100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS

1.	Resolve\[\frac{x}{(x+1)^{2}(x+2)}\]
Answer» If you are talking about partial fraction function. Let \(\frac x{(x+1)^2(x+2)}\) = \(\frac A{x+1}+\frac B{(x+1)^2}+\frac C{x+2}\) ⇒ x = A (x+1) (x+2) + B (x+2) + C (x+1)² put x = -1, we get B = -1 put x = -2, we get C = -2 put x = 0, we get 2A+2B+C = 0 ⇒ 2A = -C - 2B = 2+2 = 4 ⇒ A = 4/2 = 2 ∴ \(\frac x{(x+1)^2(x+2)}\) = \(\frac2{x+1}-\frac1{(x+1)^2}-\frac2{x+2}\)

1.

Resolve\[\frac{x}{(x+1)^{2}(x+2)}\]

Answer»

If you are talking about partial fraction function.

Let \(\frac x{(x+1)^2(x+2)}\) = \(\frac A{x+1}+\frac B{(x+1)^2}+\frac C{x+2}\)

⇒ x = A (x+1) (x+2) + B (x+2) + C (x+1)²

put x = -1, we get B = -1

put x = -2, we get C = -2

put x = 0, we get 2A+2B+C = 0

⇒ 2A = -C - 2B = 2+2 = 4

⇒ A = 4/2 = 2

∴ \(\frac x{(x+1)^2(x+2)}\) = \(\frac2{x+1}-\frac1{(x+1)^2}-\frac2{x+2}\)

Discussion

2.	(xii)\( \left\|\begin{array}{ccc}a & b & c \\ a^{2} & b^{2} & c^{2} \\ b+c & c+a & a+b\end{array}\right\|=(b-c)(c-a)(a-b)(a+b+c) \)
Answer» \(\begin{vmatrix}a&b&c\\a^2&b^2&c^2\\b+&c+a&a+b\end{vmatrix}\) Applying C₂→C₂→C₁, C₃→C₃ - C₁ \(=\begin{vmatrix}a&b-a&c-a\\a^2&(b-a)(b+a)&(c-a)(c+a)\\b+c&-(b-a)&-(c-a)\end{vmatrix}\) Applying C₂→C₂/b-a, C₃→C₃/c-a \(=(b-a)(c-a)\begin{vmatrix}a&1&1\\a^2&(b+a)&(c+a)\\b+c&-1&-1\end{vmatrix}\) Applying C₃→ \(\frac{C_3-C_2}{c-b}\) \(=(b-a)(c-a)(c-b)\begin{vmatrix}a&1&0\\a^2&(b+a)&1\\b+c&-1&0\end{vmatrix}\) on expanding determinant along column C₃ = (a - b) (b -c) (c - a) (-1)\(\begin{vmatrix}a& 1\\b+c&-1\end{vmatrix}\) = (a - b) (b - c) (c - a) (-1) (-a - b - c) = (a - b) (b - c) (c - a) (a + b +c)

2.

(xii)\( \left|\begin{array}{ccc}a & b & c \\ a^{2} & b^{2} & c^{2} \\ b+c & c+a & a+b\end{array}\right|=(b-c)(c-a)(a-b)(a+b+c) \)

Answer»

\(\begin{vmatrix}a&b&c\\a^2&b^2&c^2\\b+&c+a&a+b\end{vmatrix}\)

Applying C₂→C₂→C₁, C₃→C₃ - C₁

\(=\begin{vmatrix}a&b-a&c-a\\a^2&(b-a)(b+a)&(c-a)(c+a)\\b+c&-(b-a)&-(c-a)\end{vmatrix}\)

Applying C₂→C₂/b-a, C₃→C₃/c-a

\(=(b-a)(c-a)\begin{vmatrix}a&1&1\\a^2&(b+a)&(c+a)\\b+c&-1&-1\end{vmatrix}\)

Applying C₃→ \(\frac{C_3-C_2}{c-b}\)

\(=(b-a)(c-a)(c-b)\begin{vmatrix}a&1&0\\a^2&(b+a)&1\\b+c&-1&0\end{vmatrix}\)

on expanding determinant along column C₃

= (a - b) (b -c) (c - a) (-1)\(\begin{vmatrix}a& 1\\b+c&-1\end{vmatrix}\)

= (a - b) (b - c) (c - a) (-1) (-a - b - c)

= (a - b) (b - c) (c - a) (a + b +c)

Discussion

3.	\[D=\left\|\begin{array}{ccc}p & q & p \alpha-q \\q & r & q_{\alpha}-r \\2 & 1 & 0\end{array}\right\|\]If \( q^{2} \neq P_{r} \), got what value of \( \alpha, D \) becomes zero
Answer» \(D=\begin{vmatrix}p&q&p\alpha-q\\q&r&q\alpha-r\\2&1&0\end{vmatrix}=0\) Applying c₃ → c₃ - (αc₁- c₂) \(D=\begin{vmatrix}p&q&0\\q&r&0\\2&1&-(2\alpha-1)\end{vmatrix}=0\) ⇒ -(2α - 1) \(\begin{vmatrix}p&q\\q&r\end{vmatrix}=0\) (By expanding determinant along column c₃) ⇒ -(2α - 1) (pr - q²) = 0 ⇒ 2α - 1 = 0 (∵ pr ≠ q² (given)) ⇒ α = 1/2.

