14949 + Interview Questions in Maths in Class 11 Page 242 InterviewSolution

12051.	If one of the lines of the pair ax^(2)+2hxy+by^(2)=0 bisects the angle between positive direction of the axes then a, b, h satisfy the relation
Answer» a+2h-B=0 a+2h+b=0 a-2h+b=0 a-2h-b=0 Answer :B

Discussion

12052.	If cot x =- 5/12, x lies in second quadrant, find the values of other five trignometric functions.
Answer» ANSWER :`13/12`

Discussion

12053.	Let OAB be a quadrant of a circle with boundary radii OA = 1, OB = 1and bunding arc AB. Then Maximum area of the reactangle inscribed in it with two vertices on OA and OB and two on the are AB
Answer» `SQRT2` `1/sqrt2` `sqrt2 - 1` `sqrt2 + 1` ANSWER :C

Discussion

12054.	The sum of first three terms of a G.P. is 13/12 and their product is – 1. Find the common ratio and the terms.
Answer» ANSWER :`-4/3`

Discussion

12055.	If x = log_(e) [cot((pi)/(4) + theta)] then sin hx =
Answer» `TAN 2 THETA` `cot 2 theta` `-tan 2 theta` `-cot 2 theta` ANSWER :C

Discussion

12056.	Find the sum of all natural numbers between 100 and 1000 which are multiple of 5.
Answer» ANSWER :98450

Discussion

12057.	Let f be continuous and differentiable function such that f(x) and f(x) have opposite signs evergywhere . Then
Answer» F is increasing f is DECREASING `\|f\|` is NON - MONOTONIC `\|f\|` is decreasing Answer :D

Discussion

12058.	Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : { a, b, c } . . . { b, c, d }
Answer» ANSWER :`⊄`

Discussion

12059.	Find the derivative of the w.r.t.x a ^(x) e ^(x)
Answer» ANSWER :`a ^(X) E ^(2X)`

Discussion

12060.	Let A={1,2} and B={3,4}. Write A xx B. How many subsets will A xx B have? List them.
Answer» ANSWER :16

Discussion

12061.	Find the coefficient ofa^5 b^7 in (a-2b)^12.
Answer» ANSWER :-101376

Discussion

12062.	f(x) is a contiuous function satisfying f(x)*f((1)/(x))=f(x)+f((1)/(x)) and f(1) gt 0, then underset(x to 1) (Lt)f(x) is equal to
Answer» 2 1 3 `-2` ANSWER :C

Discussion

12063.	Evaluate the following limits : Lim_( x to 0 ) x/(sqrt((x+1)-1))
Answer» ANSWER :2

Discussion

12064.	Consider the complex number z_1 = 3+i and z_2 = 1+i .Using the value of 1/z_2, find (z_1)/z_2
Answer» ANSWER :2 - i

Discussion

12065.	(sin(3alpha))/(1+2cos(2alpha))= ..........
Answer» ANSWER :`SINALPHA`

Discussion

12066.	A letter is chosen at random from the word 'ASSASSINATION' Find the probability that latter is a vowel (ii) a consonant
Answer» ANSWER :(i) `6/13` (II) `7/13`

Discussion

12067.	Find the value of: (i) sin 75^(@) (ii) tan 15 ^(@)
Answer» ANSWER :`(i) (SQRT3+1)/(2SQRT2) ` (II)` 2- sqrt3`

Discussion

12068.	The value of k such that the lines 6x^(2)+17xy+12y^(2)=0 and kx^(2)+5xy+3y^(2)=0 may have one line in common is
Answer» 1 2 `-1` `-2` ANSWER :B

Discussion

12069.	If X={1,2,3,........10} and A={1,2,3,4,5}, find the number of sets B subseteq X such that A-B={4}
Answer» ANSWER :32

Discussion

12070.	Examine the continuity of the following: e^x tan x
Answer» Answer :` (2N + 1) (PI)/(2) , N in ZZ ` .

Discussion

12071.	If in a triangle (r_(2)- r_(1))(r_(3)-r_(1))=2r_(3)r_(3) then the triangle is :-
Answer» RIGHT ANGLED isosecels EQUILATERAL NONE of these ANSWER :A

