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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.
| 251. |
The angle `theta` between the vector `p=hati+hatj +hatk` and unit vector along X-axis isA. `cos^(-1)((1)/(sqrt(3)))`B. `cos^(-1)((1)/(sqrt(2)))`C. `cos^(-1)(sqrt(3)/(2))`D. `cos^(-1)((1)/(2))` |
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Answer» Correct Answer - A (A) the angle between `P=hati+hatj+hatk` And X -axis ,s=hati" is givern by 3" ` `costheta (p.x)/(|P||x|)=((hati+hatj+hatk)(hati))/(sqrt(1^(2)+1^(2)+1^(2)).sqrt(1^(2)))=(1)/(sqrt(3))` `theta=cos^(-1)((1)/(sqrt(3)))` |
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| 252. |
If a unit vector is represented by `0.5 hat(i) + 0.8 hat(j) + c hat(k)` , then the value of `c` isA. 1B. `sqrt(0.11)`C. `sqrt(0.01)`D. `sqrt(0.39)` |
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Answer» Correct Answer - B (b) For a unit vector `sqrt((0.5)^(2)+(0.8)^(2)+C^(2))=1` ON solving ,we get `c=sqrt(0.11)` |
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| 253. |
The area of the triangle whose adjacent sides are represented by the vector `(4hat i + 3 hat j + 4 hat k)` and `5hat i` in sq. units isA. 25B. 12.5C. 50D. 45 |
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Answer» Correct Answer - B Area of triangle `=(1)/(2)|vecAxxvecB|` |
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| 254. |
If a unit vector is represented by `0.5 hat(i) + 0.8 hat(j) + c hat(k)` , then the value of `c` isA. `1`B. `sqrt(0.11)`C. `sqrt(0.01)`D. `sqrt(0.39)` |
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Answer» Correct Answer - B `sqrt((0.5)^(2) + (0.8)^(2) + c^(2)) = 1` `c^(2) = 0.89 rArr c = sqrt(0.11)` |
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| 255. |
The area of the parallelogram whose sides are represented by the vector `hat(j)+3hat(k)` and `hat(i)+2hat(j)-hat(k)` isA. `sqrt(16)sq.unit`B. `sqrt(59)sq.unit`C. `sqrt(49)sq.unit`D. `sqrt(52)sq.unit` |
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Answer» Correct Answer - B `vec(A)= hat(j)+3hat(k), vec(B)= hat(i)+2hat(j)-hat(k)` `vec(C )= vec(A)xxvec(B) = |(hati, hatj, hatk), (0, 1, 3), (1, 2, -1)| = -7hat(i)+3hat(j)-hat(k)` Hence area `=|vec(C )|= sqrt(49+9+1)= sqrt(59) sq.unit` |
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| 256. |
A particle undergoes three successive displacements given by `s_(1) =sqrt(2)` m morth - east , `s_(1)=2` m due south and `s_(3) =4 m, 30^(@)` north of west , then mngnitude of net displecement isA. `sqrt(14+4sqrt(3))`B. `sqrt(14-4sqrt(3))`C. `sqrt(4)`D. None of these |
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Answer» Correct Answer - B `"we have "S_(1)=(sqrt(2)cos45^(@))hati+(sqrt(2)sin 45^(@)) hatj=hati+hatj` `S_(2)=-2hatjand S_(3)=(-4cos30^(@))hati+(4sin 30^(@)) hatj` `Now ,S=S_(1)+S_(2)+S_(3)=(1-2sqrt(3))hati+hatj` |
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| 257. |
For what value of x , will the two vector `A= 2hati + 2hatj -x hatk and B =2 hati - hatj - 3hatk ` are perpendicular to each other ?A. `x=-2//3`B. `x=-3//2`C. `x=-4//3`D. `x=-2//3` |
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Answer» Correct Answer - A (a) For vector to be perpendicular , `A.B=0` `implies(2hati+2hatj-xhatk).(2hati-hatj-3hatk)=0` `implies4-2+3x=0` `implies3x=- or x=(-2)/(3)` |
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| 258. |
If `A =a_(1) hat"i"+ b_(1)hat"j"and B=a_(2)hat"i"+b_(2)hat"j"` the condition that they are perpendicula to each other isA. `(a_(1) )/(b_(1))=-(b_(2))/(a_(2))`B. `a_(1)b_(1)= a_(2) b_(2)`C. `(a_(1) )/(b_(1))=-(b_(1))/(b_(2))`D. None of these |
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Answer» Correct Answer - A (a) For vector to be perpendicular ,dot product should be zero . `therefore(a_(1)hatj+b,hatj).(a_(2)hati+b_(2)hatj)=0` or`(a_(1))/(b_(1))=-(b_(2))/(a_(2))` |
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| 259. |
