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.

1.

P (-2,-1) and (0,-3) are the limiting points of a coaxial system of whichC -= x^(2) + y^(2)+ 5x + y + 4 = 0is a member. The circleS -= x^(2) + y^(2) - 4x - 2y - 15 = 0is orthogonal to the circle C . The point where the polar of P cuts the circle S is

Answer» <html><body><p>(3,6)<br/>(-3,6)<br/>(-6,3)<br/>(6,3)</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> :D</body></html>
Discussion
2.

Which of the following is/are discontinous at x = 1 ?

Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/f-455800" style="font-weight:bold;" target="_blank" title="Click to know more about F">F</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>)=(1)/(1+2^(<a href="https://interviewquestions.tuteehub.com/tag/tanx-1239117" style="font-weight:bold;" target="_blank" title="Click to know more about TANX">TANX</a>))`<br/>`g(x)=lim_(nrarroo)(1)/(1+n <a href="https://interviewquestions.tuteehub.com/tag/sin-1208945" style="font-weight:bold;" target="_blank" title="Click to know more about SIN">SIN</a>^(-2)(<a href="https://interviewquestions.tuteehub.com/tag/pix-2222284" style="font-weight:bold;" target="_blank" title="Click to know more about PIX">PIX</a>))`<br/>`h(x)=2^(-2^((1)^((1)/(1-x)))), x ne 1 and h(1)=1`<br/>`phi(x)=(x-1)/(|x1|+2(x-1)^(2)), x ne 1 and phi(1) =1`</p>Answer :B::C::D</body></html>
Discussion
3.

Write Minors and Cofactors of the elments of following determinants : |{:(1,0,4),(3,5,-1),(0,1,2):}|

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> :`M_(11)=11,M_(12)=-6,M_(13)=3,M_(<a href="https://interviewquestions.tuteehub.com/tag/21-293276" style="font-weight:bold;" target="_blank" title="Click to know more about 21">21</a>)=-4,M_(22)=<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>,M_(23)=-1,M_(31)=-20,M_(32)=-13,M_(33)=<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/> `A_(11)=11,A_(12)=-6,A_(13)=3,A_(21)=4,A_(22)=2,A_(23)=-1,A_(31)=20,A_(32)=-13,A_(33)=5`</body></html>
Discussion
4.

The vertex of the parabola (y-1)^2 =8 (x-1) is at the centre of a circle and the parabola cuts that circle atthe ends of its latusrectum. Then the equation of that circle is

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/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>)+y^(2)=<a href="https://interviewquestions.tuteehub.com/tag/20-287209" style="font-weight:bold;" target="_blank" title="Click to know more about 20">20</a>`</body></html>
Discussion
5.

{{:(5x-3y=10),(6y=kx-42):} In the system of linear equations above, k represents a constant. If the system of equations has no solution, what is the value of 2k?

Answer» <html><body><p>`5/2`<br/>5<br/>10<br/>20</p>Solution :Start by recognizing that for two lines to be parallel, the coefficients for x must be identical in the two equations, dutto for the coefficients for y. Manipulate the second <a href="https://interviewquestions.tuteehub.com/tag/equation-974081" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATION">EQUATION</a> so that it is in the same format as the first one: <br/> `kx - 6y=42` <br/> The y-coefficient in the first equation, `5x-3y=10, is <a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>.` Divide the second equation by 2 in <a href="https://interviewquestions.tuteehub.com/tag/order-1138220" style="font-weight:bold;" target="_blank" title="Click to know more about ORDER">ORDER</a> to make the y-coefficients in both equatinos equal: <br/> `k/2x -3y=21` <br/> Now set the x-coefficient equal to the x-coefficient in the first equation: <br/> ` k /2=5` <br/> `k=10` <br/> Note that the question asks for the value of <a href="https://interviewquestions.tuteehub.com/tag/2k-300402" style="font-weight:bold;" target="_blank" title="Click to know more about 2K">2K</a>, so the correct answer is (D), 20.</body></html>
Discussion
6.

f(x) ={{:(1-sqrt(1-x^(2)),if -1lexle1),(1+ log ""(1)/(x), if xgt1):}

Answer» <html><body><p>continuousanddifferentibable at x=<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/>continuousbut not differentiableat x=1<br/>neither continuousnor differentiableat =1 <br/><a href="https://interviewquestions.tuteehub.com/tag/noneof-2198387" style="font-weight:bold;" target="_blank" title="Click to know more about NONEOF">NONEOF</a> these</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
7.

