28278 + Interview Questions in Maths in Class 12 Page 238 InterviewSolution

11851.	Given the equation y=3x^2+4, what is the function of the coefficient of 3?
Answer» It moves the GRAPH of `y=3x^2+4` three UNITS HIGHER than the graph of `y=x^2+4`. It moves the graph of `y=3x^2+4` three units lower than the graph of `y=x^2+4`. It makes the graph of `y=3x^2+4` WIDER than the graph of `y=x^2+4` It makes the graph of `y=3x^2+4` narrower than the graph of `y=x^2+4`. ANSWER :D

Discussion

11852.	If the lines (x-2)/(1) = (y-3)/(1) = (4-z)/(lambda) and (x-1)/(lambda) = (y-4)/(2) = (z-5)/(1) are intersect each other than lambda =..........
Answer» 0,-3 `-3,3` `2,-2` `0,2` ANSWER :A

Discussion

11853.	If A and B are square matrices of order 3 such that \|A\| = - 1 and \|B\| = 3 , then the value of \|3AB\| isa) 27 b) -27 c) -81 d) 81
Answer» 27 `-27` `-81` 81 Answer :C

Discussion

11854.	Two consecutive sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0. One diagonal of the parallelogram is 11x+7y=9. If the other diagonal is ax + by + c = 0, then
Answer» a = -1, B=-1, C = 2 a = 1, b =-1, c = 0 a = -1, b = -1, c = 0 a = 1, b = 1, c= 0 Answer :B

Discussion

11855.	Let I_(1) = int_(4)^(5) e^((x -5)^(2)) dx and I_(2) = 3 int_(1//3)^(2//3) e^(9(x-2//3)^(2) ) dx then the value of I_(1) + I_(2)is
Answer» `0` `4//3` `7//4` `5//4` ANSWER :A

Discussion

11856.	Two players A and B each toss 5 coins. Find the probability that A gets more heads than B.
Answer» ANSWER :`(193)/(512)`

Discussion

11857.	Prove that the function given by f(x)=x^3-3x^2+3x-100 in increasing in R.
Answer» Solution :`F(X)=x^3-3x^2+3x-100,x inRf(x)=3x^2-6x+3=3(x^2-2x+1)=3(x-1)^2ge0x inRtherefore` f (x) is increasing in R.

Discussion

11858.	Integrate (e^(tan^(-1))x)/(1+x^(2)) with respect to x.
Answer» ANSWER :`e^(TAN^(-1)X)+C`

Discussion

11859.	Show that the circles x^(2)+y^(2)-8x-2y+8=0 and x^(2)+y^(2)-2x+6y+6=0 touch each other and find the point of contact.
Answer» ANSWER :`(11/5,-7/5)`

Discussion

11860.	cos alpha sin (beta-gamma)+cos betasin (gamma-alpha+cos gamma sin (alpha-beta)=
Answer» 1 `4COS alpha COS beta cos GAMMA` 0 `1//2` ANSWER :C

Discussion

11861.	If vec(a),vec(b),vec(c) are unit coplanar vectors, then [2vec(a)-vec(b).2vec(b)-vec(c).2vec(c)-vec(a)]=
Answer» 0 1 `-SQRT(3)` `sqrt(3)` ANSWER :A

Discussion

11862.	Find the area enclosed between the circles x^(2) + y^(2) = 1 and (x - (1)/(2))^(2) + y^(2) = 1
Answer» Answer :`PI - 2 sin^(-1)((1)/(4)) - (sqrt15)/(8)`

Discussion

11863.	If f(x)=[(x, cos x, e^(x^(2))),(sin x, x^(2), secx),(tan x, x^(4) ,2x^(2))] then int_(-pi//2)^(pi//2)f(x)dx=
Answer» 0 1 -1 2 Answer :A

Discussion

11864.	If X = {4^(n) - 3n - 1: n in N} " and " Y = {9(n-1): n in N}, where N is the set of natural numbers, then X cup Y is equal to
Answer» X Y N R Answer :B

Discussion

11865.	Prove the following : (1-tan^2(45^@-A))/(1+tan^2(45^@-A)) = sin2A
Answer» Solution :L.H.S. `(1-tan^2(45^@-A))/(1+tan^2(45^@-A)) = COS2(45^@-A)` = COS(`90^@`-2A) = SIN2A= R.H.S.