3.

\[D=\left|\begin{array}{ccc}p & q & p \alpha-q \\q & r & q_{\alpha}-r \\2 & 1 & 0\end{array}\right|\]If \( q^{2} \neq P_{r} \), got what value of \( \alpha, D \) becomes zero

Answer»

\(D=\begin{vmatrix}p&q&p\alpha-q\\q&r&q\alpha-r\\2&1&0\end{vmatrix}=0\)

Applying c₃ → c₃ - (αc₁- c₂)

\(D=\begin{vmatrix}p&q&0\\q&r&0\\2&1&-(2\alpha-1)\end{vmatrix}=0\)

⇒ -(2α - 1) \(\begin{vmatrix}p&q\\q&r\end{vmatrix}=0\) (By expanding determinant along column c₃)

⇒ -(2α - 1) (pr - q²) = 0

⇒ 2α - 1 = 0 (∵ pr ≠ q² (given))

⇒ α = 1/2.

Discussion

4.	Which of the following is isoelectronic?1. \( CO _{2}, NO _{2} \)2. \( NO _{2}^{-}, CO _{2} \)3. \( CN ^{-}, CO \)4. \( SO _{2}, CO _{2} \)
Answer» ions or atoms that have same number of electrons are called isoelectronic species. Here, CN^- and CO have same number of electrons — CN^-⇒ 6+7+1 = 14 e's CO ⇒ 6+8 = 14 e's Therefore, option (3) is right answer.

4.

Which of the following is isoelectronic?1. \( CO _{2}, NO _{2} \)2. \( NO _{2}^{-}, CO _{2} \)3. \( CN ^{-}, CO \)4. \( SO _{2}, CO _{2} \)

Answer»

ions or atoms that have same number of electrons are called isoelectronic species.

Here,

CN^- and CO have same number of electrons —

CN^-⇒ 6+7+1 = 14 e's

CO ⇒ 6+8 = 14 e's

Therefore, option (3) is right answer.

Discussion

5.	find rank of Matix\[A=\left[\begin{array}{rrrr}2 & 3 & -1 & -1 \\1 & -1 & -2 & -4 \\3 & 1 & 3 & -2\end{array}\right]\]
Answer» \(A=\begin{bmatrix}2&3&-1&-1\\1&-1&-2&-4\\3&1&3&-2\end{bmatrix}\) \(\leftrightarrow\begin{bmatrix}2&3&-1&-1\\0&-5&-3&-7\\0&4&9&10\end{bmatrix}\) (Applying R₃ → R₃ - R₂& R₂ → 2R₂ - R₁) \(\leftrightarrow\begin{bmatrix}2&3&-1&-1\\0&-5&-3&-7\\0&0&33&22\end{bmatrix}\) (Applying R₃→ 5R₃ + 4R₂) ∴ Rank of given matrix is 3.

5.

find rank of Matix\[A=\left[\begin{array}{rrrr}2 & 3 & -1 & -1 \\1 & -1 & -2 & -4 \\3 & 1 & 3 & -2\end{array}\right]\]

Answer»

\(A=\begin{bmatrix}2&3&-1&-1\\1&-1&-2&-4\\3&1&3&-2\end{bmatrix}\)

\(\leftrightarrow\begin{bmatrix}2&3&-1&-1\\0&-5&-3&-7\\0&4&9&10\end{bmatrix}\) (Applying R₃ → R₃ - R₂& R₂ → 2R₂ - R₁)

\(\leftrightarrow\begin{bmatrix}2&3&-1&-1\\0&-5&-3&-7\\0&0&33&22\end{bmatrix}\) (Applying R₃→ 5R₃ + 4R₂)

∴ Rank of given matrix is 3.

Discussion

6.	A is 3 x 3 metrics and \|adj\| = 4 then find(i) \|2A\|(ii) \|-3A-1\|(iii) A.AdjA
Answer» A is matrix of order 3. \(\|adjA\| = 4\) \(\because \|adjA\| = \|A\|^{3 - 1}= \|A\|^2\) \(\therefore \|A\|^2 = 4\) ⇒ \(\|A\| = \pm 2\) (i) \(\|2A\| = 2^3\|A\|= 8(\pm2) = \pm 16\) (ii) \(\|-3A^{-1}\| = (-3)^3 \|A^{-1}\| = \frac{-27}{\|A\|} = \frac{-27}{\pm2}= \pm\frac{27}2\) (iii) \(A.adj A = \|A\|I= \pm 2I= \begin{bmatrix}\pm2&0&0\\0&\pm2&0\\0&0&\pm2\end{bmatrix}\)

6.

A is 3 x 3 metrics and |adj| = 4 then find(i) |2A|(ii) |-3A-1|(iii) A.AdjA

Answer»

A is matrix of order 3.

