28278 + Interview Questions in Maths in Class 12 Page 3 InterviewSolution

101.	Let bar(a) = 2bar(i) + 3bar(j) + bar(k), bar(b) = 4bar(i) + bar(j) and bar(c ) = bar(i) - 3bar(j) -7bar(k). Find the vector bar(r )such that bar(r ).bar(a) = 9, bar(r ).bar(b) = 7 and bar(r ).bar(c ) =6.
Answer» <html><body><p><br/></p>Answer :`bar(<a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a> ) = bar(i) + <a href="https://interviewquestions.tuteehub.com/tag/3bar-1862765" style="font-weight:bold;" target="_blank" title="Click to know more about 3BAR">3BAR</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>) - 2bar(k)`</body></html>

Discussion

102.	Critical points of y=a log x + bx^(2)+x are x=-1 and x = 2. Then find a and b.
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/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>=-(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(2)`</body></html>

Discussion

103.	Find the values of a for whch sin^*(-1)x=\|x-a\| will have at least one solution.
Answer» <html><body><p></p>Solution :<img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_GRA_C04_S01_003_S01.png" width="80%"/> <br/> (i) When `alt0` <br/> In this <a href="https://interviewquestions.tuteehub.com/tag/case-910082" style="font-weight:bold;" target="_blank" title="Click to know more about CASE">CASE</a>, y = a-x <a href="https://interviewquestions.tuteehub.com/tag/must-2185568" style="font-weight:bold;" target="_blank" title="Click to know more about MUST">MUST</a> pass through `(1,pi/2)` <br/> `thereforepi/2=a-1rArra=1+pi/2` <br/> (<a href="https://interviewquestions.tuteehub.com/tag/ii-1036832" style="font-weight:bold;" target="_blank" title="Click to know more about II">II</a>) When `alt0` <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_GRA_C04_S01_003_S02.png" width="80%"/> <br/> In this case, <br/> `y=x-a" must pass <a href="https://interviewquestions.tuteehub.com/tag/though-2306877" style="font-weight:bold;" target="_blank" title="Click to know more about THOUGH">THOUGH</a> "(1,pi/2)` <br/>`pi/2=1-a` <br/> `a=1-pi/2` <br/> For at least on solution. <br/> `1-pi/2leale1+pi/2`</body></html>

Discussion

104.	Find the vector equation of the line that passes through the points (3,-2,-5)and(3,-2,6)
Answer» <html><body><p>`barr=hati+2hatj+3hatk+lambda(3hati-2hatj-5hatk)`<br/>`barr=-3hati-2hatj-6hatk+lambda(11hatk)` <br/>`barr=3hati-2hatj-5hatk+lambda(11hatk)`<br/>`barr=hati-2hatj+3hatk+lambda(3hati-2hatj+6hatk)`</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

105.	If the normals at the four points (x_1,y_1),(x_2,y_2),(x_3,y_3) and (x_4,y_4) on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 are concurrent. Prove that (x_1+x_2+x_3+x_4)((1/x_1+1/x_2+1/x_3+1/x_4)=4
Answer»

Discussion

106.	I= int cos ("In" 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> :`I= (<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>)/(2) [ <a href="https://interviewquestions.tuteehub.com/tag/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a> ("In" x) + sin ("In" 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

107.	If ab = a +b - abon Q^(+) , then the identity and the inverse of a for are respectively ..........
Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a> and (a)/(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>)`<br/>`1 and (a-1)/a`<br/>`-1 and a`<br/>`0,(1)/a` </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

108.	If A=[{:(0,-1,2),(4,3,-4):}]andB=[{:(4,0),(1,3),(2,6):}]then verify that : (i) (A')=A (ii)(AB)'=B'A' (iii)(kA)'=(k*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> :`=<a href="https://interviewquestions.tuteehub.com/tag/ka-528931" style="font-weight:bold;" target="_blank" title="Click to know more about KA">KA</a>`'</body></html>

Discussion

109.	In the physics lab, a student determined the kinetic energy, KE, of an object at various velocities, V, and found a strong positive association between KE and V. Which of the above scatterplots show this relationship?
Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/graph-17327" style="font-weight:bold;" target="_blank" title="Click to know more about GRAPH">GRAPH</a> (1)<br/>Graph (<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/>Graph (3)<br/>Graph (4)`</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