Discussion

12072.	Find the equation of that parabol whose : (i) vertex is (0,0) and focus is (1,0). (ii) vertex is (0,0) and focus is (0,3). (iii) vertex is (4,0) and focus is (2,0). (iv) vertex is (-2,0) and focus is (2,0). (v) vertex is (1,1) and focus is (1,2).
Answer» ANSWER :(i) `y^(2)=16y` , (ii) `x^(2)=12y` (III) `y^(2)+8x=32` , (iv) `y^(2)=16x+32` (V) `x^(2)-2x-4y+5=0`

Discussion

12073.	If A=("x y"),B=((a,h),(h,b)),C=((x),(y)) then ABC=
Answer» `[AX+hy]` `[ax^(2)+2hxy+by^(2)]` `[BX^(2)-2hxy+ay^(2)]` `[ay+hx]` ANSWER :B

Discussion

12074.	If the origin is the centroid of the triangle PQR with vertices P(2a, 2, 6), Q(-4, 3b, -10) and R(8, 14, 2c), then find the values of a, b and c.
Answer» ANSWER :a=2,B=`-16/3,c=2`

Discussion

12075.	sin 100 in terms of functions of5 theta ,
Answer» ANSWER :`SIN 5 THETA COS 5 theta `

Discussion

12076.	Assertion (A) : If Tan((pi)/(4)+ theta)+Tan ((pi)/(4)- theta)=k then Tan^(3)((pi)/(4)+ theta)+Tan^(3) ((pi)/(4)- theta)=k^(3)-3k Reason (R) : If A+B=(pi)/(2) then Tan A tan B=1
Answer» A is TRUE, r is true and R is correct EXPLANATION for A A is true, R is true and R is not correct explanation for A A is true, R is false A is false, R is true Answer :B

Discussion

12077.	check whether it is statement or notToday isSunday and tomorrowis Monday.
Answer» Answer :Compound statement. The COMPONENTS are TODAY is SUNDAY. Tomorrow is MONDAY".

Discussion

12078.	Write the following interval in set builder form. (6, 12)
Answer» ANSWER :`={X : x in R, 6 LT x LE 12}`

Discussion

12079.	Radius of the circle x^2+y^2+8x+10y=8 is 7 unit.
Answer» ANSWER :TRUE STATEMENT

Discussion

12080.	sin alpha + sin beta = 1/4 and cos alpha + cos beta = 1/3 The value of tan (alpha + beta)is
Answer» `25/7` `25/12` `25/13` `24/7` ANSWER :B

Discussion

12081.	f:R-{0}rarrR,f(x)=(1)/x+px " and "f(1/5)=28/5 then p = …. .
Answer» ANSWER :3

Discussion

12082.	A particle is acted upon by constant forces 4bari+barj-3bark and 3bari+barj-bark which displace it from a point bari+2barj+3bark " to the point " 5bari+4barj+bark. The work done in standard unity by the forces is given by
Answer» 40 15 25 30 Answer :A

Discussion

12083.	Find the value of a and b: (2a-5, 4)= (5,b+ 6)
Answer» ANSWER :a=5, b=-2

Discussion

12084.	If one of the lines of my^(2)+(1-m^(2))xy-mx^(2)=0 is abisector of angle between the lines xy=0 then m is
Answer» 1 2 `-(1)/(2)` 2 Answer :A

Discussion

12085.	sin alpha + sin beta = 1/4 and cos alpha + cos beta = 1/3 The value of sin (alpha + beta) is
Answer» `24/25` `13/25` `12/13` NONE of these ANSWER :A

Discussion

12086.	Find the number of distinct solutions of secx +tanx = sqrt(3), where 0 le xle3pi.
Answer» Solution :Here, `secx +tanx=sqrt(3) rArr 1+sinx = sqrt(3)cosx` or `sqrt(3)cosx-sinx=1` `sqrt(3)cosx-sinx=1` DIVIDING both sides by `sqrt(a^(2)+b^(2))`. i.e., `sqrt(4)=2`, we get `rArr sqrt(3)/2 cosx-1/xsinx=1/2` `rArr cospi/6cosx-sinpi/6 sinx=1/2 rArr cos(x+pi/6) = 1/2` As `0lexle3pi` `pi/6 le x +pi/6 le3pi+pi/6` `rArr x+pi/6=pi/3, (5pi)/3, (7pi)/(3) rArr x=pi/6, (3pi)/(2), (13pi)/(6)` But at `x=(3pi)/(2)`,`tanx` and `secx` is not defined `THEREFORE` Total NUMBER of solutions are 2.

