Explore topic-wise InterviewSolutions in Class 12.

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your Class 12 knowledge and support exam preparation. Choose a topic below to get started.

151.

Show that sin A sin ((pi)/(3)+A) sin ((pi)/(3) -A)=(1)/(4) sin 3A

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`=(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>). (<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)/(4)=(3)/(<a href="https://interviewquestions.tuteehub.com/tag/16-276476" style="font-weight:bold;" target="_blank" title="Click to know more about 16">16</a>)`</body></html>
Discussion
152.

If the matrix A= |{:(1,2,3,0),(2,4,3,2),(3,2,1,3),(6,8,7,alpha):}| is of rank 3, then alpha equals to

Answer» <html><body><p>`-<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>`<br/>5<br/>4<br/>1</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>
Discussion
153.

C_0 + C_1 + 2.C_2(3) + 3.C_3(3^2)+ 4.C_4(3^3) + ……+n.C_n 3^(n-1) =

Answer» <html><body><p>`n.<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>^(n-<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>) + 1` <br/>`<a href="https://interviewquestions.tuteehub.com/tag/2n-300431" style="font-weight:bold;" target="_blank" title="Click to know more about 2N">2N</a>. 4^(n-1) + 1 ` <br/>`n.4^(n-1) - 1` <br/>`n.4^(n+1) - 1` </p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :A</body></html>
Discussion
154.

If A ={x:x in I, -2 le x le 2 }, B={x : x in I , 0 le x le 3 }, C={x :x in N , 1 le x le 2}, D={(x,y): (x,y) in N xx N , x+y=8}. Then :

Answer» <html><body><p>`n (B uuC)`=<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a><br/>n(D)=<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a><br/>`n(Auu(B uu C))=5`<br/><a href="https://interviewquestions.tuteehub.com/tag/none-580659" style="font-weight:bold;" target="_blank" title="Click to know more about NONE">NONE</a> of these </p>Answer :D</body></html>
Discussion
155.

If A and B be independent events with P(A) = 1/4 and (P(A cupB) = 2P(B) - P(A), then P(B) is equal to

Answer» <html><body><p>`2/5`<br/>`1/5`<br/>`3/5`<br/><a href="https://interviewquestions.tuteehub.com/tag/none-580659" style="font-weight:bold;" target="_blank" title="Click to know more about NONE">NONE</a> of these</p>Answer :A</body></html>
Discussion
156.

L: 3x - 4y = 0 is a diameter of the ellipsex^2/20+y^2/9=1. Y=m'x is the diameter of the ellipse bisecting 20 9 the chords parallel to L. If m represents the slope of L, then the value of (m + m') is equal to

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :0.15</body></html>
Discussion
157.

underset(x to 0)lim ((e^(1//x) -1)/(e^(1//x) + 1))=

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`<a href="https://interviewquestions.tuteehub.com/tag/log-543719" style="font-weight:bold;" target="_blank" title="Click to know more about LOG">LOG</a>(<a href="https://interviewquestions.tuteehub.com/tag/e-444102" style="font-weight:bold;" target="_blank" title="Click to know more about E">E</a>^(<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>)+e^(-x))+<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>`</body></html>
Discussion
158.

Find the principle value of cot^(-1)((-1)/(sqrt(3)))

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(<a href="https://interviewquestions.tuteehub.com/tag/2pi-1838601" style="font-weight:bold;" target="_blank" title="Click to know more about 2PI">2PI</a>)/<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>`</body></html>
Discussion
159.

Six coins are tossed simultaneously . The odds in favour of getting 2 heads is

Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/10-261113" style="font-weight:bold;" target="_blank" title="Click to know more about 10">10</a> : 11`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a> : 5`<br/>`5 : 3`<br/>`15 : <a href="https://interviewquestions.tuteehub.com/tag/49-318440" style="font-weight:bold;" target="_blank" title="Click to know more about 49">49</a>`</p>Answer :D</body></html>
Discussion
160.

If y=tan^(-1)[(5cosx-12sinx)/(12cosx+5sinx)], then (dy)/(dx)=

Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a><br/>-1<br/>-<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a><br/>`(1)/(2)`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>
Discussion
161.

(sqrt3+i)^7+(sqrt3-i)^7=

Answer» <html><body><p>`128sqrt3`<br/>`256sqrt3`<br/>`-128sqrt3`<br/>`-256sqrt3`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>
Discussion
162.