110.	Examine thatf(x) = sin \|x\| is a continuous 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> :f(<a href="https://interviewquestions.tuteehub.com/tag/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</a>) is <a href="https://interviewquestions.tuteehub.com/tag/also-373387" style="font-weight:bold;" target="_blank" title="Click to know more about ALSO">ALSO</a> everywhere <a href="https://interviewquestions.tuteehub.com/tag/continuous-932035" style="font-weight:bold;" target="_blank" title="Click to know more about CONTINUOUS">CONTINUOUS</a>.</body></html>

Discussion

111.	Find all the three digit numbers for which one obtains when dividing the number by 11, the sum of the squares of the digits of the initials.
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> :550803</body></html>

Discussion

112.	Let ABCD be a parallelogram whose equations for the diagonals AC and BD are x+2y=3 and 2x+y=3, respectively. The length of side AB is equal to
Answer» <html><body><p>`2sqrt(<a href="https://interviewquestions.tuteehub.com/tag/58-325922" style="font-weight:bold;" target="_blank" title="Click to know more about 58">58</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>`<br/>`4sqrt(58)//9`<br/>`3sqrt(58)//9`<br/>`4sqrt(58)//9`</p>Solution :`"cos" (pi-theta) = (<a href="https://interviewquestions.tuteehub.com/tag/ap-380277" style="font-weight:bold;" target="_blank" title="Click to know more about AP">AP</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/pb-597752" style="font-weight:bold;" target="_blank" title="Click to know more about PB">PB</a>^(2)-AB^(2))/(2AP xx PB)` <br/> `"or " -(4)/(5) = (4+(100//9)-AB^(2))/(2 xx 2 xx (10//3))` <br/> `"or " AB = (2sqrt(58))/(3)`</body></html>

Discussion

113.	Write the vale of intxa^(x^(2+1))dx
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> :`<a href="https://interviewquestions.tuteehub.com/tag/intxa-3677888" style="font-weight:bold;" target="_blank" title="Click to know more about INTXA">INTXA</a>^(x^2+1)dx=1/2inta^tdt` (Where`x^2+1=timplies2xdx=dt) =a^t/(2Ina)+<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

114.	Equation to the circles which pass through the point (2,3) and cut off equal chords of length 6 units along the lines y-x-1=0 and y+x-5=0 is
Answer» <html><body><p>`(x-3)^<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-2sqrt3)^2=(3sqrt2)^2`<br/>`(x-2)^2+(y-3-3sqrt2)^2=(3sqrt2)^2`<br/>`(x-2sqrt3)^2 + (y-3)^2 =(3sqrt2)^2`<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><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

115.	If z‌_(1), z_(2), z_(3) , z_(4) are the affixes of the vertices of a parallelogram taken in order in Argand plane, then
Answer» <html><body><p>`z_(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)+z_(3)=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_(<a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a>)`<br/>`z_(1)+z_(2)=z_(3)+z_(4)`<br/>`z_(1)-z_(3)=z_(2)-z_(4)`<br/>None of these</p>Answer :A</body></html>

Discussion

116.	If the system of linear equations above has o solution, and a is a constant, then what is the value of a ?
Answer» <html><body><p>`-2`<br/>`-1/2`<br/>`2`<br/>6</p>Solution :Graphically, a system of linear equations that has no solution <a href="https://interviewquestions.tuteehub.com/tag/indicates-1041501" style="font-weight:bold;" target="_blank" title="Click to know more about INDICATES">INDICATES</a> two parallel lines-that is, two lines that have the same slope but different y-intercepts. To have the same slope, the x-and y-coefficient must be the same. To get from `-2/3` to `-8,` you multiply by 12, so multiply `-1/2x ` by 12 as well to yield 6x. Because the other x-coeffieient is a, it must be that `a =6,` and (D) is correct. Note that, even though it is more work, you could <a href="https://interviewquestions.tuteehub.com/tag/also-373387" style="font-weight:bold;" target="_blank" title="Click to know more about ALSO">ALSO</a> write each <a href="https://interviewquestions.tuteehub.com/tag/equation-974081" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATION">EQUATION</a> in slope-intercept <a href="https://interviewquestions.tuteehub.com/tag/form-996208" style="font-weight:bold;" target="_blank" title="Click to know more about FORM">FORM</a> and <a href="https://interviewquestions.tuteehub.com/tag/set-11758" style="font-weight:bold;" target="_blank" title="Click to know more about SET">SET</a> the slopes equal to each other to solve for a.</body></html>

