14949 + Interview Questions in Maths in Class 11 Page 46 InterviewSolution

2251.	Find the odd man out.
Answer» `(VECB X veca)=- (veca X vecb)` `veci.veci=0` SCALAR PRODUCT is commutative `veca X (vecb .VECC)` is not defined. Answer :B

Discussion

2252.	If sqrt(1+sinA)-sqrt(1-sinA)=2"sin"A/2"then"A/2 in
Answer» `(2n PI-pi/4, 2n pi+pi/4)` `(2n pi+pi/4, 2n pi+(3PI)/4)` `(2n pi+(3pi)/4, 2n pi+(5pi)/4)` `(2n pi+(5pi)/4, 2n pi+(7pi)/4)` ANSWER :A

Discussion

2253.	If the pair of lines given by (x^2+y^2)sin^2alpha=(xcosalpha-ysinalpha)^2 are perpendicular to each other then alpha=
Answer» `pi//2` 0 `pi//4` `pi//3` ANSWER :C

Discussion

2254.	Find approximate value of sin(62)^(@)
Answer» ANSWER :0.8834

Discussion

2255.	Which the following statement is true In /_\ABC ,b,c are fixed and error in A is deltaA then error is a=(2/_\.deltaA)/a
Answer» true false true EITHER false false nor true Answer :A

Discussion

2256.	Find a, b and c if Lt_(xto0)((ae^(x)-bcosx+ce^(-x))/x^(2))=2
Answer» ANSWER :a = 1, B = 2, C = 1

Discussion

2257.	Solve the general value. 2 + sqrt3 sec x - 4 cos x = 2 sqrt3
Answer» ANSWER :`2n pi pm (pi)/(3), 2 N pi pm (5PI)/(6)`

Discussion

2258.	For what value of m are the three lines y=x+1, y=2(x+1) and y=mx+3 concurrent ?
Answer» ANSWER :m = 3

Discussion

2259.	A straight line passing through A (1, -2) makes an angle Tan^(-1) 4/3 with the positive direction of the X-axis in the anticlock wise sense. Find the point on the straight line whose distance from A is 5 units.
Answer» ANSWER :`(-2,-6)`.

Discussion

2260.	If a sec alpha+ b tan alpha= 1 and a^(2) sec^(2) alpha-b^(2) tan^(2) alpha=5 then 4a^(2)-9b^(2)=
Answer» `-a^(2)B^(2)` `a^(2)b^(2)` AB `-ab` ANSWER :A

Discussion

2261.	Ifcos alpha = -12//13 , cot beta = 24//7 , 90^(@) lt alpha lt 180^(@) and 180^(@) lt beta lt 270^(@) , then the quadrant in whichalpha + betalies
Answer» I II III IV Answer :D

Discussion

2262.	If ax ^(2) + 2 hxy + by ^(2) =0 then (dy )/(dx) =
Answer» ANSWER :`- ((AX + HY)/( BX + by))`

Discussion

2263.	Find the square roots of the following : -11-60i
Answer» ANSWER :`+-(5-6i)`

Discussion

2264.	Write the complex number in a+ib form 2i(1+2i)
Answer»

Discussion

2265.	If 1/6 sin theta, cos theta, tan theta are in G.P. then theta is equal to (n in Z)
Answer» `2N PI +-(pi)/3` `2n pi +-(pi)/6` `n pi+(-1)^(n)(pi)/3` `n pi +(pi)/3` ANSWER :A

Discussion

2266.	The value of lambda " such that " lambdax^2-10xy+12y^2+5x-16y-3=0 represents a pair of straight lines, is
Answer» 1 -1 2 -2 Answer :C

Discussion

2267.	If f(x)=(e^(x)+e^(-x))/(2) then the inverse of f(x) is
Answer» `log_(e)(X + sqrt(x^(2)+1))` `log_(e)sqrt(x^(2)+1)` `log_(e)(x + sqrt(x^(2)-1))` `log_(e) ( x-sqrt(x^(2)-1))` ANSWER :C

Discussion

2268.	The maximum possible area that can be enclosed by a wire of length 20 cm by bending it into the from of a sector in sq cms is
Answer» 20 25 30 15 Answer :B

Discussion

2269.	The range of y such that the equation of x,y+cos x=sin x has a real solutiions is
Answer» `[-2,2]` `[-SQRT(2),sqrt(2)]` `[-1,1]` `[-1//2,1//2]` ANSWER :B

Discussion

2270.	Consider the complex number z_1 = 2 - i and z_2 = -2 + iFind (z_1z_2)/z_1. Hence, find abs((z_1z_2)/z_1)
Answer» ANSWER :`-2/5+11/5i, SQRT5`