Let `a=a_(1)hati+a_(3)hatk, b=b_(1)hati+b_(3)hatk, c=c_(1)hati+c_(2)hatj+c_(3)hatk`. If `|c|=1 and (axxb)xxc=0`, then `|(a_(1),a_(2),a_(2)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))|` is equal to |
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Answer» Correct Answer - D Given, `(axxb)xxc=0, " then " c = (axxb)/(|axxb|) ` `therefore (a xxb)*c = |axxb| ` `rArr |(a_(1),a_(2),a_(3)),(b_(1),b_(2), b_(3)),(c_(1),c_(2),c_(3))|=|axxb|^(2)` |
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| 260. |
Five equal forces of `10 N` each are applied at one point and all are lying one plane. If the angles between them are equal, the resultant force will beA. zeroB. 10NC. 20ND. `10sqrt(2)N` |
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Answer» Correct Answer - A (a) when drawn as per polygon law of vector addition ,then will form a closed regular ,Hence Reultant will be zero. |
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| 261. |
Two equal vector have a resultant equal to either of them, then the angle between them will be:A. `120^(@)`B. `90^(@)`C. `60^(@)`D. `0^(@)` |
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Answer» Correct Answer - D Let `F_(1)= F_(2) = F` be forces them , `F_(2)= 2F` `F_(R)= sqrt(F_(1)^(2) + F_(2)^(2) + 2F_(1)F_(2) cos theta)` `(2F)^(2) = 2F^(2)+ 2F^(2) costheta ` `cos theta =1` `theta = 0^(@)` |
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| 262. |
Asserion: Magnitude of the resultant of two vectors may be less than the magnitude of either vector. Reason: The resultant of two vectors is obtained by means of law of parallelogram of Vectors.A. If both assertion and reason are true and reason is the correct explanation of assertion.B. If both assertion and reason are true but reason is not the correct explanation of assertionC. If assertion is true but reason is false.D. If both aseertion and reason are false. |
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Answer» Correct Answer - B If `vec(a)` and `vec(b)` are inclined at an angle greater than `90^(@)`, their resultant has magnitude `R=sqrt(a^(2)+b^(2)+2ab cos theta)` Which is less than both a and b, when they are nearly equal. |
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| 263. |
Statement-1:If ,`|vec A+vec B| =|vecA-vecB|` then angle between `vecA` and `vecB` is `90^(@)` Statement-2 :`vecA+vecB=vecB+vecA`A. If both assetion and reason are true and the reason is the correct explanation of the assertion.B. If both assertion and reason are true but reason is not the correct explanation of the assertionC. If assertion is true but reason is falseD. If the assertion and reason both are false. |
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Answer» Correct Answer - B |
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| 264. |
Two forces of magnitudes 30, 60 and P newton acting at a point are in equilibrium. If the angle between the first two is `60 ^(@) `, the value of P is :A. `(mv)/(sqrt(2))`B. 2 mvC. `sqrt(2)mv`D. `sqrt(2)/(mv)` |
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Answer» Correct Answer - D `P= sqrt( 60^(2) + 30^(2) + 2.60.30 cos60^(@))` |
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| 265. |
If `bar a,bar b,bar c` are non coplanar vectors and `lambda` is a real number then `[lambda(bar a+bar b)lambda^2 bar b lambda bar c]=[bar a bar b+bar c bar b]` forA. exactly two values of `lambda`B. exactly three values of `lambda`C. no volue of `lambda`D. exactly one value of `lambda` |
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Answer» Correct Answer - C Given , `[lambda(a+b) lambda^(2)b lambdac]= [a(b+c)b]` `|{:(lambda(a_(1)+b_(1)),lambda(a_(2)+b_(2)),lambda(a_(3) + b_(3))),(lambda^(2)b_(1),lambda^(2)b_(2),lambda^(2)b_(3)),(lambdac_(1),lambdac_(2),lambdac_(3)):}|=|{:(a_(1),b_(1)+c_(1),b_(1)),(a_(2),b_(2)+c_(2) ,b_(2)),(a_(3),b_(3)+c_(3),b_(3)):}| = |{:(a_(1),a_(2),a_(3)),(b_(1)+c_(1),b_(2)+c_(2),b_(3)+c_(3)),(b_(1),b_(2),b_(3)):}|` `rArr lambda^(4)|{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|= - |{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|` `rArr lambda^(4) = - 1` So, no value of `lambda` exists. |