A tangent to the circle x^(2)+y^(2)=4 meets the coordinate axes at P and Q. The locus of midpoint of PQ is

Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>/(<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>))+1/(y^(2))=1`<br/>`1/(x^(2))+1/(y^(2))=1/2`<br/>`1/(x^(2))+1/(y^(2))=1/3`<br/>`1/(x^(2))+1/(y^(2))=1/4`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :A</body></html>
Discussion
163.

Assertion (A): In theexpansion of (1+x)^n, three consecutive terms are 5, 10,10 then n = 5 Reason (R ): If the coefficient of r^(th), (r + 1)^(th), (r + 2)^(th) terms of (1 +x)^n are in A.P. then (n-2r)^2 = n +2

Answer» <html><body><p>A and R are true , R is <a href="https://interviewquestions.tuteehub.com/tag/correct-409949" style="font-weight:bold;" target="_blank" title="Click to know more about CORRECT">CORRECT</a> explanation of A<br/>A and R are true, R is not the correct explanation of A <br/>A is true , R is false <br/>A is false R is true </p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :D</body></html>
Discussion
164.

If real numbers a, b, c, d, e satisfy a+1=b + 2 = c+ 3 = d + 4 = e + 5 = a + b + c + d + e + 3 then find the value of a^2 + b^2 + c^2 + d^2 + e^2

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/10-261113" style="font-weight:bold;" target="_blank" title="Click to know more about 10">10</a></body></html>
Discussion
165.

bar(x),bar(y),bar(z) are non zero vectors. If (bar(x)""_(,)^(hat)bar(y))=(pi)/(2 and bar(z)=bar(x)+bar(y), then ……..

Answer» <html><body><p>`|<a href="https://interviewquestions.tuteehub.com/tag/bar-892478" style="font-weight:bold;" target="_blank" title="Click to know more about BAR">BAR</a>(x)|^(2)+|bar(y)|^(2)+|bar(<a href="https://interviewquestions.tuteehub.com/tag/z-750254" style="font-weight:bold;" target="_blank" title="Click to know more about Z">Z</a>)|^(2)=3`<br/>`|bar(x)|^(2)+|bar(y)|^(2)+|bar(z)|^(2)=<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>`<br/>`|bar(x)|^(2)-|bar(y)|^(2)=|bar(z)|^(2)` <br/>`|bar(x)|^(2)+|bar(y)|^(2)=|bar(z)|^(2)` </p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :D</body></html>
Discussion
166.

Solve 4x^(2)-8x-3=0 by completing the square.

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>-(<a href="https://interviewquestions.tuteehub.com/tag/sqrt-1223129" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT">SQRT</a>(<a href="https://interviewquestions.tuteehub.com/tag/7-332378" style="font-weight:bold;" target="_blank" title="Click to know more about 7">7</a>))/(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)`</body></html>
Discussion
167.

The point ef intersection of the tangents to the circle passing through (4, 7), (5,6) (1,5) at the points where it is cut by the line 5x+y+17=0

Answer» <html><body><p>(-4,2)<br/>(4,2)<br/>(6,4)<br/>(8,4)</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :A</body></html>
Discussion
168.

If a,P are the eccentric angles of the extremeties of a focal chord of the ellipse (i) e cos (alpha+beta)/(2)=cos (alpha-beta)/(2) (ii) tan (alpha)/(2) tan (beta)/(2)=(e-1)/(e+1)

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(1-e)/(1+e)`</body></html>
Discussion
169.

The vector c is perpendicular to both a = (1, -2, -1), b = (2, 1, -1) and c also satisfyies |c xx (I - j + k)| = 2 sqrt(6) then c =

Answer» <html><body><p>`+- (3i - j + <a href="https://interviewquestions.tuteehub.com/tag/5k-326491" style="font-weight:bold;" target="_blank" title="Click to know more about 5K">5K</a>)`<br/>`+- (-<a href="https://interviewquestions.tuteehub.com/tag/4i-318769" style="font-weight:bold;" target="_blank" title="Click to know more about 4I">4I</a> + <a href="https://interviewquestions.tuteehub.com/tag/5j-326488" style="font-weight:bold;" target="_blank" title="Click to know more about 5J">5J</a> + k)`<br/>`+- (I + j + k)` <br/>none</p>Answer :A</body></html>
Discussion
170.