Discussion

2271.	If sintheta+costheta=1, then the value of sin(2theta) is
Answer» 1 `(1)/(2)` 0 `-1` ANSWER :C

Discussion

2272.	Ifacos2theta+bsin2theta=c" has "theta_(1),theta_(2)as its solutions then show that tantheta_(1)+tantheta_(2)=(2b)/(c+a)tantheta_(1).tantheta_(2)=(c-a)/(c+a) and hence show that tan(theta_(1)+theta_(2))=b//a.
Answer» ANSWER :`(B)/(a)`

Discussion

2273.	Altitude AD of an equilateral triangle ABC is a diameter of circle. If circle intersect AB and AC at E and F then (EF)/(BC) =
Answer» `3/4` `4/3` `1/2` NONE ANSWER :A

Discussion

2274.	The value of (3 + cot 76^(@) cos 16^(@))/( cot 76^(@) + cot 16^(@))is
Answer» `tan 44 ^(@)` `COT 46 ^(@)` `tan 2^(@)` `tan 46^(@)` Answer :D

Discussion

2275.	Assertion (A): In the expansion of (a +b)^(n) n in N the coefficient at equidistant from the beginning and from the end are equal.Reason(R): nC_(r)=nC_(n-r)
Answer» SINCE Reason is TRUE ASSERTION is true Reason is not correct EXPLANATION for Assertion Both Assertion and Reason are not correct Reason is correct but Assertion is not correct. Answer :a

Discussion

2276.	Assertion: The equation ax^(2)+bx+c=0has two roots. Reason: ax^(2)+bx+c=0 can be written as (x-alpha)(x-beta) = 0 for some alpha and beta
Answer» REASON is CORRECT and so ASSERTION is correct Reason is correct and so Assertion is not correct. Both Assertion and Reason are incorrect There is no LINK between Assertion and Reason. Answer :A

Discussion

2277.	The sum of fournumbers in G.Pis 60 and the arithmetic mean of the first and the last numbers is 18 . Find the numbers .
Answer» ANSWER :4,8,16,32 or 32,16,8,4

Discussion

2278.	Find the derivative of w.r.to x cosec ^(4)x
Answer» ANSWER :`4 COSEC ^(4) COT X `

Discussion

2279.	Find the coefficient of the term involving x^(32) and x^(-17) in the expansion of (x^(4)-(1)/(x^(3)))^(15)
Answer» ANSWER :`=-1365`

Discussion

2280.	The value of alpha such that "sin"^(-1)2/(sqrt(5)),"sin"^(-1)3/(sqrt(10)), sin^(-1) alpha are the angles of a triangle is
Answer» `(-1)/(SQRT(2))` `1/2` `1/(sqrt(3))` `1/(sqrt(2))` ANSWER :D

Discussion

2281.	If an arc of length l of a circle of radius r subtends an angle theta radians at the centre what is the relation connecting l , r , theta
Answer» SOLUTION :`l=rtheta`

Discussion

2282.	Find the derivative of the w.r.t.x (ac + b )^(n ) (cx + d) ^(n)
Answer» ANSWER :`(AXC + B ) ^(N)`

Discussion

2283.	Ifa= 3, b=4, c= 5 thensin""(A)/(2) =
Answer» ` (1)/(SQRT(10))` ` ( 2)/(sqrt(10 )) ` ` ( 3)/(sqrt(10))` ` (4)/(sqrt(( 10 ))` ANSWER :A

Discussion

2284.	A stone is dropped into a quiet lake and ripples move in circles at the speed of 5 cm/sec. At the instant when the radius of circular ripple is 8cm, how fast is the enclosed area increases?
Answer» ANSWER :`80 PI cm^(2)//sec`

Discussion

2285.	Find equation of line passes from point of intersection at lines 5x-3y=1 and 2x+3y-23=0 and perpendicular to line 5x-3y=1.
Answer» Answer :`63X + 105y - 781 =0`, which is required EQUATION of line.

Discussion

2286.	A man starts repaying a loan as first instalment of Rs. 100. If he increases theinstalment by Rs 5 every month, what amount he will pay in the 30^("th")instalment?
Answer» ANSWER :RS 245

Discussion

2287.	If cos theta = (cos alpha - cos beta)/(1-cos alpha cos beta), then one of the values of tan((theta)/(2)) is
Answer» `"COT"(BETA)/(2)"tan"(ALPHA)/(2)` `tan alpha "tan"(beta)/(2)` `"tan"(beta)/(2)"cot" (alpha)/(2)` `"tan"^(2) (alpha)/(2) "tan"^(2) (beta)/(2)` ANSWER :A

Discussion

2288.	If y= sqrt(logx+sqrt(logx+sqrt(logx+...oo))), then(dy)/(dx) is
Answer» `X/(2y-1)` `(x)/(2y+1)` `(1)/(x(2y-1))` `1/(x(1-2y))` ANSWER :C