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| 266. |
In Q-2, if vectors are perpendicular to each other then find the value of `lambda`. |
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Answer» If `vec(A)` and `vec(B)` are perpendicular to each other,then `vec(A).vec(B)=orArra_(1)b_(1)+a_(2)b_(2)+a_(3)b_(3)=0` So, `2(-4)+3(-6)+(-1)(lambda)=orArrlambda=-26` |
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| 267. |
Two vectors `vecP` and `vecQ` that are perpendicular to each other are :A. `vecP = 3hati +3hatj + 2hatk, vecQ = 2hati - 2hatj + 2hatk`B. `vecP = 2hati +3hatj + 2hatk, vecQ = 2hati - 2hatj + 2hatk`C. `vecP = 2hati -3hatj + 2hatk, vecQ = 2hati - 2hatj - 2hatk`D. `vecP = hati -3hatj + 2hatk, vecQ = 2hati - 2hatj + hatk` |
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Answer» Correct Answer - B `vecP, vecQ =0` |
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| 268. |
`veca, vecb and vecc` are three coplanar unit vectors such that `veca + vecb + vecc=0`. If three vectors `vecp, vecq and vecr` are parallel to `veca, vecb and vecc`, respectively, and have integral but different magnitudes, then among the following options, `|vecp +vecq + vecr|` can take a value equal toA. `1`B. `0`C. `sqrt3`D. `2` |
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Answer» Correct Answer - C::D Let `veca, vecb and vecc` lie in the x-y plane. Let `veca = hati, vecb = -(1)/(2) hati and vecc = -(1)/(2) hati - (sqrt3)/(2)hatj`. Therefore, `|vecp+ vecq + vecr| = |lamda veca + mu vecb + vvecc|` `= | lamda hati + mu(-(1)/(2)hati + (sqrt3)/(2)hatj) + v(-(1)/(2)hati- (sqrt3)/(2)hatj)|` `= |(lamda - (mu)/(2) - (v)/(2))hati + (sqrt3)/(2)(mu - v) hatj|` ` = sqrt((lamda - (mu)/(2) - (v)/(2))^(2) + (3)/(4)(mu-v)^(2))` `= sqrt(lamda^(2)+ mu^(2) + v^(2) -lamda mu -lamda v - mu v)` `" "=(1)/(sqrt2) sqrt((lamda-mu)^(2)+ (mu-v)^(2) +(v-lamda)^(2)) ge (1)/(sqrt2) sqrt(1+1+4) = sqrt3 ` Hence, `|vecp + vecq + vecr|` can take a value equal to `sqrt3` and 2. |
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| 269. |
Choose the correct statements:A. `vecA xx (vecB xx vecC)= (vecA xx vecB) xx vecC`B. `vecA . (vecB xx vecC)= vecC.(vecA xx vecB) `C. The area of parallelogram of sides `vecA` and `vecB` is equal to magitude of `vecA xx vecB`D. `vecB xx vecC = vecC xx vecB` |
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Answer» Correct Answer - A::C Vector properties. |
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| 270. |
To get a rsultant displacement of 10m, two displacement vectors, one of magnetic 6 m and another of 8 m,should be combined :A. parallelB. anti-parallelC. at an angle `60^(@)`D. perpendicular to each |
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Answer» Correct Answer - D Let `|vecr_(1)|= 6m " "|vecr_(2)|= 8m and |vecr|=10m` Then `sqrt(r_()^(2) + r_(2)^(2) + 2r_(1)r_(2) cos theta) = 10` `6^(2) + 8^(2) + 2r_(1)r_(2) cos theta = 10^(2)` `" "cos theta = 0^(@)` `" "theta= (pi)/(2)` |
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| 271. |
If `veca=mvecb+vecc`. The scalar m isA. `(veca.vecb-vecb.vecc)/(b^(2))`B. `(vecc.vecb-veca.vecc)/(a^(2))`C. `(vecc.veca-vecb.vecc)/(c^(2))`D. `(veca.vecb-vecb.vecc)/(a^(2))` |
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Answer» Correct Answer - A `mvecb.vecb=(veca-vecc).vecb` |
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| 272. |
Angle between the vectors `(hat(i)+hat(j))`and `(hat(j)-hat(k))` isA. `90^(@)`B. `0^(@)`C. `180^(@)`D. `60^(@)` |
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Answer» Correct Answer - D `cos theta =(vec(A).vec(B))/(|vec(A)||vecB|)=1/(sqrt(2)sqrt(2))=1/2 :. theta= 60^(@)` |
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| 273. |
The angle between the two vector `vec(A)= 5hat(i)+5hat(j)` and `vec(B)= 5hat(i)-5hat(j)` will beA. ZeroB. `45^(@)`C. `90^(@)`D. `180^(@)` |
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Answer» Correct Answer - C `vec(A).vec(B)=0 :. theta = 90^(@)` |