\(|adjA| = 4\)

\(\because |adjA| = |A|^{3 - 1}= |A|^2\)

\(\therefore |A|^2 = 4\)

⇒ \(|A| = \pm 2\)

(i) \(|2A| = 2^3|A|= 8(\pm2) = \pm 16\)

(ii) \(|-3A^{-1}| = (-3)^3 |A^{-1}| = \frac{-27}{|A|} = \frac{-27}{\pm2}= \pm\frac{27}2\)

(iii) \(A.adj A = |A|I= \pm 2I= \begin{bmatrix}\pm2&0&0\\0&\pm2&0\\0&0&\pm2\end{bmatrix}\)

Discussion

7.	A particle executes `SHM` on a straight line. At two positions, its velocities are `u` and `v` whle accelerations are `alpha` and `beta` respectively `[beta gt alpha gt ]`.The distance between these two positions isA. `(u^(2)-v^(2))/(alpha+beta)`B. `(u^(2)+v^(2))/(alpha+beta)`C. `(u^(2)-v^(2))/(alpha-beta)`D. `(u^(2)+v^(2))/(alpha-beta)`
Answer» Correct Answer - A Let distance by `x_(1)` when velocity if u and accleration `alpha`. Let distance by `x_(2)` when velocity is v and acceleration `beta`. If `omega` is the angular frequencey then, `alpha=omega^(2)x_(2)` `therefore alpha+beta=omega^(2)(x_(1)+x_(2)),.......(1)` `"Also," u^(2)=omega^(2)A^(2)-omega^(2)x_(1)^(2)` `and v^(2)=omega^(2)A^(2)-omega^(2)x_(2)^(2` `v^(2)-u^(2)=omega^(2)(x_(1)^(2)-x_(2)^(2))` `v^(2)-u^(2)=omega^(2)(x_(1)-x_(2))(x_(1)+x_(2)).....(ii)` By. eq (i) we get `v^(2)-u^(2)=(x_(1)-x_(2))(alpha+beta)` `therefore x_(1)-x_(2)=(u^(2)-v^(2))/(alpha+beta) or x_(2)-x_(1)=(u^(2)-v^(2))/(alpha+beta)`

Discussion

8.	Let x-2/3 = y+1/-2 = z+3/-1 lie on the plane px – qy + z = 5, for some p, q ∈ R .The shortest distance of the plane from the origin is:(A) √(3/109)(B) √(5/142)(C) √(5/71)(D) √(1/142)
Answer» Correct option is (B) √(5/142) (2, –1, –3) satisfy the given plane. So 2p + q = 8 .... (i) Also given line is perpendicular to normal plane so 3p + 2q – 1 = 0 .... (ii) ⇒ p = 15, q = –22 Eq. of plane 15x – 22y + z – 5 = 0 its distance from origin = 6/√710 = √(5/142)

8.

Let x-2/3 = y+1/-2 = z+3/-1 lie on the plane px – qy + z = 5, for some p, q ∈ R .The shortest distance of the plane from the origin is:(A) √(3/109)(B) √(5/142)(C) √(5/71)(D) √(1/142)

Answer»

Correct option is (B) √(5/142)

(2, –1, –3) satisfy the given plane.

So 2p + q = 8 .... (i)

Also given line is perpendicular to normal plane so

3p + 2q – 1 = 0 .... (ii)

⇒ p = 15, q = –22

Eq. of plane 15x – 22y + z – 5 = 0

its distance from origin

= 6/√710 = √(5/142)

Discussion

9.	If the line px + qy =1 is a tangent to the parabola `y^(2)` =4ax, thenA. `p^(2)-aq=0`B. `p+aq^(2)=0`C. `p-aq^(2)=0`D. `p-2aq^(2)=0`
Answer» Correct Answer - 2 `px+qy-1=0` `qy=px+1` `y=(-p)/(q)x+1/q` `Y^(2)=4ax` C.T `c=a//m` `1/q=a//-p//q` `p=-aq^(2)` `p+aq^(2)=0`

Discussion

10.	The equation of the plane passing through the lines `(x-4)/(1)=(y-3)/(1)=(z-2)/(2) and (x-3)/(1)=(y-2)/(-4)=(z)/(5)`, isA. 11x-y-3z=35B. 11x+y-3z=35C. 11x-y+3z=35D. None of these
Answer» Correct Answer - 4 `\|{:(x-x_(1),y-y_(1),z-z_(1)),(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)):}\|=0` `-13x+3y+5y+33=0`

Discussion

11.	If the volume oftetrahedron `A B C D`is 1 cubic units, where `A(0,1,2),B(-1,2,1)a n dC(1,2,1),`then the locus of point `D`isa. `x+y-z=3`b. `y+z=6`c. `y+z=0`d. `y+z=-3`A. x+y-z=3B. y+z=6C. y+z=-3D. None of these
Answer» Correct Answer - 2 `A(0,1,2),B(-1,2,1),C(1,2,1)& D(u,v,w)` (volume of tetralfhedrom ABCD) `\|(1)/(6)[overset(rarr)(AB" ")overset(rarr)(AC" ")overset(rarr)(AD" ")]=1` cubic units `=\|{:(-1,1,-1),(" "1,1,-1),(u-0,v-1,w-2):}\|` `rArr{:{(y-1+z-2=+-3),(y+z=6 or y+z=0):}`

Discussion

12.	Match the following :Column IColumn IIIIf the planes 2x - 4y + 3z = 7 and x + 2y + λz = 18 are perpendicular then λ = 1(a) -1IIThe length of projection of vector a = vector(i - 2j + k) on vector b = vector(4i - 4j + 7k) is(b) 0IIIIf A = [(2,3),(5,7)] then [AT] = (c) 2IVIf D = \|(3,2,7),(8,9,11),(11,11,18)\| the D = (d) 19/9
Answer» Answer is I. (c) 2 II. (d) 19/9 III. (a) -1 IV. (b) 0

12.