Let X be a discrete random variable whose probability distribution is defined as follows: P(X=x)={(k(x+1)",",x="1, 2, 3, 4"),(2kx",",x="5,6,7"),(0"", "Otherwise"):}Where k is a constant. Calculate (i) the value of k (ii) E(X) (iii) Standard deviation of X.

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(i) (<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/50-322056" style="font-weight:bold;" target="_blank" title="Click to know more about 50">50</a>), (<a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a>) 5.2, (<a href="https://interviewquestions.tuteehub.com/tag/iii-497983" style="font-weight:bold;" target="_blank" title="Click to know more about III">III</a>) 1.7`</body></html>
Discussion
171.

Form the differential equations corresponding to the family of curves. (i) y = c(x-2c) where c is a parameter. (ii) y= a cos 3x + b sin 3x where a, b are parameters. (iii) y = a cos x + b sin x where a, b are parameters. (iv) y = a e^(x) + b e^(-x) where a, b are parameters.

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :(i) `y = xy_(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>) - 2y_(1)^(2)` (<a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a>) `y_(2) + 9y = <a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>` <br/> (iii) `y_(2) + y = 0` (iv) `y_(2) = y`</body></html>
Discussion
172.

Find the set of all values of a for which the roots of the equation x^2-2ax + a^2 + a-3=0 are less than 3,

Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/altbr2-1974331" style="font-weight:bold;" target="_blank" title="Click to know more about ALT2">ALT2</a>`<br/>`2leale3`<br/>`3ltale4`<br/>`agt4`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :A</body></html>
Discussion
173.

If f(x)=a+bx+cx^(2)where cgt0 and b^(2)-4aclt0 then the area enclosed by the co-ordinate axes, the line x=2, and the curve y=f(x) is given by

Answer» <html><body><p>`(1)/(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>){4f(1)+f(2)}`<br/>`(1)/(2){f(0)+4f(1)}`<br/>`(1)/(2){f(0)+4f(1)+f(2)}`<br/>`(1)/(3){f(0)+4f(1)+f(2)}`</p>Solution :Area`=underset(0)overset(2)(int)ydx=underset(0)overset(<a href="https://interviewquestions.tuteehub.com/tag/20-287209" style="font-weight:bold;" target="_blank" title="Click to know more about 20">20</a>)(int)(a+bx+cx^(2))dx=2a +<a href="https://interviewquestions.tuteehub.com/tag/2b-300274" style="font-weight:bold;" target="_blank" title="Click to know more about 2B">2B</a>+(<a href="https://interviewquestions.tuteehub.com/tag/8c-340069" style="font-weight:bold;" target="_blank" title="Click to know more about 8C">8C</a>)/(3)`<br/> `=(1)/(3)(6a+6b+8c)`<br/> `=(1)/(3){f(0)+4f(1)+f(2)}`<br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/VBA_IRP_FST_2_E01_166_S01.png" width="80%"/></body></html>
Discussion
174.

Evaluate : int_(0)^(pi//2) ( sin x)/(1 +cos^2 x) dx

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`pi//4`</body></html>
Discussion
175.

Evaluate the following integrals int(dx)/(1+x^(4))

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(1)/(2sqrt(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>))<a href="https://interviewquestions.tuteehub.com/tag/tan-1238781" style="font-weight:bold;" target="_blank" title="Click to know more about TAN">TAN</a>^(-1)((x^(2)-1)/(xsqrt(2)))+(1)/(4sqrt(2))<a href="https://interviewquestions.tuteehub.com/tag/log-543719" style="font-weight:bold;" target="_blank" title="Click to know more about LOG">LOG</a>|(x^(2)+1+sqrt(2)x)/(x^(2)+1-sqrt(2)x)|+<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>`</body></html>
Discussion
176.