Discussion

117.	int_(log2)^(t)(dx)/(sqrt(e^(x)-1))=(pi)/(6), then t=
Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/ln-1076444" style="font-weight:bold;" target="_blank" title="Click to know more about LN">LN</a> 8<br/>ln 6<br/>ln 4<br/>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

118.	If the d.c.'s (l, m, n) of two lines are connected by the relations l+m+n=0 " and " 2mn+3ln-5lm=0 then the angle between the lines is
Answer» <html><body><p>`pi//4`<br/>`pi//3`<br/>`pi//6`<br/>`pi//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

119.	Find the number of positive integral solutions of x_(1)x_(2)x_(3)=54 where x_(1),x_(2),x_(3)ne1
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/9-340408" style="font-weight:bold;" target="_blank" title="Click to know more about 9">9</a></body></html>

Discussion

120.	Match the following. {:(,"List -I",,"List-II",),(,"(Differential equation)",,"(Order O, Degree = D)",),((1),[((dy)/(dx))^(3)+(d^(2)y)/(dx^(2))]^(2) = a(dy)/(dx),(a),2O + 3D = 8,),((2),3y = 7x(dy)/(dx)+(5)/(dy//dx),(b),O^(D)+D^(O) = 4,),((3),(d^(2)y)/(dx^(2)) - 5(dy)/(dx)+6y = 0,(c) ,O=D,),((4),((dy)/(dx)+4x)^(3//2) = x+5(dy)/(dx),(d),3^(O)+2^(D) = 11,):} The correct match from List-I from List -II
Answer» <html><body><p>1-a, 2-<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-b, 4-d<br/>1-b, 2-d, 3-c, 4-a<br/>1-c, 2-a, 3-d, 4-b<br/>1-d, 2-b, 3-a, 4-c</p>Answer :C</body></html>

Discussion

121.	There are three bags B_1,B_2 and B_3. The bag B_1 contains 5 red and 5 green balls, B_2 contains 3 red 5 green balls, and B_3 contains 5 red and 3 green balls. Bags B_1, B_2 and B_3 have probabilities (3)/(10),(3)/(10) and (4)/(10) respectively of being chosen. A bag is selected at random and a ball is chosen at random form the bag. then which of the following options is/are correct ?
Answer» <html><body><p>Probability that the <a href="https://interviewquestions.tuteehub.com/tag/chosen-2515513" style="font-weight:bold;" target="_blank" title="Click to know more about CHOSEN">CHOSEN</a> ball is green, <a href="https://interviewquestions.tuteehub.com/tag/given-473447" style="font-weight:bold;" target="_blank" title="Click to know more about GIVEN">GIVEN</a> that the selected bag is `B_3` equals `(3)/(8)`. <br/>Probability that the selected bag is `B_3` , given that the chosen ball is green equals `(5)/(13)` .<br/>Probability that the chosen ball is green equals `(39)/(80)` .<br/>Probability that the selcted bag is `B_3` and the chosen ball is green equals `(3)/(80)` </p>Solution :Key Idea : Use conditional probability. Total probability and Baye's theorem. <br/> It is given that there are three bags, `B_1,B_2` and `B_3` and probabilities of being chosen, `B_1,B_2 and B_3` are <a href="https://interviewquestions.tuteehub.com/tag/respectively-1186938" style="font-weight:bold;" target="_blank" title="Click to know more about RESPECTIVELY">RESPECTIVELY</a>. <br/> `<a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a> P(B_1)=(3)/(10),P(B_2)=(3)/(10) and P(B_3)=(4)/(10)` <br/> Now, probability that the chosen ball is green, given that selected bag is `B_3P((G)/(B_3))=(3)/(8)` <br/> Now, probability that the chosen selected bag is `B_3`, given that the chosen ball is green `=P((B_3)/(G))` <br/> `=(P((G)/(B_3))P(B_3))/(P((G)/((B_1))P(B_1))+P((G)/(B_2))P(B_2)+P((G)/(B_3))P(B_2))["by Baye's theorem"]` <br/> `=(((3)/(8)xx(4)/(10)))/(((5)/(10)xx(3)/(10))+((5)/(8)xx(3)/(10))+((3)/(8)xx(4)/(10)))=((1)/(2))/((1)/(2)+(5)/(8)+(1)/(2))=(4)/(13)` <br/> Now, probability that the chosen ball is green `=P(G)=P(B_1)P((G)/(B_1))+P(B_2)P((G)/(B_2))+P(B_3)P((G)/(B_3))` <br/> [By using theorem of total probability] <br/> `=((3)/(10)xx(5)/(10))+((3)/(10)xx(5)/(8))+((4)/(10)xx(3)/(8))` <br/> `=(3)/(20)+(3)/(16)+(3)/(20)=(12+15+12)/(80)=(39)/(80)` <br/> Now, probability that the selected bag is `B_3` and the chosen ball is green `=P(B_3)xxP((G)/(B_3))=(4)/(10)xx(3)/(8)=(3)/(20)` <br/> Hence, <a href="https://interviewquestions.tuteehub.com/tag/options-1137914" style="font-weight:bold;" target="_blank" title="Click to know more about OPTIONS">OPTIONS</a> (a) and (c) is are correct.</body></html>