Match the following :Column IColumn IIIIf the planes 2x - 4y + 3z = 7 and x + 2y + λz = 18 are perpendicular then λ = 1(a) -1IIThe length of projection of vector a = vector(i - 2j + k) on vector b = vector(4i - 4j + 7k) is(b) 0IIIIf A = [(2,3),(5,7)] then [AT] = (c) 2IVIf D = |(3,2,7),(8,9,11),(11,11,18)| the D = (d) 19/9

Answer»

Answer is

I. (c) 2

II. (d) 19/9

III. (a) -1

IV. (b) 0

Discussion

13.	Figure shows a path followed by a particle and position of a particle at any instant. Four different students have represented the velocity vectors and acceleration vectors at the given instant. Which vector diagram cannot be true in any situation? (In each figure, velocity is tangential to the trajectory). A. `15ms^(-1)`B. `30ms^(-1)`C. `10ms^(-1)`D. `25ms^(-1)`
Answer» Correct Answer - D `veca_("net")` in curved path is always within the curvature of trajectory.

Discussion

14.	A particle is projected in a smooth fixed square tube from point A. The tube is in vertical plane and D and B are at same horizontal level as shown in figure. Then : (Assume velocity of particle changes smoothly at corners) A. velocity at A is equal to velocity at CB. velocity at B is equal to velocity at DC. velocity at A is equal to negative of velocity at CD. speed ast B is equal to speed at D
Answer» Correct Answer - D A particle is ……….. At B and D magnitude of velocity are same but direactions are different.

Discussion

15.	A body is thrown horizontally with an initial velocity of `10m//s` from a cliff. At what time (in sec.) will the velocity vector make an angle of `45^(@)` with horizontal?
Answer» Correct Answer - 1 `tan 45^(@)=(v_(y))/(u_(x))=(g t)/(10)` t = 1 sec

Discussion

16.	Given `vec(A) = 3 hat(i) + 4 hat(j)` and `vec(B) = 6 hat(i) + 8 hat(j)`. (A) `vec(A) . Vec(B) = 50` (B) `(\|vec(A)\|)/(\|vec(B)\|) = (1)/(2)` (C ) `\|vec(A)\| = 5` (D) Projection vector of `vec(A)` along `vec(B)` is `3hat(i) + 4 hat(j)` Which of the following statements is correct ?A. Only A is correctB. Only A and B are correctC. Only A, B and C are correctD. All are correct
Answer» Correct Answer - D (A) `vec(A) . Vec(B) = 18 + 52 = 50` (B) `\|A\| = 5, \|B\| = 10` (D) `(50(6 hat(i) + 8 hat(j)))/(100) = 3 hat(i) + 4 hat(j)`

Discussion

17.	A particle is moving along straight line with initial velocity `+7m//sec` and uniform acceleration `-2m//sec^(2)` . The distance travlled by the particle in `4th` second of its motion is:A. `0`B. `0.25m`C. `0.5m`D. `7m`
Answer» Correct Answer - C A particle……… Distance travelled `= \|S_(3-3.5)\|+\|S_(3.5-4)\|` `\|(1+0)/(2)xx0.5\|+\|(0+(-1))/(2)xx0.5\|=0.25+0.25` `= 0.5m`.

Discussion

18.	The displacement of a particle after time t is given by `x = (k // b^(2)) (1 - e^(-bi))`. Where b is a constant. What is the acceleration fo the particle ?A. `ke^(-bt)`B. `- ke^(-bt)`C. `(k)/(b^(2))e^(bt)`D. `(- k)/(b^(2))e^(-bt)`
Answer» Correct Answer - B `v = (dx)/(dt) = (k)/(b^(2)) xx e(-bt) xx b` `(dv)/(dt) = -ke^(-bt)`

Discussion

19.	The graph to the right is a plot of position versus time. For which labeled region is the velocity positive and the acceleration negative? A. aB. bC. cD. d
Answer» Correct Answer - D For d slope `dx//dt` is `+ve`, so velocity is `+ve` But `(d.((dx)/(dt)))/(dt)` is -vebecause slope decreasing so `(d.((dx)/(dt)))/(dt)= (d^(2)x)/(dt^(2))` is -ve, therefore acceleration is -ve

Discussion

20.	A particle is moving in a straight line with initial velocity `u` and uniform acceleration `f`. If the sum of the distances travelled in `t^(th) and (t + 1)^(th)` seconds is `100 cm`, then its velocity after `t` seconds, in `cm//s`, is.A. 20B. 30C. 50D. 80
Answer» Correct Answer - C `a = f` `(dv)/(dt) = f " " rArr underset(u) overset(v)int dv = underset(0) overset(t) int fdt` `rArr v = u + ft` `v = (dx)/(dt) = u + ft` `rArr underset(0) overset(100)int dx = underset(t - 1)overset(t + 1)int (u + ft) dt rArr 2u + 2f t` `= 100 rArr u + ft = 50` ....(1) `v t sec rArr v = u + ft = 50 cm//s` by (1)