Given that alpha, beta, gamma, delta are in a geometric progression. If alpha, beta are the roots of x^(2)-x+p=0 " and "gamma, delta are the roots of x^(2)-4x+q=0, where p and q are integers, then the ordered pair (p, q) =

Answer» <html><body><p>(<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/32-307188" style="font-weight:bold;" target="_blank" title="Click to know more about 32">32</a>)<br/>(2, -32)<br/>(-2, 32)<br/>(-2, -32)</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
8.

A poor , frustrated artist named Fresco created a plan to make money. He collected trash, repurposed it into sculptures, then asked various celebrities to write and paint on these trash objects, which he then sold on his own as modern high art. The chart below separately showsthe cost and revenue of his plan. The linear cost function, C(x) , represents the total money spent to make and market the art , while the linear revenue function, R(x) , shows the amount of money he has made in sculpture sales. Fresco initially spent money promoting the project in the media . He also had to pay the celebrities to participate . After 6 months , Fresco had created and sold x number of trash sculptures and finally broke even : he hadn't made or lost any money . How many sculptures did Fresco sell in his first 6 months of the project ?

Answer» <html><body><p>3<br/>5<br/>7<br/>10</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
9.

A poor , frustrated artist named Fresco created a plan to make money. He collected trash, repurposed it into sculptures, then asked various celebrities to write and paint on these trash objects, which he then sold on his own as modern high art. The chart below separately showsthe cost and revenue of his plan. The linear cost function, C(x) , represents the total money spent to make and market the art , while the linear revenue function, R(x) , shows the amount of money he has made in sculpture sales. The cost function in the chart is determined by a constant production cost per sculpture - in this case, the amount Fresco pays each celebrity to participate - as well as a fixed cost , or the initial cost of promoting the project . What is the fixed cost of Fresco's trash sculpture project ?

Answer» <html><body><p>`$1,000`<br/>`$5,000`<br/>`$10,000`<br/>`$15,000`</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
10.

An ellipse is incribed in a rectangle and if the angle between the diagonals is tan ^(-1)2sqrt2then e=

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>)/(sqrt3) ` <br/>` (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>) ` <br/>` (1)/(sqrt2) ` <br/>` (1)/(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</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 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
11.

A poor , frustrated artist named Fresco created a plan to make money. He collected trash, repurposed it into sculptures, then asked various celebrities to write and paint on these trash objects, which he then sold on his own as modern high art. The chart below separately showsthe cost and revenue of his plan. The linear cost function, C(x) , represents the total money spent to make and market the art , while the linear revenue function, R(x) , shows the amount of money he has made in sculpture sales. The selling price of each trash sculptureis an integer number of dollars . According to the revenuefunction , what is the selling price of one trash sculpture ?

Answer» <html><body><p>`$1,000`<br/>`$1,667`<br/>`$2,000`<br/>`$3,000`</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
12.

Determine whether or not each of the defination of ** given below gives a binary opertion. In the even that ** is not a binary opertion, give justification for this. (i) On Z ^(+), define ** by a ** b =a -b (ii) On Z ^(+), define ** by a **b b =ab (iii) On R, define ** by a **b =ab ^(2) (iv) On Z ^(+), define ** by a ** b = |a-b| (v) On Z ^(+), define ** by a ** b =a

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) NO (<a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a>) Yes (iii) <a href="https://interviewquestions.tuteehub.com/tag/es-446539" style="font-weight:bold;" target="_blank" title="Click to know more about ES">ES</a> (iv) Yes (v) Yes</body></html>
Discussion
13.

The unit vector perpendicular to both the vectors (3, -1, 0) and (-2, 1, 3) is …………..

Answer» <html><body><p>`+-(-3,-9,1)`<br/>`+-(-3,9,-1)`<br/>`+-(1)/(<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/91-341989" style="font-weight:bold;" target="_blank" title="Click to know more about 91">91</a>))(-3,-9,1)`<br/>`+-(1)/(sqrt(91))(-3,9,-1)`</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
14.

The product of the perpendiculars from (-1,2) to the pair of lines 2x^(2) – 5xy + 2y^(2) + 3x – 3y + 1 = 0 is

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>)/(<a href="https://interviewquestions.tuteehub.com/tag/12-269062" style="font-weight:bold;" target="_blank" title="Click to know more about 12">12</a>)`<br/>`(12)/(5)`<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)/(6)`</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
15.

