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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 12451. |
2"Tan"^(-1)(1)/(5)+"Sec"^(-1)(5 sqrt(2))/(7)+"Tan"^(-1)(1)/(8)= |
| Answer» ANSWER :D | |
| 12452. |
If vecx=3hati-6hatj-hatk, vecy=hati+4hatj-3hatk and vecz=3hati-4hatj-12hatk, then the magnitude of the projectionof vecx xx vecy on vecz is |
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Answer» 12 |
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| 12454. |
Let l_(1), l_(2), l_(3) be the lengths of the internal bisectors of angles A,B,C of DeltaABC respectively. Statement-1: ("cos"(A)/(2))/(l_(1))+("cos"(B)/(2))/(l_(2))+("cos"(C)/(2))/(l_(3))=2((l_(1))/(a)+(l_(2))/(b)+(l_(3))/(c)) Statement-2 : l_(1)^(2)=bc[1-((a)/(b+c))^(2)]l_(2)^(2)=ca[1-((b)/(c+a))^(2)]l_(3)^(2)=ab[1-((c)/(a+b))^(2)] |
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Answer» Statement-1 is TRUE, Statement-2 is True, Statement-2 is a CORRECT EXPLANATION for Statement-1 |
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| 12455. |
Two dice are thrown at random. Match the following |
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Answer» <P> Solution :P(sum of the face number thrown is 5) `rarr1/9`P(the number on ONE DIE is double the number on the other)`rarr1/6` P(one die gives the number 5 and the other a number less than 5)`rarr2/9` P(both DICE show the same number other than 6)`rarr5/36` |
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| 12456. |
A committee of 7 members has to be formed from 9boys and 4 girls. In how many ways can this be done when the committee consists ofat least 3 girls |
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| 12457. |
A committee of 7 members has to be formed from 9boys and 4 girls. In how many ways can this be done when the committee consists ofatmost three girls |
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| 12458. |
A committee of 7 members has to be formed from 9boys and 4 girls. In how many ways can this be done when the committee consists ofexactly 3 girls |
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| 12459. |
If a,b,c are in A.P, then prove that: 2sinA/2.sinC/2=sinB/2 |
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Answer» Solution :Let `2sinA/2.sinC/2=sinB/2` `rArr 2sqrt((s-b)(s-c))/(BC).sqrt((s-a)(s-b))/(AB)=sqrt((s-a)(s-c))/(ac)` `rArr 2(s-b)/b.sqrt((s-a)(s-c))/(ac)=sqrt((s-a)(s-c))/(ac)` `rArr 2(s-b)/(b)=1` `rArr 2s-2b=b` `rArr a+b+c-2b=b` `rArr a+c=2b` `rArr a+c=2b` `rArr` a,b,c are in A.P. Which is given. Therefore, `2sinA/2.sinC/2=sinB/2`, if a,b,c are in A.P. Hence PROVED. |
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| 12460. |
Find (dy)/(dx)," if "x= at^(2), y= 2at. |
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| 12461. |
If2 sin^(2) x - 5 sin x cos x - 8 cos ^(2) x = -then |
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Answer» `x = {n pi + TAN ^(-1) (2), n in Z} cup{m pi + tan ^(-1)((-3)/(4)), m in Z}` |
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| 12462. |
sec h^(-1) (sin theta) = |
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Answer» `"log TAN" (THETA)/(2)` |
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| 12465. |
If P(2,3,-6) , Q (3, -4,5) are two points, find the d.c's of vec(OP), vec(QO) and vec(PQ) where O is the origin. |
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| 12466. |
Find equation of the line which is equidistant from parallel lines 9x+6y-7=0 and 3x+2y+6=0. |
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| 12467. |
Let U= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}, A= {4, 8, 16, 12}, B= {1, 2, 3, 4, 5}, C= {4, 8, 12, 16, 20} then find the following sets. B'. |
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| 12468. |
Let U= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}, A= {4, 8, 16, 12}, B= {1, 2, 3, 4, 5}, C= {4, 8, 12, 16, 20} then find the following sets. (B- C)' |
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| 12469. |
Let U= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}, A= {4, 8, 16, 12}, B= {1, 2, 3, 4, 5}, C= {4, 8, 12, 16, 20} then find the following sets. (A cap B)' |
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| 12470. |
Let U= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}, A= {4, 8, 16, 12}, B= {1, 2, 3, 4, 5},C= {4, 8, 12, 16, 20} then find the following sets. (A cup C)' |
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| 12471. |
Evaluate the following limits : Lim_( x to oo) (5x-6) /(sqrt(4x^(2)+9)) |
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| 12472. |
Let U= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}, A= {4, 8, 16, 12}, B= {1, 2, 3, 4, 5},C= {4, 8, 12, 16, 20} then find the following sets. A' |
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| 12473. |
Solve inequality2 (x-1) lt x + 5, 3 (x+2) gt 2-x and represent solution graphically on number line. |