Discussion

122.	Find the period of cos^(4)x.
Answer» <html><body><p>`<a href="https://interviewquestions.tuteehub.com/tag/pi-600185" style="font-weight:bold;" target="_blank" title="Click to know more about PI">PI</a>` <br/>`<a href="https://interviewquestions.tuteehub.com/tag/2pi-1838601" style="font-weight:bold;" target="_blank" title="Click to know more about 2PI">2PI</a>` <br/>`pi//2`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/3pi-1863811" style="font-weight:bold;" target="_blank" title="Click to know more about 3PI">3PI</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

123.	If y = sum_(n=2)^(oo) (""^nc_2 .(3^(n-2))/(n!)) then 2y =
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><br/>`e^2`<br/>`e^3`<br/>`e^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 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

124.	If O is the origin and A is (a, b, c), then find the direction cosines of the line OA and the equation of plane through A at right angle to OA.
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/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a> ax+by+cz=a^2+b^2+c^2`</body></html>

Discussion

125.	Evalute the following integrals int (5x^(4) + 7)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/x-746616" style="font-weight:bold;" target="_blank" title="Click to know more about X">X</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>)+7x+c`</body></html>

Discussion

126.	Findthe value of a,b,cand d. [{:(a,3a-b),(2a+c,3b-d):}]=[{:(3,2),(7,7):}]
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=3,b=7,c=1,d=14`</body></html>

Discussion

127.	(vec(a).hat(i))hat(i)+(vec(a).hat(j))hat(j)+(vec(a).hat(k))hat(k)=
Answer» <html><body><p><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/>`<a href="https://interviewquestions.tuteehub.com/tag/vec-723433" style="font-weight:bold;" target="_blank" title="Click to know more about VEC">VEC</a>(a)`<br/>`2vec(a)`<br/>`3vec(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/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a></body></html>

Discussion

128.	If a line has direction cosines 2/3,-1/3,-2/3, then find its direction.
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/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>,-2</body></html>

Discussion

129.	If side of a cube is 10 cm and error in it is 0.05 cm then match the following {:("I.","Error in surface are of cube","a",15),("II".,"Percentage error in surface area",b,6),("III.","Error in volume",c,1.5),("IV.","Percentage error in volume",d,0.05),("","",e,1):}
Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a>,d,<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<br/>a,c,c,d<br/>a,c,b,e<br/>b,e,a,c</p>Answer :D</body></html>

Discussion

130.	If a,b,c are three consevutive terms of an AP and x,y,z are three consecutive terms of a GP, then the value of X^(b-c).Y^(c-a). Z^(a-b) 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)xyz<br/>3)-1<br/>4)1</p>Answer :D</body></html>

