+k)=16(2^(n)-1), where the function satisfies the relation f(x+y)=f(x).f(y) for all natural numbers x, y and further f(1)=2 is

Find themodulus of (1+i)/(1-i) - (1-i)/(1+i)

Find the dimensions and the volume of the greatest cylinder that can be inscribed in a sphere of radius a.

Number of common points for the curves y=sin^(-1)(2x)+tan^(-1)(1/([2x]))+2 and y=cos^(-1)(2x+5)+1 is (where [.] denotes greatest integer function)

If tan(pi cos theta)=cot(pi sin theta), 0 lt theta lt (3pi)/(4) then sin(theta+(pi)/(4))=

Write down the slopes of the following lines: 3x+4y-2(x+x_(1))-5(y+y_(1))+2=0

If side of a cube is 10 cm and error in it is 0.05 cm then match the following and choose correct answer.

Evaluate the following limits in lim_(xrarr2)((1)/(x)+(1)/(2))/(x+2)

The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below: sum_(i=1)^(50)x_(i)=212, sum_(i=1)^(50)x_(i)^(2)=902.8, sum_(i=1)^(50)y_(i)=261, sum_(i=1)^(50)y_(i)^(2)=1457.6 Which is more varying, the length or weight?

Area of circle with centre (1,2) and passes from (4,6) is ..........

The period of the function f(x) = p|sin x| + p^(2)|cos x| + g(p) is (pi)/(2), if p is

Find the equation of locus of P, if A=(4,0),B=(-4,0) and |PA-PB|=4

Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n) = (n^(3)+1)/(2)

If y = (x^4 - x^2 + 1)/(x^2 + sqrt(3)x + 1) and (dy)/(dx) = ax + b , then the value of a - b is

The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is ………….

Find deltay and dy for the following functions y=x^(2)+x,x=10,deltax=0.1

The negation of the statement Rajesh or Rajni lived in Bangalore is………….

Find the union of each of the following pairs of sets : X = {1, 3, 5} Y = {1, 2, 3}

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

Let P(n) denotes the statement 2^(n+3) le (n+3)! Are P(1) and P(2) true? Justify your answer.

Solve the system of equations 2x+4y-z=0,x+2y+2z=5,3x+6y-7z=2 by Gauss Jordan Method.

Find the principal solution of the equation tan x =- (1)/(sqrt3).

Ifcos alpha + cos beta = 1//2 and sin alpha + sin beta = 1//3, then

What is the value of C_1+C_3+C_5+...?

Find the roots 2x^(2) + x+1=0