Discussion

21.	If tension in string A and string B are `T_(A)` and `T_(B)` then find out `(T_(A))/(T_(B))` (assume that stringe are light and `g = 10 m//s^(2))` :
Answer» Correct Answer - 1 If tension ………… `(T_(c ))/(sqrt(2)) = T_(A) = T_(B)` `+`

Discussion

22.	A uniform circular disc placed on a horizontal rough surface has initially a velocity `v_(0)` and an angular velocity `omega_(0)` as shown in the figure. The disc comes to rest after moving some distance in the direction of motion. Then `v_(0)//omega_(0)` is `:` A. `r//2`B. `r`C. `3r//2`D. 2
Answer» Correct Answer - A `mV_(0)R-(mR^(2))/(2).omega_(0)=0` `(V_(0))/(omega_(0))=(R)/(2)`

Discussion

23.	A block of mass `m = 2 kg` is connected to a spring of force constant `k = 50 n//m`. Initially the block is at rest and the spring has natural length . A constant force `f = 60 N`, is applied horizontally towards right, the maximum speed of the block (in `m//s` will be (neglect frication).
Answer» Correct Answer - 6 A block of ……………… For maximum speed, `(dv)/(dt) = 0 implies a = 0` If at maximum speed, elongation is x, then `F = kx implies x = (F)/(k)` Now, by WET, `-(1)/(2)kx^(2)+Fx=(1)/(2)mv^(2)` `:. V = (F)/(sqrt(mk))=6 m//s`

Discussion

24.	A particle starts with constant angular acceleration of `"2 rad/s"^(2)` in a circle of radius 4m. Find angle between net acceleration and radial acceleration after 2 s :-A. `theta=tan^(-1)((1)/(8))`B. `theta=tan^(-1)((1)/(4))`C. `theta=tan^(-1)((1)/(2))`D. `theta=tan^(-1)((1)/(16))`
Answer» Correct Answer - A `vec(alpha)=2"rad/s"` `r=4m` `omega=0+2(2) rArr omega=4"rad/s"` `a_("cp")=omega^(2)r=64` `a_(t)=alphar=8` `tan alpha=((a_(t))/(a_(r))), alpha=tan^(-1)((1)/(8))`

Discussion

25.	A solid sphere is given an angular velocity `zeta` and kept on a rough fixed incline plane. The choose the correct statement. A. If `mu=tantheta`, then the sphere will be in linear equilibrium for some time and after that pure rolling down the plane will startB. If `mu=tantheta`, then sphere will move up the plane and frictional force acting all the time will be `2mgsinrho`.C. If `mu=tantheta//2` there will never be pure rolling (consider inclined plane to be long enough).D. If the incline plane is not fixed at it is on the smooth horizontal surface, then the linear momentum of the system (wedge and sphere) can be conserved in the horizontal direction.
Answer» Correct Answer - A::D Due to the torque of friction about CM `zeta` eventually decreases to zero, initially there is no translation. Friction is sufficient for pure rolling, therfore after sometime pure rolling begins. There is no external force in `x` direction, therefore momentum is conserved along `x` direction.

Discussion

26.	If you are interested in becoming a ________ of the club, telephone the secretary during office hours. A) member B) partner C) sharer D) player E) student
Answer» Correct option is A) member

Discussion

27.	Number of carbonyl units co-ordinated to iron metal in its carbonyl is:
Answer» Iron carbonyl is `Fe(CO)_(3)`.

Discussion

28.	The first English dictionary was ________ by Dr Johnson. A) compiled B) co-ordinated C) collected D) composed E) constructed
Answer» Correct option is A) compiled

Discussion

29.	write about the fertility rate and 5 point or 10 points in social science
Answer» The fertility rate (FR) is the number of live births per 1,000 women of reproductive age (ages 15 to 49 years) per year. This is a more refined way to measure fertility than crude birth rate because the FR accounts for the percentage of women aged 15 to 49 years in a population.

Discussion

30.	Social and Cultural issues which may provoke public sentiments :1. Should not be referred in the classroom2. Should not be discussed in the classroom3. Should be discussed with sufficient caution4. None of the above
Answer» Correct Answer - Option 3 : Should be discussed with sufficient caution In every society, there are socio-cultural issues that need to be addressed and tackled. Some of the important socio-cultural issues that need to be addressed today are casteism, dowry, communalism, drinking, drug addiction, etc. To teach students about social and cultural issues a teacher should - Express interest in the ethnic background of your students. Encourage your students to research and share information about their ethnic background as a means of fostering a trusting relationship with fellow classmates. Redirect your role in the classroom from instructor to facilitator. Maintain a strict level of sensitivity and should be discussed with sufficient caution. Maintain high expectations for student performance. Given that culturally responsive instruction is a student-centered philosophy, it should come as no surprise that expectations for achievement are determined and assigned individually for each student. Incorporate methods for self-testing. Teaching students to self-test while learning new information will help them better remember and use what they’ve learned in class and will help them realize on their own when they need to study a topic in greater depth. Maintain an “inclusive” curriculum that remains respectful of differences. A social and culturally responsive curriculum also encourages teachers’ understanding and recognition of each student’s non-school cultural life and background and provides a means for them to incorporate this information into the curriculum, thus promoting inclusion. Therefore, Social and Cultural issues which may provoke public sentiments should be discussed with sufficient caution in the classroom.

30.