Write the first three terms of the expansion of (2+x)^(-1//2)

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> :N/A</body></html>
Discussion
16.

If for sequence lt a_n gtsum of n terms S_n= 2n^2+3n then find the sum {:(""Sigma Sigma),(1lei lt j le 10):}a_ia_j

Answer» <html><body><p><br/></p>Solution :We have `S_(<a href="https://interviewquestions.tuteehub.com/tag/n-568463" style="font-weight:bold;" target="_blank" title="Click to know more about N">N</a>)=2n^(<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/3n-310768" style="font-weight:bold;" target="_blank" title="Click to know more about 3N">3N</a>` <br/> `thereforea_(n)=S_(n)-S_(n-1)` <br/> `=2n^(2)+3n-2(n-1)^(2)-3(n-1)` <br/> =4n+1 <br/> Therefore, the sequence is 5,9,13… <br/> `thereforeunderset(1leiltjle10)(SigmaSigma)a_(i)a_(<a href="https://interviewquestions.tuteehub.com/tag/j-520843" style="font-weight:bold;" target="_blank" title="Click to know more about J">J</a>)=(sum_(i=1)^(<a href="https://interviewquestions.tuteehub.com/tag/10-261113" style="font-weight:bold;" target="_blank" title="Click to know more about 10">10</a>)sum_(j=1)^(10)(4i+1)cdot(4j+1)-sum_(i=1)^(10)(4i+1)^(2))/2` <br/> `=((sum_(i=1)^(10)(4i+1))^(2)-sum_(i=1)^(10)(4i+1)^(2))/2` <br/> =23145</body></html>
Discussion
17.

Differentiate (x^2-x+2)^2

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> :`y=(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>-x+2)^2`<br/> `dy/dx=2(x^2-x+2)xxd/dx(x^2-x+2)`<br/>`=2(x^2-x+2)(2x-1)`</body></html>
Discussion
18.

Solve the following differential equations sec x (dy)/(dx) - y = sin 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> :`y = -(<a href="https://interviewquestions.tuteehub.com/tag/sin-1208945" style="font-weight:bold;" target="_blank" title="Click to know more about SIN">SIN</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/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>) + <a href="https://interviewquestions.tuteehub.com/tag/ce-407660" style="font-weight:bold;" target="_blank" title="Click to know more about CE">CE</a>^(sin x)`</body></html>
Discussion
19.

Match the following :

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;<br/></p>Answer :(A)- r ,(B)- p , (<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>)-s (D) <a href="https://interviewquestions.tuteehub.com/tag/q-609558" style="font-weight:bold;" target="_blank" title="Click to know more about Q">Q</a></body></html>
Discussion
20.

Solve the equation : 6x^4 -35x^(3) + 62x^(2) -35x + 6=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 href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>+-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>), 2+-sqrt(3)`</body></html>
Discussion
21.

Probability of an event that one male person lives 10 years more is (1)/(4) . His wife lives 10 years more is (1)/(3) . Then of least one person lives has ......... probability.

Answer» <html><body><p>`(5)/(12)`<br/>`(1)/(2)`<br/>`(<a href="https://interviewquestions.tuteehub.com/tag/7-332378" style="font-weight:bold;" target="_blank" title="Click to know more about 7">7</a>)/(12)`<br/>`(11)/(12)`</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
22.

Evaluate int_(0)^(pi) sin^(3) theta(1+2 cos theta)(1+ cos theta)^(2) d theta

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/8-336412" style="font-weight:bold;" target="_blank" title="Click to know more about 8">8</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
23.

If A=[{:(0,1),(1,1):}]andB=[{:(0,-1),(1,0):}]show that (A+B)*(A-B)neA^(2)-B^(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> :`=[{:(2,1),(1,3):}]`</body></html>
Discussion
24.

Ifa,bare any twooddpositiveintegers suchthata gt b .Then thelargestpositiveintegerwhichdividesallthenumbersof thenumbers of theforma^1 -b^2 Is

Answer» <html><body><p>6<br/>5<br/>8<br/>9</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
25.

Evaluate int_(0)^(pi//2) cos^(5) 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> :`8/15`</body></html>
Discussion
26.