A: In a Delta ABC, if r_1=2r_2=3r_3 then a:b=5:4. R: In a Delta ABC, if xr_1=yr_2=zr_3=(x+y+z)r then a:b:c=y+z:z+x:x+j

Answer» <html><body><p>A is <a href="https://interviewquestions.tuteehub.com/tag/true-713260" style="font-weight:bold;" target="_blank" title="Click to know more about TRUE">TRUE</a>, <a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a> is true and R is <a href="https://interviewquestions.tuteehub.com/tag/correct-409949" style="font-weight:bold;" target="_blank" title="Click to know more about CORRECT">CORRECT</a> <a href="https://interviewquestions.tuteehub.com/tag/explanation-455162" style="font-weight:bold;" target="_blank" title="Click to know more about EXPLANATION">EXPLANATION</a> of A<br/>A is true, R is true and R is not correct explanation of A<br/>A is true, R is false<br/>A is false, R is true</p>Answer :A</body></html>
Discussion
177.

If C_1 (1, 3) and C_2(4, 3)are the centres of two circles whose radical axis is y-axis. If the radius of the 1st circle is 2sqrt2 units, then the radius of the second circle is

Answer» <html><body><p>`sqrt23`<br/>3<br/>4<br/>`<a href="https://interviewquestions.tuteehub.com/tag/2sqrt2-1838926" style="font-weight:bold;" target="_blank" title="Click to know more about 2SQRT2">2SQRT2</a>`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :A</body></html>
Discussion
178.

The symmetric equation of the line passing through (3, 1, - 1) and (3, 2, -6) is …............

Answer» <html><body><p>`(x-3)/(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)=(1-y)/(1)=(z+1)/(<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>)`<br/>`x=3,(y-1)/(1)=(z+1)/(-5)`<br/>`x=3,(y-1)/(1)=(z+1)/(-5)`<br/>`x=3,(1-y)/(1)=(z+1)/(-5)`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>
Discussion
179.

A matrix denotes a number .

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/false-459184" style="font-weight:bold;" target="_blank" title="Click to know more about FALSE">FALSE</a></body></html>
Discussion
180.

Let f,g:RrarrR be two functions defined as f(x)=|x|+x and g(x)=|x|-xAAx in R. Then f(g) (x) for xlt0 is

Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)0<br/>2)4x<br/>3)-4x<br/>4)2x</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>
Discussion
181.

int_(1)^(e) e^(x)((x-1)/(x^(2)))dx=

Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/e-444102" style="font-weight:bold;" target="_blank" title="Click to know more about E">E</a>^(e-1)-e`<br/>`e^(e-1)`<br/>`e^(e-1)+e`<br/>`e`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :A</body></html>
Discussion
182.

Let P(x) be a polynomial of degree n with leading coefficient 1. Let v (x) be any function and v_(1)(x) = int v (x) dx, v_(2)(x)=intv_(1)(x)dx...v_(n+1)=intv_(n)(x)dx. then int P(x) v(x) dx is equal to

Answer» <html><body><p>&lt;<a href="https://interviewquestions.tuteehub.com/tag/p-588962" style="font-weight:bold;" target="_blank" title="Click to know more about P">P</a>&gt;`P(<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>)v_(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)(x)+(p'(x)v_(2)(x))/(2!)+(P''(x)v_(3)(x))/(3!)...+(v_(n+1)(x))((n+1)!)`/<br/>`P(x)v_(1)(x)-P(x)v_(2)(x)+P''(x)v_(3)(x)...+(-1)^(n)n!v_(n+1)(x)`<br/>`P(x)v_(1)(x)+P'(x)v_(2)+P''(x)v_(3)(x)...+nv_(n)+1(x)`<br/>`P(x)v_(1)(x)-(p'(x)v_(2)(x))/(2!)+(P''(x)v_(3)(x))/(3!)...+(-1)^(n)(v_(n+1)(x))/((n+1))!`</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>
Discussion
183.

{:("Respiration","Atmosphere","Alveoli","Deoxygenated blood","Oxygenated blood","Tissue"),(O_(2),159,104,B,95,D),(CO_(2),0.3,A,45,C,45):} Correct option for A, B, C, D respectively is :-

Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/40-314386" style="font-weight:bold;" target="_blank" title="Click to know more about 40">40</a>, <a href="https://interviewquestions.tuteehub.com/tag/45-316951" style="font-weight:bold;" target="_blank" title="Click to know more about 45">45</a>, <a href="https://interviewquestions.tuteehub.com/tag/95-342378" style="font-weight:bold;" target="_blank" title="Click to know more about 95">95</a>, 40<br/>40, 40, 40, 40<br/>45, 40, 95, 40<br/>40, 45, 40, 40</p>Answer :A</body></html>
Discussion
184.