Social and Cultural issues which may provoke public sentiments :1. Should not be referred in the classroom2. Should not be discussed in the classroom3. Should be discussed with sufficient caution4. None of the above

Answer» Correct Answer - Option 3 : Should be discussed with sufficient caution

In every society, there are socio-cultural issues that need to be addressed and tackled. Some of the important socio-cultural issues that need to be addressed today are casteism, dowry, communalism, drinking, drug addiction, etc.

To teach students about social and cultural issues a teacher should -

Express interest in the ethnic background of your students. Encourage your students to research and share information about their ethnic background as a means of fostering a trusting relationship with fellow classmates.
Redirect your role in the classroom from instructor to facilitator.
Maintain a strict level of sensitivity and should be discussed with sufficient caution.
Maintain high expectations for student performance. Given that culturally responsive instruction is a student-centered philosophy, it should come as no surprise that expectations for achievement are determined and assigned individually for each student.
Incorporate methods for self-testing. Teaching students to self-test while learning new information will help them better remember and use what they’ve learned in class and will help them realize on their own when they need to study a topic in greater depth.
Maintain an “inclusive” curriculum that remains respectful of differences. A social and culturally responsive curriculum also encourages teachers’ understanding and recognition of each student’s non-school cultural life and background and provides a means for them to incorporate this information into the curriculum, thus promoting inclusion.

Therefore, Social and Cultural issues which may provoke public sentiments should be discussed with sufficient caution in the classroom.

Discussion

31.	A string is fixed at both ends. The tension in the string and density of the string are accurately known but the length and the radius of cross section of the string are known with some errorl If maximum errors made in the measurements of length and radius are `1%` and `0.5%` respectively them what is the maximum possible percentage error in the calculation of fundamental frequencyof the that string ?
Answer» Correct Answer - `1.5%` `f=(1)/(2l)sqrt((T)/(mu))=(1)/(2l)sqrt((T)/(rhoS))=(1)/(2l)sqrt((T)/(rho.pir^(2)))=(1)/(2lr)sqrt((T)/(rho pi))` `:. (Deltaf)/(f)=-(Deltal)/(l)-(Deltar)/(r)` `((Deltaf)/(f))_(max)=1+0.5=1.5% Ans. `

Discussion

32.	The Communal Award, which was subsequently changed following Gandhi’s fast unto death in a jail at Poona, had been given by (a) Ramsay Mcdonald (b) Lloyd George (c) Stanley Baldwin (d) AV Alexander
Answer» (a) Ramsay Mcdonald

Discussion

33.	A Bus cover an equal distance at the speed of 200 km/hr, 400 km/hr and 600 km/hr, then find the average speed (approx.)of the bus for the whole journey. 1. 327 km/hr2. 320 km/hr3. 430 km/hr4. 420 km/hr
Answer» Correct Answer - Option 1 : 327 km/hr GIVEN: Different speed for the equal distance is 200 km/hr, 400 km/hr and 600 km/hr FORMULA USED: Average Speed = Total Distance/Total Time CALCULATION: Let the equal distance be d km ⇒ Average Speed = Total Distance/Total Time \(⇒ \frac{{3d}}{{\frac{d}{{200}} + \frac{d}{{400}} + \frac{d}{{600}}}}\) \( ⇒ \frac{{3d}}{{\frac{{6d \; + \; 3d \; + \; 2d}}{{1200}}}}\) \(⇒ \frac{{3d \; \times\; 1200}}{{11d}}\) ⇒ 3600/11 ⇒ 327.27 km/hr ≈ 327 km/hr ∴ The average speed is 327 km/hr

33.

A Bus cover an equal distance at the speed of 200 km/hr, 400 km/hr and 600 km/hr, then find the average speed (approx.)of the bus for the whole journey. 1. 327 km/hr2. 320 km/hr3. 430 km/hr4. 420 km/hr

Answer» Correct Answer - Option 1 : 327 km/hr

GIVEN:

Different speed for the equal distance is 200 km/hr, 400 km/hr and 600 km/hr

FORMULA USED:

Average Speed = Total Distance/Total Time

CALCULATION:

Let the equal distance be d km

⇒ Average Speed = Total Distance/Total Time

\(⇒ \frac{{3d}}{{\frac{d}{{200}} + \frac{d}{{400}} + \frac{d}{{600}}}}\)

\( ⇒ \frac{{3d}}{{\frac{{6d \; + \; 3d \; + \; 2d}}{{1200}}}}\)

\(⇒ \frac{{3d \; \times\; 1200}}{{11d}}\)

⇒ 3600/11

⇒ 327.27 km/hr ≈ 327 km/hr

∴ The average speed is 327 km/hr

Discussion

34.	The ______ will arrive at Amsterdam railway station at 3:00 PM. A) train B) plane C) bus D) truck
Answer» Correct option is A) train

Discussion

35.	As they like traveling a lot, instead of buying a house, they bought a ______. A) caravan B) building C) car D) truck
Answer» Correct option is A) caravan

Discussion

36.	Volvo will make a new ______ which will be able to carry 25 cars. A) transporter B) van C) pick-up truck D) bus
Answer» Correct option is A) transporter

Discussion

37.	Fifty students and four teachers were traveling in a ______. A) bus B) van C) truck D) taxi
Answer» Correct option is A) bus

Discussion

38.	The vehicle whose roof can fold back or removed is a ______. A) bus B) tanker C) van D) convertible
Answer» Correct option is D) convertible

Discussion

39.	______ is a vehicle bigger than a normal car and smaller than a bus, which can carry 8-12 people. A) van B) train C) minibus D) truck
Answer» Correct option is C) minibus

Discussion

40.	list the main features of the non cooperation Movement in towns and cities
Answer» Middle class people mainly participated in non cooperation movement in towns. Thousands of students left government-controlled schools and colleges, headmasters and teachers resigned, and lawyers gave up their legal practices. The council elections were boycotted in most provinces except Madras.