Discussion

11866.	Sum to n terms the series (3)/(1 ^(2) . 2 ^(2)) + (5)/( 2 ^(2) . 3 ^(2)) + (7)/( 3 ^(2) . 4 ^(2)) +.............
Answer» ANSWER :`(2N + N ^(2))/( (n +1 ) ^(2))`

Discussion

11867.	If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain of f, then f, if many-one else one-one. If f: R rarr R and f(x)=a_(1)x+a_(3)x^(3)+a_(5)x^(5)+...+a_(2n+1)-cot^(-1)x " where " 0 lt a_(1) lt a_(3) lt ... lt a_(2n+1), then the function f(x) is
Answer» one-one into many-one onto one-one onto many-one into Answer :C

Discussion

11868.	If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain of f, then f, if many-one else one-one. f:R rarr R and f(x)=(x(x^(4)+1)(x+1)+x^(4)+2)/(x^(2)+x+1), then f(x) is
Answer» one-one into many-one onto one-one onto many-one into Answer :d

Discussion

11869.	If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain of f, then f, if many-one else one-one. If f:R rarr R and f(x)=2ax +sin2x, then the set of valuesof a for which f(x) is one-one and onto is
Answer» `a in (-1/2,1/2)` `a in (-1,1)` `a in R -(-1/2,1/2)` `a in R-(-1,1)` ANSWER :d

Discussion

11870.	The area bounded by the circle x^(2)+y^(2)=a^(2) and the line x+y=a in the first quadrant is
Answer» ANSWER :`pia^2`

Discussion

11871.	If A = [(1,2,1),(0,1,-1),(3,-1,1)], then A^(3) - 3A^(2) - A +9Iequals :
Answer» I O A `A^(2)` ANSWER :B

Discussion

11872.	Formthe polynomialequationwhoseroot are 2,1 +- 3i
Answer» ANSWER :`x^4 -6x^3 +23x^3-34x+26 =0`

Discussion

11873.	The value of "^(12)C_(2)+^(13)C_(3)+^(14)C_(4)+...+^(999)C_(989) is
Answer» `"^(1000)C_(11)-12` `"^(1000)C_(11)+12` `"^(900)C_(11)-12` `"^(1000)C_(989)` SOLUTION :`(a)` Since `.^(10)C_(0)+.^(11)C_(1)+.^(12)C_(2)+.^(13)C_(3)+...+.^(999)C_(989)` `=.^(1000)C_(989)=.^(1000)C_(11)` (Since, `.^(10)C_(0)=.^(11)C_(0)` and `.^(n)C_(r )+.^(n)C_(r-1)=.^(n+1)C_(r )`) So, `.^(12)C_(2)+.^(13)C_(3)+.^(14)C_(4)+....+.^(999)C_(989)=.^(1000)C_(11)-12`

Discussion

11874.	int_(-1)^(1) (2 sinx - 3x^(2))/(4-\|x\|)dx=
Answer» `6 int_(0)^(1) (x^(2))/(4-\|x\|)DX` `-6 int_(0)^(1) (x^(2))/(4-\|x\|)dx` `-6 int_(0)^(1) (x^(2))/(4+\|x\|)dx` 0 Answer :B

Discussion

11875.	Assertion (A) : The value of (2)/(1!) +6/(2!)+(12)/(3!) +(20)/(4!) + .......o = 3e Reason (R) : The n^(th) term of the series 2,6,12,20 , ....... Is n (n+1)
Answer» A is TRUE, R is true and R is CORRECTEXPLANATION of A A is true, R is true and R is not correct EXPLANATION of A A is true , R is FALSE A is false, R is true Answer :A

Discussion

11876.	Integrate the functions ((sinx)/(1+cosx))
Answer»

Discussion

11877.	The vertices of the triangle PQR are P(0, b), Q(0, 0) and R(a, 0). If the medians PM and QN of PQR are perpendicular, then
Answer» `B^(2)=2A^(2)` `b^(2)=a^(2)` `a^(2)=2B^(2)` a = b Answer :C

