Class 12th

This is a long answer type question as classified in NCERT Exemplar

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- a, b

Explanation - |A+B|= |A|or |A+B|²=|A|²

|A|² +|B|²+2|A|B|cos $\theta$ = |A|²

|B| (|B|+2|A|cos $\theta$ )= 0

|B|=0 or |B|+2|A|cos $\theta$ =0

Cos $\theta$ = $\frac{-\left|B\right|}{2\left|A\right|}$

If A and B are antiparallel then $\theta$ =180

-1= $\frac{\left|B\right|}{2\left|A\right|}=\left|B\right|=2\left|A\right|$

When no current flows in the circuit, the total potential difference provided by a source is known as the Electromagnetic force (EMF). On the other hand, when current flows in the circuit, the actual voltage across the terminals of the cell is called the terminal voltage. The formula that depicts the relation is:

Where r is the internal resistance and I is the current.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- b, d

Explanation – given A+B+C = 0

B $*\left(A+B+C\right)=B*0=0$

B $*A$ +B $*B+B*C$ =0

B $*A+0+B*C=0$

B $*A=-B*C$

A $*B=B*C$

(A $*B$ ) $*C=\left(B*C\right)*C$

It cannot be zero

(b) (A $*B$ ).C= (B $*AC$ ).C=0 . if b|C then B $*C$ =0 then (B $*C$ ) $*C=0$

(c) (A $*B$ )=X=ABsin $?X$ . The direction of X is perpendicular to the plane containing A and B (A $*B$ ) $*C=X*C.$

(d) if c²= A²+B², then angle between A and B is 90⁰

(A $*B$ ).C= (AB sin90⁰X).C=AB (X.C)

= ABC cos90⁰= 0

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer-b, d

Explanation- as given motion is two-dimensional motion and given that instantaneous speed v_o is positive constant. Acceleration is rate of change of velocity. hence it will also be in the plane of motion.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- d

Explanation – speed = total distance travelled /time taken

Total distance travelled = path length

= speed $*$ time

We should be very careful with the fact, that speed is related with total distance covered not with displacement.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- b

Explanation – we know that impulse J= f. $?t$ = $?p$ , where F is force . $?t$  is time duration and $?p$  is change in momentum. As $?p$ is a vector quantity, hence impulse is also a vector quantity. Sometimes area can also be treated as vector.

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- c

Explanation - we know that $\theta$ =15⁰ and R= 50m

Range, R= $\frac{u^{2}sin2\theta }{g}$

50 = $\frac{u^{2}sin2*15}{g}$

So u²= 980

So u = $\sqrt[]{980}=7*2*\sqrt[]{5}$ m/s

So u= 14 $*2.23$ = 31.304m/s

$\theta$ = 45⁰, R= $\frac{u^{2}sin2\left(45\right)}{9.8}=\frac{u^2}{g}$

R= $\frac{({14\sqrt[]{5)}}^2}{g}$ = $\frac{14*14*5}{9.8}$ = $100m$

This is a Multiple Choice Questions as classified in NCERT Exemplar

Answer- b

Explanation – ler r makes an angle $?$ with positive x axis component if r along x-axis.

So  r_x= |r|cos $?$

(r_x)_maximum= |r| (cos $?$ )_maximum

= |r|cos $0$ = r

$?$ =0⁰

R is along positive x-axis.