If B sub C, prove that A\\B =A\\C.Is this result true when difference is replaced by symmetric difference ? Give reason.

Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :If `<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a> <a href="https://interviewquestions.tuteehub.com/tag/sub-1230791" style="font-weight:bold;" target="_blank" title="Click to know more about SUB">SUB</a> C`, then `x in B impliesx in C`<br/>Now `x in A -C <impliesx:x a="" c="" in="" x=""> `<implies :x="" a="" b="" in="" x="">` <implies a-b="" in="">`:. A -C =A -B` <br/> But `A <a href="https://interviewquestions.tuteehub.com/tag/delta-947703" style="font-weight:bold;" target="_blank" title="Click to know more about DELTA">DELTA</a> B != A Delta C`</implies></implies></impliesx:x></body></html>
Discussion
185.

Consider the frequency distribution If the variance of this distribution is 60000, then the coefficient of variation of the distribution is

Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/60-328817" style="font-weight:bold;" target="_blank" title="Click to know more about 60">60</a><br/>`(400sqrt(<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a>))/(17)`<br/>`(400sqrt(6))/(<a href="https://interviewquestions.tuteehub.com/tag/9-340408" style="font-weight:bold;" target="_blank" title="Click to know more about 9">9</a>)`<br/>`595.75`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>
Discussion
186.

If ((x-3)^((-|x|)/x) sqrt((x-4)^(2))(17-x))/(sqrt(-x)(-x^(2)+x-1)(|x|-32))lt0 then no. of integers x satisfying the inequality is:

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :`00031.00`</body></html>
Discussion
187.

underset(n to oo)lim (1.1!+2.2!+3.3!+...+n.n!)/((n+1)!)=

Answer» <html><body><p>only I is true<br/>only <a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a> is true<br/>both I and II are true<br/>neither I nor II are true</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>
Discussion
188.

An open topped box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminimum and folding up the sides. Find the volume of the largest such box.

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(<a href="https://interviewquestions.tuteehub.com/tag/200-288914" style="font-weight:bold;" target="_blank" title="Click to know more about 200">200</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/27-298706" style="font-weight:bold;" target="_blank" title="Click to know more about 27">27</a>)("<a href="https://interviewquestions.tuteehub.com/tag/meter-1095017" style="font-weight:bold;" target="_blank" title="Click to know more about METER">METER</a>")^(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)`</body></html>
Discussion
189.

The vertices of a triangle ABC are A-=(2,0,2), B(-1,1,1) and C-=(1,-2,4). The points D and E divide the sides AB and CA in the ratio 1:2 respectively. Another point F is taken in space such that the perpendicular drawn from F to the plane containing DeltaABC, meets the plane at the point of intersection of the line segments CD and BE. If the distance of F from plane of triangle ABC issqrt(2), units, ten

Answer» <html><body><p>the volume of the tetrahdron `ABCD` is `7/3` <a href="https://interviewquestions.tuteehub.com/tag/cubic-940181" style="font-weight:bold;" target="_blank" title="Click to know more about CUBIC">CUBIC</a> units<br/>the volume of the tetrahedron `ABCF` is `7/6` cubic units<br/>one of the equation of the line `AF` is `vecr=(2hati+2hatk)+<a href="https://interviewquestions.tuteehub.com/tag/lamda-536483" style="font-weight:bold;" target="_blank" title="Click to know more about LAMDA">LAMDA</a>(2hatk-hati)(lamda in R)` <br/>one of the equuation of the line `AF` is `vecr=(2hati+2hatk)+mu(hati+7hatk)`</p>Solution :`CD:vecr(hati-2hatj+4hatk)+(lamda)/3(7hatj-7hatk)` <br/> `BE:vecr=(-hati+hatj+k)+(mu)/3(7hati-7hatj+7hatk)` <br/> `P-=(hati-hatj+3hatj)` <br/> Area of tetrahedron `ABCD` <br/> `=1/3` (Area of base triangle) `<a href="https://interviewquestions.tuteehub.com/tag/xx-747671" style="font-weight:bold;" target="_blank" title="Click to know more about XX">XX</a>` height `=7/3` cubic units <br/> `vec(AB)xxvec(AC)=7hatj+7hatk,|vec(<a href="https://interviewquestions.tuteehub.com/tag/pf-1152667" style="font-weight:bold;" target="_blank" title="Click to know more about PF">PF</a>)|=PF=sqrt(2)` units <br/> `vec(PF)=sqrt(2)((7hatj+7hatk)/(sqrt(49+49)))=hatj+hatk=P.V`. of `F-P.V.` of `P` <br/> `P.V.` of `F=hati+4hatk` <br/> Vector equation of `AF` is `vecr=2(hati+hatk)+<a href="https://interviewquestions.tuteehub.com/tag/alpha-858274" style="font-weight:bold;" target="_blank" title="Click to know more about ALPHA">ALPHA</a>(-hati+2hatk)` <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/FIT_JEE_PT3_P1_E01_294_S01.png" width="80%"/></body></html>
Discussion
190.