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| 274. |
If three vector along coordinate axis represent the adjacent sides of a cube of length b, then the unit vector along its diaonal passing thourth the origin will beA. `(hati+hatj+hatk)/(sqrt(2))`B. `(hati+hatj+hatk)/(sqrt(36))`C. `hati+hatj+hatk`D. `(hati+hatj+hatk)/(sqrt(3))` |
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Answer» Correct Answer - D (d) Diagonal vector ,`A=bhati+bhatj+bhatk` `Or A=sqrt(b^(2)+b^(2)+b^(2))=sqrt(3b)` `thereforeA=(A)/(|A|)=(hati+hatj+hatk)/(sqrt(3))` |
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| 275. |
The angle between the vector `2hati+hatj+hatk and hatj`?A. `(pi)/(6)`B. `(pi)/(4)`C. `(pi)/(3)`D. None of these |
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Answer» Correct Answer - B (b) The given vector is in XY-place .Here this is perrpendicular to Y-axis |
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| 276. |
Two vector `vecA` and `vecB` are at right angles to each other, whenA. `vecA+vecB=0`B. `vecA-vecB=0`C. `vecAxxvecB=0`D. `vecA.vecB=0` |
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Answer» Correct Answer - D |
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| 277. |
If `|vecV_(1)+vecV_(2)|=|vecV_(1)-vecV_(2)|` and `V_(2)` is finite, thenA. `V_(1)` is parallel to `V_(2)`B. `vecV_(1)=vecV_(2)`C. `V_(1)` and `V_(2)` are mutually perpendicularD. `|vecV_(1)|=|vecV_(2)|` |
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Answer» Correct Answer - C |
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| 278. |
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vector, the angle between these Vector isA. `90^(@)`B. `45^(@)`C. `180^(@)`D. `0^(@)` |
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Answer» Correct Answer - A (a) suppose two vector sr eP and Q . It is given that `|P+Q|=|P-Q|` Let angle between PandQ is `phi` `therefore P^(2)+Q^(2) +2PQ cosphi=P^(2)+Q^(2)-2PQcosphi` `implies4PQcosphi=0` `implies cosphi=0 [thereforeP,Qne0]` `=.phi=(pi)/(2) =90^(@)` |
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| 279. |
If a vector `2hati +3hatj +8hatk` is perpendicular to the vector `4hati -4hatj + alphahatk,` then the value of `alpha` isA. -1B. `(1)/(2)`C. `-(1)/(2)`D. 1 |
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Answer» Correct Answer - B `(2hati+3hatj +8hatk).(4hati - 4hatj+alpha hatk)=0` `:. 8-12 + 8alpha=0`c `:. alpha=(1)/(2).` |
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| 280. |
If `vecC=vecAxxvecB`, then `vecC` isA. parallel to `vecA`B. parallel to `vecB`C. perpendicular to `vecA` and parallel to `vecB`D. perpendicular to both `vecA` and `vecB` |
| Answer» Correct Answer - D | |
| 281. |
`(vecAxxvecB)+(vecBxxvecA)` is equal toA. 2ABB. `A^(2)B^(2)`C. zeroD. null vector |
| Answer» Correct Answer - D | |
| 282. |
A person pushes a box kept on a horizontal surface with force of `100 N`.In unit vector natation force can be expressed as: A. `100(hat(i)+hat(j))`B. `100(hat(i)-hat(j))`C. `50sqrt(2)(hat(i)-hat(j))`D. `50sqrt(2)(hat(i)+hat(j))` |
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Answer» Correct Answer - C `F= F cos 45^(@)hat(i)+ F sin 45^(@)(-hat(j))` `implies vec(F)= 50sqrt(2)hat(i)-50sqrt(2)hat(j)` |
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| 283. |
the value of `(vecA+vecB)xx(vecA-vecB)` is |
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Answer» Correct Answer - D |
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| 284. |
The vector triple production `vecA xx (vecB xx vecC)` will be zero if :A. `vecB= vecC`B. `vecA, vecB` and `vecC` are mutually perpendicularC. `vecA, vecB` and `vecC` are coplanar vectorsD. `vecA, vecB ` and `vecC` are collinear vectors |
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Answer» Correct Answer - A::B::D If `vecB = vecC`, then `vecB xx vecC = 0 rArr vecA xx(vecB xx vecC)=0` If `vecA, vecB` and `vecC` are mutually perpendicular , then `vecA. vecC ` and f `vecB. vecA` both are zero. `therefore" "vecA xx (vecB xx vecC)=vecB(vecA. vecC)- vecC( vecB . vecA)=0` If `vecA,vecB` and `vecC` are colliner, `vecB xx vecC =0` Hence, `vecA xx (vecB xx vecB ) = 0` |