Discussion

12087.	The plane (qrs)x + (rsp)y + (pqs)z + (pqr)=0, where p, q, r, s are in H.P., represents a family of planes. Find the equation of the plane in the family passing through the point (-3, -2, 1).
Answer» ANSWER :`x+2y+3z+4=0`.

Discussion

12088.	cot16^(0)cot44^(0)+cot44^(0)cot76^(0)-cot76^(0)cot16^(0)
Answer» 0 1 3 4 Answer :C

Discussion

12089.	A(5,4,6), B(1,-1,3),C(4,3,2) are three points. Find the coordinates of the point in which the bisector of \|__BAC meets the side BC.
Answer» Answer :`((23)/(8),(3)/(2),(19)/(8))`

Discussion

12090.	A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel is
Answer» ANSWER :`4/11`

Discussion

12091.	The probability of an event A occuring is 0.5 and of B is 0.3 If A and B are mutually exclusive events , then find the probability of neither A nor B occurring.
Answer» ANSWER :0.2

Discussion

12092.	Iff : R to Rbe defined f(x) = {(a^(2) cos^(2) x + b^(2) sin^(2) x " if " x le 0),(e^(ex + b) "if " x gt0):}is a continuous function show thatb = 2 log \| a\| (a ne 0).
Answer» ANSWER :` RARR B = 2 log\|a\|` .

Discussion

12093.	Express the following in the form of a+bi, (i) (-5i) (1/8 i), (ii) (-i)(2i)(-1/8i)^(3)
Answer» ANSWER :(i) `=5/8 + I0` (II) `i=1/256 i`

Discussion

12094.	In triangle ABC. Dis on AC such that AD = BC, BD = DC, angleDBC = 2theta angleBAD=3 theta then theta=
Answer» `60^(@)` `15^(@)` `30^(@)` `10^(@)` ANSWER :D

Discussion

12095.	P(n):2^n - 1, for n = ……………it is a primenumber.
Answer» 1 3 4 8 Answer :B

Discussion

12096.	Find the number ofpermutations of the letter of the words 'INDIA '
Answer» ANSWER :` 60`

Discussion

12097.	Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P(0, -4) and B(8, 0).
Answer» ANSWER :Slope of `BAR(OM) = (y_1 - y_2)/( x_1 - x_2) = ( -2 -0)/( 4-0) = - (1)/(2)`

Discussion

12098.	Which one of the following is a finite set ?
Answer» `{x:x inZZ,xlt5}` `{x:x in WW,xgt=5}` `{x:x in NN,xgt5}` {x:x is an even PRIME NUMBER } ANSWER :A::B

Discussion

12099.	(a+b+c)/( a+b+c) =
Answer» ` TAN ""(A)/(2) tan ""(B)/(2)` ` Tan ""(A)/(2) tan ""( C )/(2)` ` Tan ""(B)/(2)tan ""( C )/(2) ` `1` Answer :A

Discussion

12100.	Find the orthocentre of the triangle whose vertices are given by (5,-2), (-1,2), (1,4)
Answer» ANSWER :ORTHOCENTRE `=(1/5, 14/5)`

Discussion

Explore topic-wise InterviewSolutions in .

If one of the lines of the pair ax^(2)+2hxy+by^(2)=0 bisects the angle between positive direction of the axes then a, b, h satisfy the relation

If cot x =- 5/12, x lies in second quadrant, find the values of other five trignometric functions.

Let OAB be a quadrant of a circle with boundary radii OA = 1, OB = 1and bunding arc AB. Then Maximum area of the reactangle inscribed in it with two vertices on OA and OB and two on the are AB

The sum of first three terms of a G.P. is 13/12 and their product is – 1. Find the common ratio and the terms.

If x = log_(e) [cot((pi)/(4) + theta)] then sin hx =

Find the sum of all natural numbers between 100 and 1000 which are multiple of 5.

Let f be continuous and differentiable function such that f(x) and f(x) have opposite signs evergywhere . Then

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces : { a, b, c } . . . { b, c, d }

Find the derivative of the w.r.t.x a ^(x) e ^(x)

Let A={1,2} and B={3,4}. Write A xx B. How many subsets will A xx B have? List them.