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Answer» `(##NCERT_TEL_MAT_XI_C06_E04_008_A01##)` |
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| 12474. |
If the distance between the points (a, 2, 1) and (1, -1, 1) is 5, then a ____ . |
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| 12475. |
If(cos(alpha-3theta))/(cos^(3)theta)=(sin(alpha-3theta))/(sin^(3)theta)=m then |
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Answer» `cos2 alpha=(2M^(2)-9M^(2)+8)/(m^(2))` |
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| 12477. |
Find (dy)/(dx)if x = ( 3 at)/(1+ t ^(3)), y = (3 at ^(2))/( 1 + t ^(3)). |
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| 12478. |
If H_(n) = 1+ (1)/(2) + (1)/(3) + …. + (1)/( n) , AA n in N, then H_(1) + H_(2) + H_(3)+ …. + H_(n) = |
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Answer» `(N+1)H_(n) -n` |
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| 12479. |
Find the probability that when a hand of 7 cards is drawn from well sheffled deck of 52 cards, it contians (i) all kings (ii) 3 Kings (iii) atleast 3 Kings. |
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Answer» <P> |
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| 12481. |
A and B are mutually disjoint sets. Then n(A cup B)="…………." |
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Answer» `N(A)+ n(B)` |
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| 12482. |
(x^(2))/(9)-(y^(2))/(16)=1 |
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Answer» (ii) `A(-3,0),B(3,0) ` (iii) `F_(1) (-5,0),F_(2)(5,0)` `(IV) e=(5)/(3) ` ` (v) 10(2)/(3)` units |
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| 12483. |
Consider the lines L _(1) : (x +1)/( 3) = (y+2)/(1) = (z+1)/(2), L_(2): (x-2)/(1) = (y+2)/(2) = (z-3)/(3) The distance ofthe point (1,1,1) from the plance passing through the point (-1,-2,-1) and whose normal is perpendicular to both the lines L _(1) and L _(2) is |
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Answer» `(12)/(sqrt65)` |
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| 12484. |
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the latus rectum of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 |
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| 12485. |
Which of the following is meaningless ? |
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Answer» `(BARAXXBARB).(barcxxbard)` |
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| 12486. |
Express the following in the form of a+ib: (2-sqrt(-25))/(1-sqrt(-16)) |
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| 12487. |
The sum of series 1 + 2x + 3x^(2) + 4x^(3) + ...... up to infinity when x lies between 0 and 1 i.e., 0 lt x lt 1 is |
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Answer» `(1-x)^(-2)` |
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| 12488. |
Fill in the blanks (i) The x axis and y axis taken together determine a plane known as ______ (ii) The coordinates of points in the XY plane are of the form _______ (iii) Coordinate planes divide the space into _________octants |
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| 12489. |
Let U={1, 2, 3, 4, 5, 6, 7, 8, 9 }A= {1, 2, 3, 4} B = { 2,4, 6, 8} C = { 3, 4, 5, 6 } Find (A ∪ C)′ |
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| 12490. |
The point on x-axis with is equidistant to (2,-1-4), (-4,3,0) is |
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Answer» `(13/3,0,0)` |
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| 12491. |
If f(x)=(sin ([x]pi))/(x^(2)+x+1) , where [.] denotes the greast integer function, then |
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Answer» F is one-one |
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| 12492. |
Prove that |{:((1+ax)^(2),(1+ay)^(2),(1+az)^(2)),((1+bx)^(2),(1+by)^(2),(1+bz)^(2)),((1+cx)^(2),(1+cy)^(2),(1+cz)^(2)):}|=2(a-b)(b-c)(c-a)(x-y)(y-z)(z-x). |
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| 12496. |
Solve the following systems of homogeneous equations. 2x+3y-z=0 x-y-2z=0 3x+y+3z=0 |
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| 12497. |
Statement-IIn a DeltaABC ifa lt b lt cand tau is inradius and r_(2),r_(2) are the exradii opposite to angle A,B, C respectively then r lt r_(1) lt r_(2) lt r_(3). Statement -2 : for DABC, r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r) |
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Answer» Statement-1 is True, Statement-2 is True: Statement-2 is a CORRECT explanation for Statement-I |
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| 12498. |
Of the parabola, 4(y-1)^(2)= -7(x-3) find The coordinates of the focus and the vertex. |
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| 12500. |
(cos x )/( cos (x-2y))= lambda implies tan(x-y) tan y= |
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Answer» `(1 + LAMDA)/( 1 - lamda)` |
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