Discussion

131.	Evaluate the following determinates \|{:(sin10^@,-cos10^@),(sin80^@, cos80^@):}\|
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></body></html>

Discussion

132.	If ABCD is a cyclic quadrilateral with AB = 6, BC = 4, CD = 5, DA= 3 and angleABC = theta ,then cos theta=
Answer» <html><body><p>A`(3)/(<a href="https://interviewquestions.tuteehub.com/tag/13-271882" style="font-weight:bold;" target="_blank" title="Click to know more about 13">13</a>)`<br/>B`(18)/(<a href="https://interviewquestions.tuteehub.com/tag/76-335558" style="font-weight:bold;" target="_blank" title="Click to know more about 76">76</a>)`<br/>C`(16)/(<a href="https://interviewquestions.tuteehub.com/tag/78-335791" style="font-weight:bold;" target="_blank" title="Click to know more about 78">78</a>)`<br/>D`(78)/(<a href="https://interviewquestions.tuteehub.com/tag/86-339622" style="font-weight:bold;" target="_blank" title="Click to know more about 86">86</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

133.	A circle having centre as O' and radius r' touches the incircle of Delta ABC externally at. F, where F is on BC and also touches its circumcircle internally at G. It O is the circumcentre of Delta ABC and I is its incentre, then
Answer» <html><body><p><a href="https://interviewquestions.tuteehub.com/tag/oo-583684" style="font-weight:bold;" target="_blank" title="Click to know more about OO">OO</a>'=R-r'<br/>Perpendicular distance from O to line joining IO' is `\|(b-c)/(2)\|`<br/>Projection of OO' on line joining IO'=r'+R cos A <br/>`r'=(<a href="https://interviewquestions.tuteehub.com/tag/delta-947703" style="font-weight:bold;" target="_blank" title="Click to know more about DELTA">DELTA</a>)/(a)tan^(2)A`</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> :From <a href="https://interviewquestions.tuteehub.com/tag/figure-987693" style="font-weight:bold;" target="_blank" title="Click to know more about FIGURE">FIGURE</a>, OO' = OG - O'G = R-r' <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_TRI_DPP_6_3_E01_298_S01.png" width="80%"/> <br/> `OE=DE=\|BF-BD\|=\|s-b-(a)/(2)\|=(\|c-b\|)/(2)` <br/> OD = EF = R cos A <br/> From `Delta OEO'`, using Pythagoras theorem, we get <br/> `(R-r')^(2)=(R cos A+r')^(2)+((c-b)/(2))^(2)` <br/> `rArr r' =(<a href="https://interviewquestions.tuteehub.com/tag/bc-389540" style="font-weight:bold;" target="_blank" title="Click to know more about BC">BC</a>)/(4R)"tan"^(2)(A)/(2)` <br/> `= (Delta)/(a)"tan"^(2)(A)/(2)`</body></html>

Discussion

134.	The value of ("sin"(2019pi)/2-cos2019pi)/("tan"(2020pi)/3) is
Answer» <html><body><p>1<br/>-1<br/>0<br/>`<a href="https://interviewquestions.tuteehub.com/tag/sqrt3-3056952" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT3">SQRT3</a>`</p></body></html>

Discussion

135.	Differentiate cotx^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> :<a href="https://interviewquestions.tuteehub.com/tag/let-11597" style="font-weight:bold;" target="_blank" title="Click to know more about LET">LET</a> `y=cotx^2`<br/> Then `dy/dx=-"<a href="https://interviewquestions.tuteehub.com/tag/cosec-426601" style="font-weight:bold;" target="_blank" title="Click to know more about COSEC">COSEC</a>"^2x^2xxd/dx(x^2)`<br/>`=-"cosec"^2x^2 cdot2x`<br/>`=-2xcdot "cosec"^2x^2`</body></html>