Discussion

11878.	Find the probability that a non- leap year contains i)53 Sunday ii) 52 Sundays only.
Answer» ANSWER :`(i) (1)/(7)` `(II) (6)/(7)`

Discussion

11879.	A point P is taken on the circle x^(2)+y^(2)=a^(2) and PN, PM are draw, perpendicular to the axes. The locus of the pole of the line MN is
Answer» `X^(2)+y^(2)=a^(2)` `x^(-2)+y^(-2)=2X^(-2)` `x^(-2)-y^(-2)=a^(-2)` `x^(-2)+y^(-2)=a^(-4)` Answer :B

Discussion

11880.	Find underset(0)overset(1)int x^(3//2) sqrt(1-x)dx
Answer» ANSWER :`(PI)/(16)`

Discussion

11881.	Using differentials, find the approximate values of the following: (0.007)^(1//3)
Answer» ANSWER :`23/120`

Discussion

11882.	if A=[{:(3,2,1),(1,2,3),(3,-6,1):}],B=[{:(1,4,0),(2,-3,0),(1,2,0):}] and C=[{:(1,2,3),(3,2,1),(8,7,9):}],then find AB-AC.
Answer» SOLUTION :N/a

Discussion

11883.	Find the derivative of x^3 from the first principle.
Answer» ANSWER :`3X^(2)`

Discussion

11884.	Form the differential equation by eliminating the arbitrary constant from the equation x^(2) + y^(2) - 2ay - a^(2) = 0
Answer» `(2y^(2) + X^(2)) ((DY)/(dx))^(2) + 4xy (dy)/(dx) + x^(2) = 0` `(2y^(2) - x^(2)) ((dy)/(dx))^(2) + 4xy (dy)/(dx) + x^(2) = 0` `(2y^(2) - x^(2)) ((dy)/(dx))^(2)- 4xy (dy)/(dx) + x^(2) = 0` `(2y^(2) - x^(2)) ((dy)/(dx))^(2) - 4xy (dy)/(dx) - x^(2) = 0` Answer :B

Discussion

11885.	If (x^(4))/((x-a)(x-b)(x-c))= P(x)+(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then P(x)=
Answer» `x-a` `x-a-b` `x-a-b-c` `x+a+b+c` ANSWER :D

Discussion

11886.	Find the graph of linear inequation in xy plane 2x-5 gt 0
Answer»

Discussion

11887.	The normal to the parabola y^(2)=4x at P(9, 6) meets the parabola again at Q. If the tangent at Q meets the directrix at R, then the slope of another tangent drawn from point R to this parabola is
Answer» `11` `(11)/(3)` `(3)/(11)` `3` ANSWER :B

Discussion

11888.	If 'theta' lies in the first quadrant and 5 tan theta=4, then (5 sin theta - 3 cos theta)/(sin theta + 2 cos theta) is equal to
Answer» `5/14` `3/14` `1/14` `0` ANSWER :A

Discussion

11889.	The solution of the differential equation (dy)/(dx) = (y)/(x) + (Phi((y)/(x)))/(Phi^(1)((y)/(x))) is
Answer» `x PHI((y)/(x)) = K` `Phi ((y)/(x)) = KX` `y Phi((y)/(x)) = k` `Phi((y)/(x)) = ky` Answer :B

Discussion

11890.	Which of the following is not a correct statement?
Answer» MATHEMATICS is INTERESTING `sqrt(3)` is a PRIME `sqrt(2)` is irrational The SUN is a star Answer :B

Discussion

11891.	A company will reimburse its employees' personal expenses on weekend business trips . It will reimburse $0.80 for every $1.00 an employee spends , up to $100.00 . For the next $200 an employee spends , the company will reimburse $0.70 for every $1.00 spent. For each additional dollar spent, the company will reimburse $0.60 . If an employee was reimbursed $400.00 , approximately how many dollars must she have spent on a weekend business trip ?
Answer» 667 600 500 400 Answer :B