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| 285. |
Assertion: The some of two Vectors can be zero. Reason: The vector cancel each other, when they are equal and opposite.A. If both assetion and reason are true and the reason is the correct explanation of the assertion.B. If both assertion and reason are true but reason is not the correct explanation of the assertionC. If assertion is true but reason is falseD. If the assertion and reason both are false. |
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Answer» Correct Answer - A |
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| 286. |
If `veca` and `vecb` are two unit vectors and the angle between them is `60^(@)` then `((1+veca.vecb))/((1-veca.vecb))` isA. 2B. 3C. 0D. `1//2` |
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Answer» Correct Answer - B `(1+veca.vecb)/(1-veca.vecb)=(1+cos theta)/(1-cos theta)=cot^(2)((theta)/(2))` |
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| 287. |
Assertion: A physical quantity cannot be called as a vector if its magnitude is zero. Reason: A vector has both, magnitude and direction.A. If both assetion and reason are true and the reason is the correct explanation of the assertion.B. If both assertion and reason are true but reason is not the correct explanation of the assertionC. If assertion is true but reason is falseD. If assertion is false but reason is true. |
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Answer» Correct Answer - D |
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| 288. |
If the two directional cosiness of a vectors are `(1)/sqrt(2)` and `(1)/sqrt(3)` then the value of third directional consine isA. `(1)/sqrt(6)`B. `(1)/sqrt(5)`C. `(1)/sqrt(7)`D. `(1)/sqrt(10)` |
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Answer» Correct Answer - A `cos^(2) gamma=1-cos^(2)alpha-cos^(2)beta`, |
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| 289. |
(A) : A vectors will not change when the fram of reference in which it is existing is rotated . (R) : A scalar quantity may (or) may not be independent of arientation of frame of reference :A. If both A and R are trun and R is the correct explanation of A.B. If both A and R are true, but R is not correct expalanation of A.C. If A is true, but R is fasle .D. If A is fasle , but R is true. |
| Answer» Correct Answer - C | |
| 290. |
Find the value of `lambda` in the unit vector `0.4 hati + 0.8 hatj + lambda hatk`. |
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Answer» Correct Answer - `sqrt(0.2)` |
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| 291. |
Assertion: If `vec(A).vec(B)= vec(B).vec(C )`, then `vec(A)` may not always be equal to `vec(C )`. Reason: The dot product of two vectors involves consine of the angle between the two vectors.A. If both assetion and reason are true and the reason is the correct explanation of the assertion.B. If both assertion and reason are true but reason is not the correct explanation of the assertionC. If assertion is true but reason is falseD. If the assertion and reason both are false. |
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Answer» Correct Answer - A |
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| 292. |
Assertion: If `vec(A).vec(B)= vec(B).vec(C )`, then `vec(A)` may not always be equal to `vec(C )`. Reason: The dot product of two vectors involves consine of the angle between the two vectors.A. If both assertion and reason are true and reason is the correct explanation of assertion.B. If both assertion and reason are true but reason is not the correct explanation of assertionC. If assertion is true but reason is false.D. If both aseertion and reason are false. |