In the following cases, find the distance of each of the given points from the corresponding given plane.{:("Point","Plane"),("(a) (0, 0, 0)","3x – 4y + 12z = 3"),("(b) (3, -2, 1)","2x - y + 2z + 3 = 0"),("(C) (2, 3, -5)","x + 2y – 2z = 9"),("(d) (6, 0, 0)","2x - 3y + 6z - 2 = 0"):}

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :(a) `=(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)/(13)`<br/>(<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>) `=(13)/(3)`<br/>(<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>) =3<br/>(d) = 2</body></html>
Discussion
191.

3 numbers are chosen at random from the first 20 natural numbers. Then the probability that the product is even is

Answer» <html><body><p>`(.^(10)C_(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>))/(.^(20)C_(3))`<br/>`1-(.^(10)C_(3))/(.^(20)C_(3))`<br/>`(10)/(.^(20)C_(3))`<br/>`(1)/(.^(20)C_(3))`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :B</body></html>
Discussion
192.

f(x) is quadratic expression such that f(x) is negative when x in (-oo, - (5)/(3))cup (3,oo) and positive when x in (- (5)/(3),3) g(x) is another quadratic expression sunc that g (x) is negative when x in (3, 9/4) and positive when x in R - [3,9/2] Then, the sign of f(x) g(x) is [0,5] is

Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/positive-1159908" style="font-weight:bold;" target="_blank" title="Click to know more about POSITIVE">POSITIVE</a> in `[0,9/2]` and negative in `(9/2, <a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>)`<br/>positive in `[0,3] cup (3,9/2)` and negative in `(9/2,5]`<br/>positive in `[0,3) cup (3,9/2)` and negative in `(9/5 , 5]`<br/>positive in `(0,3) cup (3,9/2) cup (9/2,5]`</p>Answer :<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>
Discussion
193.

If x^(3) + 8xy + y^(3) = 64, then (dy)/(dx) =

Answer» <html><body><p>`-(<a href="https://interviewquestions.tuteehub.com/tag/3x-310805" style="font-weight:bold;" target="_blank" title="Click to know more about 3X">3X</a>^2 + <a href="https://interviewquestions.tuteehub.com/tag/8y-340347" style="font-weight:bold;" target="_blank" title="Click to know more about 8Y">8Y</a>)/(<a href="https://interviewquestions.tuteehub.com/tag/8x-340330" style="font-weight:bold;" target="_blank" title="Click to know more about 8X">8X</a> + 3y^2)`<br/>`(3x^2 + 8y)/(8x + 3y^2)`<br/>`(3x + 8y^2)/(8x^2 + 3y^2)`<br/>`-(3x + 8y^2)/(8x^2 + 3y^2)`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :A</body></html>
Discussion
194.

Find the values of x for which y=[x(x-2)]^(2) is an increasing function.

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>,<a href="https://interviewquestions.tuteehub.com/tag/oo-583684" style="font-weight:bold;" target="_blank" title="Click to know more about OO">OO</a>)`</body></html>
Discussion
195.

Find the differential equation of the family of all circles which pass through the origin and whose centre lie on y-axis.

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(dy)/(<a href="https://interviewquestions.tuteehub.com/tag/dx-960990" style="font-weight:bold;" target="_blank" title="Click to know more about DX">DX</a>)=(2xy)/(x^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)-y^(2))`</body></html>
Discussion
196.