Find the coefficient ofa^5 b^7 in (a-2b)^12.

f(x) is a contiuous function satisfying f(x)*f((1)/(x))=f(x)+f((1)/(x)) and f(1) gt 0, then underset(x to 1) (Lt)f(x) is equal to

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

Consider the complex number z_1 = 3+i and z_2 = 1+i .Using the value of 1/z_2, find (z_1)/z_2

(sin(3alpha))/(1+2cos(2alpha))= ..........

A letter is chosen at random from the word 'ASSASSINATION' Find the probability that latter is a vowel (ii) a consonant

Find the value of: (i) sin 75^(@) (ii) tan 15 ^(@)

The value of k such that the lines 6x^(2)+17xy+12y^(2)=0 and kx^(2)+5xy+3y^(2)=0 may have one line in common is

If X={1,2,3,........10} and A={1,2,3,4,5}, find the number of sets B subseteq X such that A-B={4}

Examine the continuity of the following: e^x tan x

If in a triangle (r_(2)- r_(1))(r_(3)-r_(1))=2r_(3)r_(3) then the triangle is :-

Find the equation of that parabol whose : (i) vertex is (0,0) and focus is (1,0). (ii) vertex is (0,0) and focus is (0,3). (iii) vertex is (4,0) and focus is (2,0). (iv) vertex is (-2,0) and focus is (2,0). (v) vertex is (1,1) and focus is (1,2).

If A=("x y"),B=((a,h),(h,b)),C=((x),(y)) then ABC=

If the origin is the centroid of the triangle PQR with vertices P(2a, 2, 6), Q(-4, 3b, -10) and R(8, 14, 2c), then find the values of a, b and c.

sin 100 in terms of functions of5 theta ,

Assertion (A) : If Tan((pi)/(4)+ theta)+Tan ((pi)/(4)- theta)=k then Tan^(3)((pi)/(4)+ theta)+Tan^(3) ((pi)/(4)- theta)=k^(3)-3k Reason (R) : If A+B=(pi)/(2) then Tan A tan B=1

check whether it is statement or notToday isSunday and tomorrowis Monday.

Write the following interval in set builder form. (6, 12)

Radius of the circle x^2+y^2+8x+10y=8 is 7 unit.

sin alpha + sin beta = 1/4 and cos alpha + cos beta = 1/3 The value of tan (alpha + beta)is

f:R-{0}rarrR,f(x)=(1)/x+px " and "f(1/5)=28/5 then p = …. .

A particle is acted upon by constant forces 4bari+barj-3bark and 3bari+barj-bark which displace it from a point bari+2barj+3bark " to the point " 5bari+4barj+bark. The work done in standard unity by the forces is given by

Find the value of a and b: (2a-5, 4)= (5,b+ 6)

If one of the lines of my^(2)+(1-m^(2))xy-mx^(2)=0 is abisector of angle between the lines xy=0 then m is

sin alpha + sin beta = 1/4 and cos alpha + cos beta = 1/3 The value of sin (alpha + beta) is

Find the number of distinct solutions of secx +tanx = sqrt(3), where 0 le xle3pi.

The plane (qrs)x + (rsp)y + (pqs)z + (pqr)=0, where p, q, r, s are in H.P., represents a family of planes. Find the equation of the plane in the family passing through the point (-3, -2, 1).

cot16^(0)cot44^(0)+cot44^(0)cot76^(0)-cot76^(0)cot16^(0)

A(5,4,6), B(1,-1,3),C(4,3,2) are three points. Find the coordinates of the point in which the bisector of |__BAC meets the side BC.

A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel is

The probability of an event A occuring is 0.5 and of B is 0.3 If A and B are mutually exclusive events , then find the probability of neither A nor B occurring.

Iff : R to Rbe defined f(x) = {(a^(2) cos^(2) x + b^(2) sin^(2) x " if " x le 0),(e^(ex + b) "if " x gt0):}is a continuous function show thatb = 2 log | a| (a ne 0).

Express the following in the form of a+bi, (i) (-5i) (1/8 i), (ii) (-i)(2i)(-1/8i)^(3)

In triangle ABC. Dis on AC such that AD = BC, BD = DC, angleDBC = 2theta angleBAD=3 theta then theta=

P(n):2^n - 1, for n = ……………it is a primenumber.

Find the number ofpermutations of the letter of the words 'INDIA '

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P(0, -4) and B(8, 0).

Which one of the following is a finite set ?

(a+b+c)/( a+b+c) =

Find the orthocentre of the triangle whose vertices are given by (5,-2), (-1,2), (1,4)