Discussion

136.	int_(0)^(pi/4) sin 2x dx
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> :`" Let I "= int_(0)^(pi//4) sin 2 x dx` <br/> `=int_(0)^(pi//4) 2 sin x <a href="https://interviewquestions.tuteehub.com/tag/cosx-936418" style="font-weight:bold;" target="_blank" title="Click to know more about COSX">COSX</a> dx `<br/> `<a href="https://interviewquestions.tuteehub.com/tag/underset-3243992" style="font-weight:bold;" target="_blank" title="Click to know more about UNDERSET">UNDERSET</a>(x=0 ""rArr t=sin 0=0)underset(x=(pi)/(4) ""rArr t= sin.(pi)/(4) =(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>(2)))("Letsin "x=t ""rArr cosx dx =dt)` <br/> `:. I=2 int_(0)^(pi//sqrt(2))t dt = 2 [(t^(2))/(2)]_(0)^(1//sqrt(2))` <br/> `=((1)/(sqrt(2)))^(2)=(1)/(2)`</body></html>

Discussion

137.	Let u,v,w be rela numbers in geometric progression such that u gt v gt w. Suppose u ^(40)= v ^(n) = w ^(60). Find the value of n .
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/48-318016" style="font-weight:bold;" target="_blank" title="Click to know more about 48">48</a></body></html>

Discussion

138.	Refers to question 27. Maximum of Z occurs at
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>,0)<br/>(6,5)<br/>(6,8)<br/>(4,10)</p>Solution :Refers to solution 27, <a href="https://interviewquestions.tuteehub.com/tag/maximum-556915" style="font-weight:bold;" target="_blank" title="Click to know more about MAXIMUM">MAXIMUM</a> of <a href="https://interviewquestions.tuteehub.com/tag/z-750254" style="font-weight:bold;" target="_blank" title="Click to know more about Z">Z</a> occurs at (5,)</body></html>

Discussion

139.	Integrate thefunction in Exercise. (x^(3)-1)^((1)/(3))x^(5)
Answer»

Discussion

140.	If x(hat(i) + hat(j) + hat(k)) is a unit vector then x equals ?
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/sqrt-1223129" style="font-weight:bold;" target="_blank" title="Click to know more about SQRT">SQRT</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>))`<br/>`<a href="https://interviewquestions.tuteehub.com/tag/pm-1156895" style="font-weight:bold;" target="_blank" title="Click to know more about PM">PM</a> sqrt(3)`<br/>`sqrt(3)`<br/>`pm (1)/(sqrt(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

141.	The sum to n terms of the series 1 + (1 + 3) + (1 + 3 + 9) + (1 + 3 + 9 + 27)+ .......... is
Answer» <html><body><p>`(3(3^(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>))/4 - 1`<br/>`(3(3^(n) - 1) - 2n)/4`<br/>`(3(3^(n) - 1) - n)/4`<br/>`(2n - 3(3^(n) - n))/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 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

142.	Centre and radius of the circle with segment of the line x+y=1 cut off by coordinate axes as diameter 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/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>,1/2),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>(2))`<br/>`(-1/2,-1/2),(1/(sqrt(2)))`<br/>`(1/2,-1/2),1/(sqrt(2))`<br/>`(-1/2,1/2),1/(sqrt(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

143.	The order and degree of the differential equation [((dy)/(dx))^(2) + ((d^(2)y)/(dx^(2)))]^(5//4) = k (d^(3) y)/(dx^(3)) is
Answer» <html><body><p>1,2<br/>2,3<br/>3,4<br/>4,5</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

144.	Integrate the following functions : intcosecx.log(cossex-cotx)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>)[log\|cosecx-cotx\|]^(2)+<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

145.	Let Abe a square matrix of order 3xx3, then \|KA\| is equalto
Answer» <html><body><p>` <a href="https://interviewquestions.tuteehub.com/tag/k-527196" style="font-weight:bold;" target="_blank" title="Click to know more about K">K</a>\|A\| ` <br/>` k^(<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\| ` <br/>` k^(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>) \|A\| ` <br/>` <a href="https://interviewquestions.tuteehub.com/tag/3k-310983" style="font-weight:bold;" target="_blank" title="Click to know more about 3K">3K</a> \|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> :C</body></html>

Discussion

146.	If f:RtoRandg:RtoR are given by f(x)=cosxandg(x)=3x^(2). Find gof and fog.
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/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a>(<a href="https://interviewquestions.tuteehub.com/tag/3x-310805" style="font-weight:bold;" target="_blank" title="Click to know more about 3X">3X</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