Discussion

41.	Which of the following statements is/are correct?1. Lord Hastings the British Resident at Delhi, was entrusted with the duty of negotiating alliances with the states of Rajasthan.2. Charles Metcalf looked upon the Rajputana States as his natural allies against the Marathas and the Pindaris. 1. 1 Only2. 2 Only3. Both 1 and 24. Neither 1 nor 2
Answer» Correct Answer - Option 4 : Neither 1 nor 2 The correct answer is Neither 1 nor 2. Charles Metcalf the British Resident at Delhi, was entrusted with the duty of negotiating alliances with the states of Rajasthan. Lord Hastings looked upon the Rajputana States as his natural allies against the Marathas and the Pindaris. Hence the correct answer is Neither 1 nor 2. British Treaty with the Rajputana States: In the latter half of 19th century, the Rajputana States were being crushed by continuous subjugation of Maratha Power and attacks of Pindaris. Almost all of Rajasthan had been virtually brought under by the Marathas, who exacted tribute, annexed territory, and extorted subsidies. Lord Wellesley (1798-1805) took interest in the Rajput- Maratha affairs to safeguard British interests in India. He wanted to curb the Maratha power in northern India and planned mutual friendship with the Rajputs against the Marathas. He succeeded in his plan but after his departure from India, the British policy towards Rajputana changed. Lord Hastings (1813-1823) sought to impose British paramountcy in India for which suppression of the Marathas and the Pindaris were essential. He looked upon the Rajputana States as his natural allies against the Marathas and the Pindaris. Charles Metcalf, the British Resident at Delhi, was entrusted with the duty of negotiating alliances with the states of Rajasthan.

41.

Which of the following statements is/are correct?1. Lord Hastings the British Resident at Delhi, was entrusted with the duty of negotiating alliances with the states of Rajasthan.2. Charles Metcalf looked upon the Rajputana States as his natural allies against the Marathas and the Pindaris. 1. 1 Only2. 2 Only3. Both 1 and 24. Neither 1 nor 2

Answer» Correct Answer - Option 4 : Neither 1 nor 2

The correct answer is Neither 1 nor 2.

Charles Metcalf the British Resident at Delhi, was entrusted with the duty of negotiating alliances with the states of Rajasthan.
Lord Hastings looked upon the Rajputana States as his natural allies against the Marathas and the Pindaris.
Hence the correct answer is Neither 1 nor 2.

British Treaty with the Rajputana States:
- In the latter half of 19th century, the Rajputana States were being crushed by continuous subjugation of Maratha Power and attacks of Pindaris.
- Almost all of Rajasthan had been virtually brought under by the Marathas, who exacted tribute, annexed territory, and extorted subsidies.
- Lord Wellesley (1798-1805) took interest in the Rajput- Maratha affairs to safeguard British interests in India.
- He wanted to curb the Maratha power in northern India and planned mutual friendship with the Rajputs against the Marathas. He succeeded in his plan but after his departure from India, the British policy towards Rajputana changed.
- Lord Hastings (1813-1823) sought to impose British paramountcy in India for which suppression of the Marathas and the Pindaris were essential.
- He looked upon the Rajputana States as his natural allies against the Marathas and the Pindaris.
- Charles Metcalf, the British Resident at Delhi, was entrusted with the duty of negotiating alliances with the states of Rajasthan.

Discussion

42.	Monuments, Inscriptions, artefacts and coins are examples of ......... sources.(a) Archaeological(b) literary(c) oral (d) recent
Answer» Correct option : (a) Archaeological Explanation: Historic sources can be divided into archaeological sources and literary sources. Archaeological sources include artefacts, monuments, coins and inscriptions. Literary sources include written records of the past, also known as manuscripts.

42.

Monuments, Inscriptions, artefacts and coins are examples of ......... sources.(a) Archaeological(b) literary(c) oral (d) recent

Answer»

Correct option : (a) Archaeological

Explanation:

Historic sources can be divided into archaeological sources and literary sources. Archaeological sources include artefacts, monuments, coins and inscriptions. Literary sources include written records of the past, also known as manuscripts.

Discussion

43.	Section 43 of the Motor Vehicles Act, 1988 allows for temporary registration of a vehicle for a period NOT exceeding ______.1. 6 months2. 12 months3. 1 month4. 2 months
Answer» Correct Answer - Option 3 : 1 month The correct answer is 1 month. Section 43 of the Motor Vehicles Act, 1988 allows for temporary registration of a vehicle for a period NOT exceeding 1 month. A registration made under this section shall be valid only for a period not exceeding one month. And shall not be renewable: Provided that where a motor vehicle so registered is a chassis to which a body has not been attached and the same is detained in a workshop beyond the said period of one month for being. Within this period, the vehicle should be registered with a permanent number. In section 40 the owner of a motor vehicle may apply to any registering authority or other prescribed authority to have the vehicle temporarily registered in the prescribed manner and for the issue in the prescribed manner of a temporary certificate of registration and a temporary registration mark. Motor Vehicles Act, 1988 The Act came into force on 1 July 1989. It replaced Motor Vehicles Act, 1939 which earlier replaced the first such enactment Motor Vehicles Act, 1914. The act is amended by The Motor Vehicles act, 2019.