Discussion

11892.	int (dx)/(sin^(2)x cos^(2)
Answer» `TAN X+cotx+c` `tanx-cotx+c` `tan x COT x+c` `tan x-cot 2x+c` ANSWER :B

Discussion

11893.	Evaluate the following:""^(15)C_(2)=
Answer»

Discussion

11894.	Evaluate the following integrals using the definition of a definite integral as the limit of a sum. int_(2)^(3)x^(3) dx
Answer» ANSWER :`(65)/(4)`

Discussion

11895.	Evaluate the following integrals using the definition of a definite integral as the limit of a sum. int_(1)^(2)x^(3) dx
Answer» ANSWER :`(15)/(4)`

Discussion

11896.	Find the acute angle or angle or intersection of the following circles. x^(2)+y^(2)+4x-14y+28=0, x^(2)+y^(2)+4x-5=0
Answer» ANSWER :`theta=60^(@)=(PI)/3`

Discussion

11897.	Evaluate the following integrals using the definition of a definite integral as the limit of a sum. int_(a)^(b) x^(2) dx
Answer» ANSWER :`(1)/(3) (B^(3) - a^(3))`

Discussion

11898.	Evaluate the following integrals using the definition of a definite integral as the limit of a sum. int_(1)^(2) x dx
Answer» ANSWER :`(3)/(2)`

Discussion

11899.	Prove that the chord joining points P(alpha) and Q (beta) on the ellipse x^2/a^2+y^2/b^2=1 subtends a right angle at the vertex A(a,0) then tan""alpha/2 tan""beta/2=(-b^2)/a^2.
Answer» ANSWER :`-b^2/a^2`

Discussion

11900.	If C_r denotes the binomial coefficient ""^n C_r then (-1) C_0^2 + 2C_1^2+5 C_2^2+…..+(3n-1) C_n^2=
Answer» `(3n-2) ^(2N) C_n` `((3n-2)/(2)) ^(2n) C_n` `(5+3n) ^(2n) C_n` `((3n-5)/(2)) 2^2n C_(n+1)` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Given the equation y=3x^2+4, what is the function of the coefficient of 3?

If the lines (x-2)/(1) = (y-3)/(1) = (4-z)/(lambda) and (x-1)/(lambda) = (y-4)/(2) = (z-5)/(1) are intersect each other than lambda =..........

If A and B are square matrices of order 3 such that |A| = - 1 and |B| = 3 , then the value of |3AB| isa) 27 b) -27 c) -81 d) 81

Two consecutive sides of a parallelogram﻿ are 4x + 5y = 0 and 7x + 2y = 0. One﻿ diagonal of the parallelogram is 11x+7y=9.﻿ If the other diagonal is ax + by + c = 0,﻿ then﻿

Let I_(1) = int_(4)^(5) e^((x -5)^(2)) dx and I_(2) = 3 int_(1//3)^(2//3) e^(9(x-2//3)^(2) ) dx then the value of I_(1) + I_(2)is

Two players A and B each toss 5 coins. Find the probability that A gets more heads than B.

Prove that the function given by f(x)=x^3-3x^2+3x-100 in increasing in R.

Integrate (e^(tan^(-1))x)/(1+x^(2)) with respect to x.

Show that the circles x^(2)+y^(2)-8x-2y+8=0 and x^(2)+y^(2)-2x+6y+6=0 touch each other and find the point of contact.

cos alpha sin (beta-gamma)+cos betasin (gamma-alpha+cos gamma sin (alpha-beta)=

If vec(a),vec(b),vec(c) are unit coplanar vectors, then [2vec(a)-vec(b).2vec(b)-vec(c).2vec(c)-vec(a)]=

Find the area enclosed between the circles x^(2) + y^(2) = 1 and (x - (1)/(2))^(2) + y^(2) = 1

If f(x)=[(x, cos x, e^(x^(2))),(sin x, x^(2), secx),(tan x, x^(4) ,2x^(2))] then int_(-pi//2)^(pi//2)f(x)dx=

If X = {4^(n) - 3n - 1: n in N} " and " Y = {9(n-1): n in N}, where N is the set of natural numbers, then X cup Y is equal to

Prove the following : (1-tan^2(45^@-A))/(1+tan^2(45^@-A)) = sin2A

Sum to n terms the series (3)/(1 ^(2) . 2 ^(2)) + (5)/( 2 ^(2) . 3 ^(2)) + (7)/( 3 ^(2) . 4 ^(2)) +.............