Discussion

2289.	Two unbiased dice are thrown . Find the probability that the sum of the numbers obtained on the two dice is neither a multiple of 3 nor a multiple of 4.
Answer» ANSWER :`(4)/(9)`

Discussion

2290.	Find unit vector perpendicular to both bar(i) + bar(j) + bar(k) and 2bar(i) + bar(j) + 3bar(k).
Answer» ANSWER :`+- ((2vec(i)-VEC(J)-vec(K)))/(SQRT6)`

Discussion

2291.	Find the ratio in which the join of A (2,1,5) and B (3,4,3) is divided by the plane 2x + 2y-2z=1. Also, find the coordinates of the point of division,
Answer» ANSWER :`5,7 ((29)/(12) , (9)/(4),(25)/(6))`

Discussion

2292.	f(x)=2x+cot^(-1)x+log (sqrt(1+x^(2))-x)
Answer» increasing in `[0,oo]` decrease in `[0,oo)` NEITHER INCREASE nor DECREASES in `[0,oo)` INCREASES in `(-oo,oo)` ANSWER :A::D

Discussion

2293.	Find the derivate of x^(-3)(5+3x)
Answer» ANSWER :`(-3)/(X^(4))[5+2x]`

Discussion

2294.	The extremevaluesof sin^(2) ((pi)/(3)+x)+ sin^(2) ((pi)/(3) -x)is
Answer» `[(1)/(2),1]` `[1,(3)/(2)]` `[(3)/(2),2]` `[(1)/(2),(3)/(2)]` ANSWER :3

Discussion

2295.	If p and q are the lengths of perpendiculars from the origin to the lines x cos theta- y sin theta = k cos 2 theta and x sec theta + y cosec theta=k respectively, prove that p^(2) + 4q^(2) = k^(2).
Answer» ANSWER :`=k^2` which is REQUIRED RESULT.

Discussion

2296.	If 'O' is circumcente and 'H' is orthocentre of DeltaABC, then {:("List-I", "List-II"), ("A) "bar(OA)+bar(OB)+bar(OC), "1) "1/2bar(HO)), ("B) "bar(HA)+bar(HB)+bar(HC), "2) "2bar(HO)), ("C) "bar(AH)+bar(HB)+bar(HC), "3) "2bar(AO)), ("D) "bar(OG), "4) "1/3bar(OH)), ("", "5) "bar(OH)):} The correct matching is
Answer» `{:(A, B, C, D), (1, 5, 3, 2):}` `{:(A, B, C, D), (5, 2, 4, 3):}` `{:(A, B, C, D), (5, 2, 3, 4):}` `{:(A, B, C, D), (2, 4, 3, 5):}` Answer :C

Discussion

2297.	Statement : if a natural number is even, then is square is also even. write this statement in 5 different forms of the same meaning.
Answer» Solution :(1).(i) a natural number is even imlies that its square is even. (ii) a natural number is even only if its square is even. (iii) for a natural number to be even it is NECESSARY that its square is even. (IV) for the square of a natural number to be even it is sufficient the number is even. (V) if the square of a natural number is not even, then the natural number is not even.

Discussion

2298.	The sum of the series sum_(r=0)^(10) .^(20)C_(r), is2^(19)+{(.^(20)C_(10))/2}.
Answer» ANSWER :FALSE

Discussion

2299.	e^(sin h^(-1)(tan theta)) =
Answer» `SEC THETA` `TAN theta` `sec theta + tan theta` `sec theta - tan theta` ANSWER :C

Discussion

2300.	The value of tan^(-1)((xcostheta)/(1-xsintheta))-cot^(-1)((costheta)/(x-sintheta)) is
Answer» `2THETA` `THETA` `theta//2` INDEPENDENT of `theta` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Find the odd man out.

If sqrt(1+sinA)-sqrt(1-sinA)=2"sin"A/2"then"A/2 in

If the pair of lines given by (x^2+y^2)sin^2alpha=(xcosalpha-ysinalpha)^2 are perpendicular to each other then alpha=

Find approximate value of sin(62)^(@)

Which the following statement is true In /_\ABC ,b,c are fixed and error in A is deltaA then error is a=(2/_\.deltaA)/a

Find a, b and c if Lt_(xto0)((ae^(x)-bcosx+ce^(-x))/x^(2))=2

Solve the general value. 2 + sqrt3 sec x - 4 cos x = 2 sqrt3

For what value of m are the three lines y=x+1, y=2(x+1) and y=mx+3 concurrent ?

A straight line passing through A (1, -2) makes an angle Tan^(-1) 4/3 with the positive direction of the X-axis in the anticlock wise sense. Find the point on the straight line whose distance from A is 5 units.