A coplanar beam of light emerging from a point surce have the equation lambda x-y+2(1+lambda)-0, AA lambda in R : the rays of beam strike an elliptical surface and get reflected inside the ellipse. The reflected rays form another convergent beam having the equation mu x-y+2(1-mu)=0, AA mu in R. Further it is found that the foot of the perpendicular from the point (2, 2) upon any tangent to the ellipse lies on the circlex^(2)+y^(2)-4y-5=0 Q. The area of the largest that an incident ray and corresponding reflected ray can enclose with the major axis of the ellipse is equal to :

Answer» <html><body><p>`4sqrt(<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/>`<a href="https://interviewquestions.tuteehub.com/tag/sqrt-1223129" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT">SQRT</a>(5)` <br/>`3sqrt(5)` <br/>`2sqrt(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> :D</body></html>
Discussion
27.

A coplanar beam of light emerging from a point surce have the equation lambda x-y+2(1+lambda)-0, AA lambda in R : the rays of beam strike an elliptical surface and get reflected inside the ellipse. The reflected rays form another convergent beam having the equation mu x-y+2(1-mu)=0, AA mu in R. Further it is found that the foot of the perpendicular from the point (2, 2) upon any tangent to the ellipse lies on the circlex^(2)+y^(2)-4y-5=0 Q. The least value of total distance travelled by an incident ray and the corresponding reflectedray is equal to :

Answer» <html><body><p>6<br/>3<br/>`<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/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>)` <br/>`2sqrt(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</body></html>
Discussion
28.

Match the following :

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;<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) - s (<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>)- p (<a href="https://interviewquestions.tuteehub.com/tag/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>) - <a href="https://interviewquestions.tuteehub.com/tag/q-609558" style="font-weight:bold;" target="_blank" title="Click to know more about Q">Q</a> (D) - s</body></html>
Discussion
29.

Match the following :

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/q-609558" style="font-weight:bold;" target="_blank" title="Click to know more about Q">Q</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>,S),(4,1,3,2):}`<br/>`{:(P,Q,R,S),(3,2,1,4):}`<br/>`{:(P,Q,R,S),(1,4,2,3):}`<br/>`{:(P,Q,R,S),(2,3,4,1):}`</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> :D</body></html>
Discussion
30.

A variable line passing through the fixed point (alpha, beta) intersects the co-ordinate axes at A and B. If O is the origin, the the locus of the centroid of the triangle OAB is

Answer» <html><body><p>`betax+alphay=3xy`<br/>`alphax+betay=3xy`<br/>`alphax-betay=3xy`<br/>`betax-alphay=3xy`</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
31.

I : The function log (log x) increases in (1,oo). II : The function x^x is decreasing in (0,1/e).

Answer» <html><body><p>only I 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><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/><a href="https://interviewquestions.tuteehub.com/tag/neither-1113494" style="font-weight:bold;" target="_blank" title="Click to know more about NEITHER">NEITHER</a> I nor II 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
32.

Prove that thefunctions do not have maxima or minima: h(x) = x^(3) +x^(2) +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> :no <a href="https://interviewquestions.tuteehub.com/tag/maxima-1089905" style="font-weight:bold;" target="_blank" title="Click to know more about MAXIMA">MAXIMA</a> or <a href="https://interviewquestions.tuteehub.com/tag/minima-1097152" style="font-weight:bold;" target="_blank" title="Click to know more about MINIMA">MINIMA</a>.</body></html>
Discussion
33.

Ifthe lines(x+1)/(2) =(y-1)/( 1) =(z+1)/(3) and (x+2)/(2) =( y-k)/(3) =(z)/(4)are , coplanar , then the value of k is

Answer» <html><body><p>` 11//2` <br/>` -11//2` <br/>`9//2` <br/>`-9//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
34.

If the latusrectum subtends a right angle at the centre of the hyperbola then its eccentricity

Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/sqrt3-3056952" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT3">SQRT3</a>`<br/>`sqrt3+1`<br/>`(sqrt3+1)/<a href="https://interviewquestions.tuteehub.com/tag/sqrt2-3056932" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT2">SQRT2</a>`<br/>`(sqrt3+1)/sqrt3`</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
35.

Find the number of positive integers from 1 to 1000. Which are divisible by atleast one of 2, 3 or 5.