43.

Section 43 of the Motor Vehicles Act, 1988 allows for temporary registration of a vehicle for a period NOT exceeding ______.1. 6 months2. 12 months3. 1 month4. 2 months

Answer» Correct Answer - Option 3 : 1 month

The correct answer is 1 month.

Section 43 of the Motor Vehicles Act, 1988 allows for temporary registration of a vehicle for a period NOT exceeding 1 month.
A registration made under this section shall be valid only for a period not exceeding one month.
And shall not be renewable: Provided that where a motor vehicle so registered is a chassis to which a body has not been attached and the same is detained in a workshop beyond the said period of one month for being.
Within this period, the vehicle should be registered with a permanent number.

In section 40 the owner of a motor vehicle may apply to any registering authority or other prescribed authority to have the vehicle temporarily registered in the prescribed manner and for the issue in the prescribed manner of a temporary certificate of registration and a temporary registration mark.
Motor Vehicles Act, 1988
- The Act came into force on 1 July 1989.
- It replaced Motor Vehicles Act, 1939 which earlier replaced the first such enactment Motor Vehicles Act, 1914.
- The act is amended by The Motor Vehicles act, 2019.

Discussion

44.	The number of motor vehicles in Brazil is growing by ____________ almost as if cars were distributed free of charge to _________________
Answer» leaps and bounds; all and sundry.

Discussion

45.	Write ‘True’ or ‘False’ against each of the following sentences. (i) The king lost his temper easily.___________ (ii) Gopal was a madman. ____________ (iii) Gopal was a clever man. _____________ (iv) Gopal was too poor to afford decent clothes. ____________ (v) The king got angry when he was shown to be wrong. _______________
Answer» (i) True (ii) False He was just acting as a madman so that people’s attention would be diverted from the hilsafish he was carrying. (iii) True (iv) False He wore rags so that people would notice them, and not talk about the hilsafish. (v) False The king laughed and congratulated Gopal for achieving the impossible yet again

45.

Write ‘True’ or ‘False’ against each of the following sentences. (i) The king lost his temper easily._____ (ii) Gopal was a madman. (iii) Gopal was a clever man. _ (iv) Gopal was too poor to afford decent clothes. (v) The king got angry when he was shown to be wrong. _________

Answer»

(i) True

(ii) False

He was just acting as a madman so that people’s attention would be diverted from the hilsafish he was carrying.

(iii) True

(iv) False

He wore rags so that people would notice them, and not talk about the hilsafish.

(v) False

The king laughed and congratulated Gopal for achieving the impossible yet again

Discussion

46.	Find out the meaning of the following words by looking them up in the dictionary. Then use them in sentences of your own.(i) challenge (ii) mystic (iii) comical (iv) courtier (v) smearing
Answer» (i) Challenge Every difficult situation should be taken up as a challenge and not be run away from. (ii) Mystic The mystic from the Himalayas had great words of wisdom to share with the villagers. (iii) Comical Everyone appreciates the comical side of a man. (iv) Courtier Birbal was Akbar’s most trusted courtier. (v) Smearing Smearing the forehead with tilak is one of the traditions of the South Indians.

46.

Find out the meaning of the following words by looking them up in the dictionary. Then use them in sentences of your own.(i) challenge (ii) mystic (iii) comical (iv) courtier (v) smearing

Answer»

(i) Challenge

Every difficult situation should be taken up as a challenge and not be run away from.

(ii) Mystic

The mystic from the Himalayas had great words of wisdom to share with the villagers.

(iii) Comical

Everyone appreciates the comical side of a man.

(iv) Courtier

Birbal was Akbar’s most trusted courtier.

(v) Smearing

Smearing the forehead with tilak is one of the traditions of the South Indians.

Discussion

47.	What three things did Gopal do before he went to buy his hilsa-fish?
Answer» Before he went to buy hilsafish, Gopal halfshaved his face, smeared himself with ash, and wore disgraceful rags.

Discussion

48.	How much did you pay for that hilsa?
Answer» The woman asked the man how much he had paid for that hilsa.

Discussion

49.	Explain why no one seemed to be interested in talking about the hilsa-fish which Gopal had bought.
Answer» No one seemed to be interested in talking about the hilsafish which Gopal had bought because of Gopal’s ridiculous appearance. Some people found him comical, others thought he was a madman, still others thought he was a mystic. They were so engrossed in discussing his appearance that the hilsafish went unnoticed.

Discussion

50.	I want to see the king. Gopal told the guards_________________.
Answer» I want to see the king. Gopal told the guards that he wanted to see the king.

50.

I want to see the king. Gopal told the guards_________________.

Answer»

I want to see the king.

Gopal told the guards that he wanted to see the king.

Discussion

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What three things did Gopal do before he went to buy his hilsa-fish?

Explain why no one seemed to be interested in talking about the hilsa-fish which Gopal had bought.