The area bounded by the circle x^(2)+y^(2)=a^(2) and the line x+y=a in the first quadrant is

If A = [(1,2,1),(0,1,-1),(3,-1,1)], then A^(3) - 3A^(2) - A +9Iequals :

Formthe polynomialequationwhoseroot are 2,1 +- 3i

The value of "^(12)C_(2)+^(13)C_(3)+^(14)C_(4)+...+^(999)C_(989) is

int_(-1)^(1) (2 sinx - 3x^(2))/(4-|x|)dx=

Assertion (A) : The value of (2)/(1!) +6/(2!)+(12)/(3!) +(20)/(4!) + .......o = 3e Reason (R) : The n^(th) term of the series 2,6,12,20 , ....... Is n (n+1)

Integrate the functions ((sinx)/(1+cosx))

The vertices of the triangle PQR are﻿ P(0, b), Q(0, 0) and R(a, 0). If the medians﻿ PM and QN of PQR are perpendicular,﻿ then

Find the probability that a non- leap year contains i)53 Sunday ii) 52 Sundays only.

A point P is taken on the circle x^(2)+y^(2)=a^(2) and PN, PM are draw, perpendicular to the axes. The locus of the pole of the line MN is

Find underset(0)overset(1)int x^(3//2) sqrt(1-x)dx

Using differentials, find the approximate values of the following: (0.007)^(1//3)

if A=[{:(3,2,1),(1,2,3),(3,-6,1):}],B=[{:(1,4,0),(2,-3,0),(1,2,0):}] and C=[{:(1,2,3),(3,2,1),(8,7,9):}],then find AB-AC.

Find the derivative of x^3 from the first principle.

Form the differential equation by eliminating the arbitrary constant from the equation x^(2) + y^(2) - 2ay - a^(2) = 0

If (x^(4))/((x-a)(x-b)(x-c))= P(x)+(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then P(x)=

Find the graph of linear inequation in xy plane 2x-5 gt 0

The normal to the parabola y^(2)=4x at P(9, 6) meets the parabola again at Q. If the tangent at Q meets the directrix at R, then the slope of another tangent drawn from point R to this parabola is

If 'theta' lies in the first quadrant and 5 tan theta=4, then (5 sin theta - 3 cos theta)/(sin theta + 2 cos theta) is equal to

The solution of the differential equation (dy)/(dx) = (y)/(x) + (Phi((y)/(x)))/(Phi^(1)((y)/(x))) is

Which of the following is not a correct statement?

int (dx)/(sin^(2)x cos^(2)

Evaluate the following:""^(15)C_(2)=

Evaluate the following integrals using the definition of a definite integral as the limit of a sum. int_(2)^(3)x^(3) dx

Evaluate the following integrals using the definition of a definite integral as the limit of a sum. int_(1)^(2)x^(3) dx

Find the acute angle or angle or intersection of the following circles. x^(2)+y^(2)+4x-14y+28=0, x^(2)+y^(2)+4x-5=0

Evaluate the following integrals using the definition of a definite integral as the limit of a sum. int_(a)^(b) x^(2) dx

Evaluate the following integrals using the definition of a definite integral as the limit of a sum. int_(1)^(2) x dx

Prove that the chord joining points P(alpha) and Q (beta) on the ellipse x^2/a^2+y^2/b^2=1 subtends a right angle at the vertex A(a,0) then tan""alpha/2 tan""beta/2=(-b^2)/a^2.

If C_r denotes the binomial coefficient ""^n C_r then (-1) C_0^2 + 2C_1^2+5 C_2^2+…..+(3n-1) C_n^2=

Two consecutive sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0. One diagonal of the parallelogram is 11x+7y=9. If the other diagonal is ax + by + c = 0, then

The vertices of the triangle PQR are P(0, b), Q(0, 0) and R(a, 0). If the medians PM and QN of PQR are perpendicular, then