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/734-334709" style="font-weight:bold;" target="_blank" title="Click to know more about 734">734</a></body></html>
Discussion
36.

If a and b are real number between 0 and 1 such that the points z_1=a+I,z_2=1 +bi and z_3=0 form an equilateral triangle then a, b, are

Answer» <html><body><p>`2-sqrt(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>),2-sqrt(3)` <br/>`2-sqrt(3),2+sqrt(3)` <br/>`2+sqrt(3),2-sqrt(3)` <br/>none</p>Answer :A</body></html>
Discussion
37.

Ifalpha, beta , gammaare the rootsofx^3 - 6x^2+11 x-6=0thenfindtheequationwhoserootsare alpha^2 + beta^2, beta^2 + gamma^2 , gamma^2 + alpha^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/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>^3 -28x^2 + <a href="https://interviewquestions.tuteehub.com/tag/245-296222" style="font-weight:bold;" target="_blank" title="Click to know more about 245">245</a> x -<a href="https://interviewquestions.tuteehub.com/tag/650-331163" style="font-weight:bold;" target="_blank" title="Click to know more about 650">650</a> =<a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>`</body></html>
Discussion
38.

If P(A cap B)= (1)/(12) and P(A' cap B')= (1)/(2) then P(A) + P(B) = .......

Answer» <html><body><p>`(7)/(12)`<br/>`(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(12)`<br/>`(<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>)/(12)`<br/>`(11)/(12)`</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
39.

Match the differential equations in List-I to their integrating factors in List-II {:(,"List - I",,"List-II",),((i), (x^(3)+1)(dy)/(dx)+x^(2)y=0,(a),x^(3),),((ii),x^(2)(dy)/(dx) +3xy = x^(6),(b),(x^(3)+1)^(2),),((iii),(x^(3)+1)(dy)/(dx)+6x^(2)(x^(3)+1)y = x^(2),(c),(x^(2) + 1)^(2),),((iv),(x^(2)+1)(dy)/(dx)+4xy = lnx,(d),x^(2)+1,),(,,(e),(x^(3)+1)^((1)/(3)),),(,,(f),(x^(3)+1)^((1)/(2)),):} The correct matching is

Answer» <html><body><p>i-d, ii-a, iii-<a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>, iv-c<br/>i-e, ii-a, iii-a, iv-c<br/>i-e, ii-b, iii-c, iv-f<br/>i-e, ii-a, iii-c, iv-d</p>Answer :B</body></html>
Discussion
40.

Determine graphically the maximize value of the subjective functionZ = 10x + 25y "…(1)" subject to the constraints : x le 3, y le 3"…(2)" x+y le 5"…(3)" x ge 0, y ge 0".. .(4)"

Answer» <html><body><p><br/></p>Answer :It has no <a href="https://interviewquestions.tuteehub.com/tag/minimum-561095" style="font-weight:bold;" target="_blank" title="Click to know more about MINIMUM">MINIMUM</a> value <a href="https://interviewquestions.tuteehub.com/tag/subject-1231009" style="font-weight:bold;" target="_blank" title="Click to know more about SUBJECT">SUBJECT</a> to the <a href="https://interviewquestions.tuteehub.com/tag/given-473447" style="font-weight:bold;" target="_blank" title="Click to know more about GIVEN">GIVEN</a> <a href="https://interviewquestions.tuteehub.com/tag/constraints-18808" style="font-weight:bold;" target="_blank" title="Click to know more about CONSTRAINTS">CONSTRAINTS</a>.</body></html>
Discussion
41.

If the normal at P to the rectangular hyperbola x^(2) - y^(2) = 4 meets the axes of x and y in G and g respectively and C is the centre of the hyperbola, then 2PC =

Answer» <html><body><p>PG<br/>pg<br/>Gg<br/>none of these </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
42.

If A =sin ^(3)+ cos ^(4) theta , then for all values of theta,A lies in the interval

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/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>]`<br/>`[(<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),1]`<br/>`[(1)/(2), (3)/(4)]`<br/>`[(3)/(4) , (<a href="https://interviewquestions.tuteehub.com/tag/19-280618" style="font-weight:bold;" target="_blank" title="Click to know more about 19">19</a>)/(16)]`</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
43.