If a sec alpha+ b tan alpha= 1 and a^(2) sec^(2) alpha-b^(2) tan^(2) alpha=5 then 4a^(2)-9b^(2)=

Ifcos alpha = -12//13 , cot beta = 24//7 , 90^(@) lt alpha lt 180^(@) and 180^(@) lt beta lt 270^(@) , then the quadrant in whichalpha + betalies

If ax ^(2) + 2 hxy + by ^(2) =0 then (dy )/(dx) =

Find the square roots of the following : -11-60i

Write the complex number in a+ib form 2i(1+2i)

If 1/6 sin theta, cos theta, tan theta are in G.P. then theta is equal to (n in Z)

The value of lambda " such that " lambdax^2-10xy+12y^2+5x-16y-3=0 represents a pair of straight lines, is

If f(x)=(e^(x)+e^(-x))/(2) then the inverse of f(x) is

The maximum possible area that can be enclosed by a wire of length 20 cm by bending it into the from of a sector in sq cms is

The range of y such that the equation of x,y+cos x=sin x has a real solutiions is

Consider the complex number z_1 = 2 - i and z_2 = -2 + iFind (z_1z_2)/z_1. Hence, find abs((z_1z_2)/z_1)

If sintheta+costheta=1, then the value of sin(2theta) is

Ifacos2theta+bsin2theta=c" has "theta_(1),theta_(2)as its solutions then show that tantheta_(1)+tantheta_(2)=(2b)/(c+a)tantheta_(1).tantheta_(2)=(c-a)/(c+a) and hence show that tan(theta_(1)+theta_(2))=b//a.

Altitude AD of an equilateral triangle ABC is a diameter of circle. If circle intersect AB and AC at E and F then (EF)/(BC) =

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

Assertion (A): In the expansion of (a +b)^(n) n in N the coefficient at equidistant from the beginning and from the end are equal.Reason(R): nC_(r)=nC_(n-r)

Assertion: The equation ax^(2)+bx+c=0has two roots. Reason: ax^(2)+bx+c=0 can be written as (x-alpha)(x-beta) = 0 for some alpha and beta

The sum of fournumbers in G.Pis 60 and the arithmetic mean of the first and the last numbers is 18 . Find the numbers .

Find the derivative of w.r.to x cosec ^(4)x

Find the coefficient of the term involving x^(32) and x^(-17) in the expansion of (x^(4)-(1)/(x^(3)))^(15)

The value of alpha such that "sin"^(-1)2/(sqrt(5)),"sin"^(-1)3/(sqrt(10)), sin^(-1) alpha are the angles of a triangle is

If an arc of length l of a circle of radius r subtends an angle theta radians at the centre what is the relation connecting l , r , theta

Find the derivative of the w.r.t.x (ac + b )^(n ) (cx + d) ^(n)

Ifa= 3, b=4, c= 5 thensin""(A)/(2) =

A stone is dropped into a quiet lake and ripples move in circles at the speed of 5 cm/sec. At the instant when the radius of circular ripple is 8cm, how fast is the enclosed area increases?

Find equation of line passes from point of intersection at lines 5x-3y=1 and 2x+3y-23=0 and perpendicular to line 5x-3y=1.

A man starts repaying a loan as first instalment of Rs. 100. If he increases theinstalment by Rs 5 every month, what amount he will pay in the 30^("th")instalment?

If cos theta = (cos alpha - cos beta)/(1-cos alpha cos beta), then one of the values of tan((theta)/(2)) is

If y= sqrt(logx+sqrt(logx+sqrt(logx+...oo))), then(dy)/(dx) is

Two unbiased dice are thrown . Find the probability that the sum of the numbers obtained on the two dice is neither a multiple of 3 nor a multiple of 4.

Find unit vector perpendicular to both bar(i) + bar(j) + bar(k) and 2bar(i) + bar(j) + 3bar(k).

Find the ratio in which the join of A (2,1,5) and B (3,4,3) is divided by the plane 2x + 2y-2z=1. Also, find the coordinates of the point of division,

f(x)=2x+cot^(-1)x+log (sqrt(1+x^(2))-x)

Find the derivate of x^(-3)(5+3x)

The extremevaluesof sin^(2) ((pi)/(3)+x)+ sin^(2) ((pi)/(3) -x)is

If p and q are the lengths of perpendiculars from the origin to the lines x cos theta- y sin theta = k cos 2 theta and x sec theta + y cosec theta=k respectively, prove that p^(2) + 4q^(2) = k^(2).

Statement : if a natural number is even, then is square is also even. write this statement in 5 different forms of the same meaning.

The sum of the series sum_(r=0)^(10) .^(20)C_(r), is2^(19)+{(.^(20)C_(10))/2}.

e^(sin h^(-1)(tan theta)) =

The value of tan^(-1)((xcostheta)/(1-xsintheta))-cot^(-1)((costheta)/(x-sintheta)) is