Let f:[0,1] rarr R be a function . Suppose the fuction f is twice differentiable with f(0) =f(1)=0and satisfies f(x)-2f(x)+f(x) ge e^x " for all " x in [0,1].Which of the following is true for x in (0,1] ?

Answer» <html><body><p>`0 lt <a href="https://interviewquestions.tuteehub.com/tag/f-455800" style="font-weight:bold;" target="_blank" title="Click to know more about F">F</a>(x) lt oo` <br/>`-1/2 lt f(x)lt 1/2` <br/>`-1/4 lt f(x) lt1`<br/>`-oo lt f(x) lt 0`</p>Solution :We have ,<br/> `f''(x)-2f(x)+f(x) ge <a href="https://interviewquestions.tuteehub.com/tag/e-444102" style="font-weight:bold;" target="_blank" title="Click to know more about E">E</a>^x " for all " x in [0,1]` <br/> `e^(x)f''(x)-2f''(x)e^(-x)+f(x)e^(-x)f(x)e^(-x)ge 1 " for all " x in [0,1]` <br/> `rArr {e^(-x) f''(x) -e^(-x)f(x)}-{-e^(-x))ge 1 " for all " x in [0,1]` <br/> `rArrd/(dx) f(x)e^)(-x)-f(x)e^(-x) ge 1 " for all " x in [0,1]` <br/> `rArr d/dx{d/dx f(x)e^(-x)} ge 1 " for all " x in [0,1]` <br/> `rArr d^2/dx^2(f(x)d^(-x) ge 1 " for all " x in [0,1]` <br/> `rArrd^2/dx^2( <a href="https://interviewquestions.tuteehub.com/tag/phi-599602" style="font-weight:bold;" target="_blank" title="Click to know more about PHI">PHI</a> (x))ge 1 " for all " x in [0,1] " where " phi (x)=f(x)e^(-x)`<br/>`rArr(x) ` is concave <a href="https://interviewquestions.tuteehub.com/tag/upward-721781" style="font-weight:bold;" target="_blank" title="Click to know more about UPWARD">UPWARD</a> on [0,1]<br/> It is given that f(0)=f(1)=0. Therefore`phi(0)= phi(1)=0` <br/> Therefore<br/> `phi(x)lt 0 " for all" x in (0,1) rArr - oo lt f(x) lt 0 " for all " x in (0,1)`</body></html>
Discussion
197.

Method of integration by parts : If int(e^(x)(1+sinx)dx)/(1+cosx)=e^(x)f(x)+c, then f(x)=

Answer» <html><body><p>`"sin"(x)/(2)`<br/>`"<a href="https://interviewquestions.tuteehub.com/tag/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a>"(x)/(2)`<br/>`"tan"(x)/(2)`<br/>`"<a href="https://interviewquestions.tuteehub.com/tag/log-543719" style="font-weight:bold;" target="_blank" title="Click to know more about LOG">LOG</a>"(x)/(2)`</p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a></body></html>
Discussion
198.

Evalute the following integrals int (x^2)/((x^(2) + 4)(x^(2) + 9))dx

Answer»
Discussion
199.

{:("Column A","", "Column B"),("The perimeter of"DeltaABC,,"The The circumference of the circle"):}

Answer» <html><body><p>If column A is <a href="https://interviewquestions.tuteehub.com/tag/larger-1067345" style="font-weight:bold;" target="_blank" title="Click to know more about LARGER">LARGER</a><br/>If column <a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a> is larger <br/>If the columns are equal <br/>If there is not <a href="https://interviewquestions.tuteehub.com/tag/enough-446095" style="font-weight:bold;" target="_blank" title="Click to know more about ENOUGH">ENOUGH</a> <a href="https://interviewquestions.tuteehub.com/tag/information-1043838" style="font-weight:bold;" target="_blank" title="Click to know more about INFORMATION">INFORMATION</a> to decide</p>Answer :B</body></html>
Discussion
200.

Using properties of determinants in Exercise 11 to 15 prove that |{:(x,x^2,1+px^3),(y,y^2,1+py^3),(z,z^2,1+pz^3):}|=(1+pxyz)(x-y)(y-z)(z-x)

Answer» <html><body><p><br/></p><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a> :`(1+pxyz)(x-y)(y-z)(z-x)`</body></html>
Discussion