147.	int_(0)^(pi//2)x sin x dx =
Answer» <html><body><p>0<br/>1<br/>-1<br/>2</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

148.	{:(I."The points" i + j + k. 4i + 3j "and" 10 i + 7j - 2k "are", a. a xx b = 7c),(II. "The vectors" 5i + 5j + 7k. 7i - 8j + k "and" i - 20 j - 5k "are",b. "collincar"),(III. a = 2i + 3j + 6k. b = 3i - 6j + 2k, c. "non-coplanar"),(IV. "The Points" 2i - j + k. i - 3j = 5k "and" 3i - 4j - 4k "are", d."vertices of equilateral triangle"),(, e. "vertices of right angled triangle"):}
Answer» <html><body><p><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/c-7168" style="font-weight:bold;" target="_blank" title="Click to know more about C">C</a>,a,e<br/>a,c,d,e<br/>a,c,b,e<br/>e,d,c,a</p>Answer :A</body></html>

Discussion

149.	If the vectors veca = 2hati + 3hatj +-6hatk and vecb = alphahati-hatj +2hatk are parallel, then alpha = ______
Answer» <html><body><p>2<br/>44257<br/>-2/3<br/>44256</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

150.	Find the non-parametric form of vector equation, and Cartesian equation vector equation, and Cartesian equation of the plane passing through the point (0, 1,-5) and parallel to the straight linesvecr=(hati=2hatj-4hatk)+s(2hati+3hatj+6hatk)andvecr=(hati=3hatj-4hatk)+t(hati+hatj+hatk)
Answer» <html><body><p><br/></p>Answer :`(vecr-veca).(vecb <a href="https://interviewquestions.tuteehub.com/tag/xx-747671" style="font-weight:bold;" target="_blank" title="Click to know more about XX">XX</a> <a href="https://interviewquestions.tuteehub.com/tag/vec-723433" style="font-weight:bold;" target="_blank" title="Click to know more about VEC">VEC</a> c)=<a href="https://interviewquestions.tuteehub.com/tag/0-251616" style="font-weight:bold;" target="_blank" title="Click to know more about 0">0</a>`, 9x-8y+z+13=0</body></html>

Discussion

Explore topic-wise InterviewSolutions in Class 12.

Let bar(a) = 2bar(i) + 3bar(j) + bar(k), bar(b) = 4bar(i) + bar(j) and bar(c ) = bar(i) - 3bar(j) -7bar(k). Find the vector bar(r )such that bar(r ).bar(a) = 9, bar(r ).bar(b) = 7 and bar(r ).bar(c ) =6.

Critical points of y=a log x + bx^(2)+x are x=-1 and x = 2. Then find a and b.

Find the values of a for whch sin^*(-1)x=|x-a| will have at least one solution.

Find the vector equation of the line that passes through the points (3,-2,-5)and(3,-2,6)

If the normals at the four points (x_1,y_1),(x_2,y_2),(x_3,y_3) and (x_4,y_4) on the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 are concurrent. Prove that (x_1+x_2+x_3+x_4)((1/x_1+1/x_2+1/x_3+1/x_4)=4

I= int cos ("In" x) dx.

If a**b = a +b - abon Q^(+) , then the identity and the inverse of a for ** are respectively ..........

If A=[{:(0,-1,2),(4,3,-4):}]andB=[{:(4,0),(1,3),(2,6):}]then verify that : (i) (A')=A (ii)(A*B)'=B'*A' (iii)(kA)'=(k*A')

In the physics lab, a student determined the kinetic energy, KE, of an object at various velocities, V, and found a strong positive association between KE and V. Which of the above scatterplots show this relationship?

Examine thatf(x) = sin |x| is a continuous function.

Find all the three digit numbers for which one obtains when dividing the number by 11, the sum of the squares of the digits of the initials.