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Answer» Correct Answer - A `vec(A).vec(B)= vec(B).vec(C )implies AB cos theta_(1)= BC cos theta_(2)` `:. A=C`, only when, `theta_(1)= theta_(2)` So when angle between `vec(A)` and `vec(B)` is equal to angle between `vec(B)` and `vec(C )` only then `vec(A)` equal to `vec(C )`. |
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| 293. |
If `|A|=2,|B|=5` and `|AxxB|=8.` Angle between A and B is acute, then `(A.B)` isA. 6B. 3C. 4D. 7 |
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Answer» Correct Answer - A (a) We have `AxxB =AB=sintheta` 8 =(5) (2) `sintheta` `sin theta=4//5 or cos theta=3//5` `A.B =AB cos theta =(5)(2) (3//5) =6` |
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| 294. |
Given `vec(P)=3hat(i)-4hat(j)`. Which of the following is perpendicular to `vec(P)`?A. `3hat(i)`B. `4hat(j)`C. `4hat(i)+3hat(j)`D. `4hat(i)-3hat(j)` |
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Answer» Correct Answer - C `vec(P)` is the fourth quadrant. `4hat(i)+3hat(j)` is in the first quadrant. Clearly, `4hat(i)+3hat(j)` can be perpendicular to `vec(P)`. For confirmation, let us check whether their dot product is zero. `(3hat(i)-4hat(j)).(4hat(i)+3hat(j))=12-12=0` This shows that `4hat(i)+3hat(j)` is perpenduicular to `3hat(i)+4hat(j)`. |
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| 295. |
A body, constrained to move in the Y-direction is subjected to a force given by `vecF=(-2hati+15hatj+6hatk)N`. What is the work done by this force in moving the body a distance 10 m along the Y-axisA. `20J`B. `150J`C. `160J`D. `190J` |
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Answer» Correct Answer - B |
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| 296. |
If `vec(A)=3hat(i)+hat(j)+2hat(k)` and `vec(B)=2hat(i)-2hat(j)+4hat(k),` then find the value of `|vec(A)xxvec(B)|.` |
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Answer» `vec(A)xxvec(B)=|(hat(i), hat(j), hat(k)) ,(3,1,2), (2 ,-2 ,4)|` `=[1xx4-2xx(-2)]hat(i)+(2xx2-4xx3)hat(j)+[3xx(-2)-1xx2]hat(k)` `8hat(i)-8hat(j)-8hat(k)` `:.` Magnitude of `vec(A)xxvec(B)=|vec(A)xxvec(B)|=sqrt((8)^(2)+(-8)^(2)-(-8)^(2))=8 sqrt(3)` |
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| 297. |
Five equal forces of `10 N` each are applied at one point and all are lying one plane. If the angles between them are equal, the resultant force will beA. ZeroB. `10 N`C. `20 N`D. `10sqrt(2)N` |
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Answer» Correct Answer - A If the angle between all forces which are equal and lying in one plane are equal then resultant force will be zero. |
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| 298. |
Five equal forces of `10 N` each are applied at one point and all are lying one plane. If the angles between them are equal, the resultant force will beA. zeroB. 10 NC. 20 ND. `10sqrt(2) N` |
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Answer» Correct Answer - A Because all forces cancel each other i.e., resultant of four forces is equal and opposite to fifth one. |
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| 299. |
Five equal forces of `10 N` each are applied at one point and all are lying one plane. If the angles between them are equal, the resultant force will beA. ZeroB. `10 N`C. `20 N`D. `10 sqrt(2) N` |
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Answer» Correct Answer - A |
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| 300. |
Two vectors acting through a point are in the ratio `3 : 5`. If the angle between them is `60^(@)` and the magnitude of their resultant is `35` , find the magnitude of vectors.A. `12 N , 20 N`B. `15 N , 25 N`C. `18 N , 30 N`D. `21 N , 28 N` |
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Answer» Correct Answer - B `P = 3x , Q = 5x , theta = 60^(@) , R = 35` `R^(2) = P^(2) + Q^(2) + 2 P cos theta` `(35)^(2) = (3x)^(2) + (5x)^(2) + 2 . 3x . 5x . Cos theta 60^(@)` `= 9x^(2) + 25 x^(2) + 15 x^(2) = 49 x^(2)` `35 xx 35 = 7 xx 7 x^(2)` `x = 5` `P = 3x = 15 N , Q = 5x = 25 N` |
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