If z_(1), z_(2) are conjugate complex numbers and z_(3), z_(4) are also conjugate, then arg.((z_(3))/(z_(2))) is :

Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/agr-851776" style="font-weight:bold;" target="_blank" title="Click to know more about AGR">AGR</a>.((z_(1))/(z_(4)))`<br/>`agr.((z_(4))/(z_(1)))`<br/>`agr.((z_(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>))/(z_(4)))`<br/>`agr.((z_(1))/(z_(3)))`</p>Answer :A</body></html>
Discussion
44.

A : If (5x+1)/((x+2)(x-1))=A/(X+2)+B/(x-1) " then "A=3, B=2. R : (px+q)/((x-a)(x-b))=(pa+q)/((x-a)(a-b))+(pb+q)/((b-a)(x-b)).

Answer» <html><body><p>Both A &amp; <a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a> are <a href="https://interviewquestions.tuteehub.com/tag/true-713260" style="font-weight:bold;" target="_blank" title="Click to know more about TRUE">TRUE</a> 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> explanation of A<br/>Both A &amp; R are true and R is not correct explanation of A<br/>A is true but R is <a href="https://interviewquestions.tuteehub.com/tag/false-459184" style="font-weight:bold;" target="_blank" title="Click to know more about FALSE">FALSE</a><br/>A is false but R is true</p>Answer :A</body></html>
Discussion
45.

overset((pi)/(2))underset(0)int (1)/((a^(2)cos^(2)x+b^(2)sin^(2)x)^(2))dx

Answer» <html><body><p><br/></p>Answer :`:. I=(<a href="https://interviewquestions.tuteehub.com/tag/pi-600185" style="font-weight:bold;" target="_blank" title="Click to know more about PI">PI</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^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)+b^(2))/(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>)+b^(3))]`</body></html>
Discussion
46.

Identify the type of conic and find centre, foci, vertices, and directices of each of the following: ((x+3)^(2))/(225)-((y-4)^(2))/(64)=1

Answer» <html><body><p><br/></p>Answer :(i) `y = ( - 257)/8` <br/> (ii) ` <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/53-324827" style="font-weight:bold;" target="_blank" title="Click to know more about 53">53</a>)/3` <br/> (<a href="https://interviewquestions.tuteehub.com/tag/iii-497983" style="font-weight:bold;" target="_blank" title="Click to know more about III">III</a>) ` 17/15` <br/> (<a href="https://interviewquestions.tuteehub.com/tag/iv-501699" style="font-weight:bold;" target="_blank" title="Click to know more about IV">IV</a>) ` y = 2 - 25/sqrt(41)`<br/> (v) ` -3 sqrt6` <br/> (<a href="https://interviewquestions.tuteehub.com/tag/vi-723586" style="font-weight:bold;" target="_blank" title="Click to know more about VI">VI</a>) `2 - 1/sqrt10 `</body></html>
Discussion
47.

Evaluate the following (i) int_(0)^(30)[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> :<a href="https://interviewquestions.tuteehub.com/tag/435-316625" style="font-weight:bold;" target="_blank" title="Click to know more about 435">435</a></body></html>
Discussion
48.

A unit vector perpendicular to each of the vector 3i+2j+4k and 2i+j-k is,

Answer» <html><body><p>`+- 6i+8j+k/sqrt(<a href="https://interviewquestions.tuteehub.com/tag/101-266127" style="font-weight:bold;" target="_blank" title="Click to know more about 101">101</a>)`<br/>`+- 6i-8j+k/sqrt(<a href="https://interviewquestions.tuteehub.com/tag/104-266430" style="font-weight:bold;" target="_blank" title="Click to know more about 104">104</a>)`<br/>`+- 6i-8j-k/sqrt(101)`<br/>`+- 6i-8j-4k/sqrt(101)`</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
49.

Evaluate int_(a)^(b) 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> :`(<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/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</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>^(2)-a^(2))`</body></html>
Discussion
50.

Let A={3,6,9,12,15,18,21} B={4,8,12,16,20} C={2,4,6,8,10,12,14,16} and D={5,10,15,20} Which of the following is incorrect? I. A-B={4,8,16,20} II. (C-B)nn(D-B)=phi III. B-CneB-D

Answer» <html><body><p>Only I and <a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a><br/>Only II &amp; <a href="https://interviewquestions.tuteehub.com/tag/iii-497983" style="font-weight:bold;" target="_blank" title="Click to know more about III">III</a><br/>Only III &amp; I<br/>None of these</p>Answer :A</body></html>
Discussion