Let ABCD be a parallelogram whose equations for the diagonals AC and BD are x+2y=3 and 2x+y=3, respectively. The length of side AB is equal to

Write the vale of intxa^(x^(2+1))dx

Equation to the circles which pass through the point (2,3) and cut off equal chords of length 6 units along the lines y-x-1=0 and y+x-5=0 is

If z‌_(1), z_(2), z_(3) , z_(4) are the affixes of the vertices of a parallelogram taken in order in Argand plane, then

If the system of linear equations above has o solution, and a is a constant, then what is the value of a ?

int_(log2)^(t)(dx)/(sqrt(e^(x)-1))=(pi)/(6), then t=

If the d.c.'s (l, m, n) of two lines are connected by the relations l+m+n=0 " and " 2mn+3ln-5lm=0 then the angle between the lines is

Find the number of positive integral solutions of x_(1)x_(2)x_(3)=54 where x_(1),x_(2),x_(3)ne1

Find the period of cos^(4)x.

If y = sum_(n=2)^(oo) (""^nc_2 .(3^(n-2))/(n!)) then 2y =

If O is the origin and A is (a, b, c), then find the direction cosines of the line OA and the equation of plane through A at right angle to OA.

Evalute the following integrals int (5x^(4) + 7)dx

Findthe value of a,b,cand d. [{:(a,3a-b),(2a+c,3b-d):}]=[{:(3,2),(7,7):}]

(vec(a).hat(i))hat(i)+(vec(a).hat(j))hat(j)+(vec(a).hat(k))hat(k)=

If a line has direction cosines 2/3,-1/3,-2/3, then find its direction.

If side of a cube is 10 cm and error in it is 0.05 cm then match the following {:("I.","Error in surface are of cube","a",15),("II".,"Percentage error in surface area",b,6),("III.","Error in volume",c,1.5),("IV.","Percentage error in volume",d,0.05),("","",e,1):}

If a,b,c are three consevutive terms of an AP and x,y,z are three consecutive terms of a GP, then the value of X^(b-c).Y^(c-a). Z^(a-b) is

Evaluate the following determinates |{:(sin10^@,-cos10^@),(sin80^@, cos80^@):}|

If ABCD is a cyclic quadrilateral with AB = 6, BC = 4, CD = 5, DA= 3 and angleABC = theta ,then cos theta=

A circle having centre as O' and radius r' touches the incircle of Delta ABC externally at. F, where F is on BC and also touches its circumcircle internally at G. It O is the circumcentre of Delta ABC and I is its incentre, then

The value of ("sin"(2019pi)/2-cos2019pi)/("tan"(2020pi)/3) is

Differentiate cotx^2

int_(0)^(pi/4) sin 2x dx

Let u,v,w be rela numbers in geometric progression such that u gt v gt w. Suppose u ^(40)= v ^(n) = w ^(60). Find the value of n .

Refers to question 27. Maximum of Z occurs at

Integrate thefunction in Exercise. (x^(3)-1)^((1)/(3))x^(5)

If x(hat(i) + hat(j) + hat(k)) is a unit vector then x equals ?

The sum to n terms of the series 1 + (1 + 3) + (1 + 3 + 9) + (1 + 3 + 9 + 27)+ .......... is

Centre and radius of the circle with segment of the line x+y=1 cut off by coordinate axes as diameter is

The order and degree of the differential equation [((dy)/(dx))^(2) + ((d^(2)y)/(dx^(2)))]^(5//4) = k (d^(3) y)/(dx^(3)) is

Integrate the following functions : intcosecx.log(cossex-cotx)dx

Let Abe a square matrix of order 3xx3, then |KA| is equalto

If f:RtoRandg:RtoR are given by f(x)=cosxandg(x)=3x^(2). Find gof and fog.

int_(0)^(pi//2)x sin x dx =

If the vectors veca = 2hati + 3hatj +-6hatk and vecb = alphahati-hatj +2hatk are parallel, then alpha = ______

Find the non-parametric form of vector equation, and Cartesian equation vector equation, and Cartesian equation of the plane passing through the point (0, 1,-5) and parallel to the straight linesvecr=(hati=2hatj-4hatk)+s(2hati+3hatj+6hatk)andvecr=(hati=3hatj-4hatk)+t(hati+hatj+hatk)

If ab = a +b - abon Q^(+) , then the identity and the inverse of a for are respectively ..........

If A=[{:(0,-1,2),(4,3,-4):}]andB=[{:(4,0),(1,3),(2,6):}]then verify that : (i) (A')=A (ii)(AB)'=B'A' (iii)(kA)'=(k*A')