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What external changes are visible after the last moult of a cockroach nymph?
1.  Mandible become harder
2.  Anal cerci develop
3.  Both fore wings and hind wings develop
4.  Labium develops

Smooth muscles occur on
(1) viscera
(2) internal organs
(3) blood vessels
(4) all the above

Identify the following simple epithelial tissues:

Identify the tissue shown in the diagram and match with its characteristics and its location:

(1) Skeletal muscle, shows striations and closely attached with the bones of the limbs
(2) Smooth muscles, show branching, found in the walls of the heart
(3) Cardiac muscles, unbranched muscles, found in the walls of the heart
(4) Striated muscles, tapering at both-ends, attached with the bones of the ribs

The epithelium which has property to move particles back and forth and is present in organs like bronchioles, fallopian tubes and uterus is?
(1) Columnar epithelium
(2) Cuboidal epithelium
(3) Ciliated epithelium
(4) Squamous epithelium

Epithelium consisting of more than one layer stacked one over the another is :
(1) Columnar
(2) Cuboidal
(3) Compound
(4) Both (1) and (3)

Location of the cells of the bone is:
(1) Bone marrow
(2) Matrix
(3) Lacunae
(4) Spleen

Which among the following statements are incorrect about cockroach?
(1) Haemocytes lack respiratory pigment.
(2) Has 13 chambered heart on the ventral side of the body.
(3) Blood from sinuses enter heart through ostia.
(4) Has 10 pairs of spiracles present on lateral side of body.

The following type of tissue is present in:

(1) Tendons and ligaments
(2) Chondrocytes
(3) Cells of adipose tissue
(4) Cells of areolar tissue

Due to the type of excretion performed by malpighian tubules, cockroach is :
(1) Ammonotelic
(2) Uricotelic
(3) Usually ammonotelic but uricotelic in unfavourable conditions
(4) Ureotelic

Tissue is

The complex animals mainly consist of how many types of tissues?

Which of the following is a type of simple epithelia?

The flattened cells with irregular boundaries are found in

The cells which possess microvilli in intestine forms which type of tissue?

The pancreatic ducts has which tissue lining?

Find the incorrect one

Connective tissue is named connective because

Human heart has which type of tissue?

The head is connected with thorax-

Male genital pouch

Choose the incorrect option from the following-
Heart of cockroach

Which of the following statements is wrong?

The nervous system of cockroach is made up of a series of ganglia which are joined by

If a female cockroach has 10 oothecae then what will be the number of total eggs

How many molting will be observed in the case of female cockroaches for 20 eggs thinking that all will be converted in adults?

The presence of anal styles distinguishes male cockroaches from females. It is present on :
1. Ninth tergite                
2. Ninth sternite
3. Tenth tergite               
4. Tenth sternite

Tick mark the statement which is not correct with respect to cockroach?
1.  In cockroach the grinding of the food particles is performed by mandibles & gizzard.
2.  Malpighian tubules help in the removal of nitrogenous wastes in the form of urea & ammonia.
3.  Midgut gut of cockroach absorb food.
4.  Main body cavity is called haemocoel.

Mark the incorrect statement regarding the Malpighian tubule in cockroach:
1. It is present at the junction of the midgut and hindgut.
2. It is lined by glandular and ciliated cells.
3. It absorbs uric acid from the hemolymph.
4. It is about 100-150 in number and is a thin yellow filamentous tubule.

Male reproductive system of cockroach consist of

Which of the following structures or substances is
incorrectly paired with a tissue ?
1. Haversian system—bone
2. platelets—blood
3. fibroblasts—skeletal muscle
4. chondroitin sulfate—cartilage

Identify the incorrect statement regarding the blood vascular system of cockroach:
1. Blood vessels are poorly developed and open into hemocoel
2. The hemolymph is composed of colorless plasma and hemocytes
3. Heart lies along the mid-ventral line of thorax and abdomen
4. Blood from sinuses enter heart through ostia

Which of the following statement is incorrect with respect to cockroach?
1. The exoskeleton of each segment consists of four plate-like pieces called sclerites
2. Labium bears tactile and gustatory sensory setae
3. In cockroach, malpighian tubules, fat bodies, nephrocytes, cuticle, and uricose glands (in some species) Helps in excretion
4. Internally mesenteron is lined by cuticle and covered by a very thin and transparent peritrophic membrane

Mark the incorrect statement with respect to head of cockroach
(1) Head is triangular in shape and lies anteriorly at right angle to the longitudinal body axis
(2) Formed by fusion by six segments and shown great mobility in all directions due to flexible neck
(3) First basal podomere of antennae is smallest and is called pedicel which articulates with antennae socket
(4) On each lateral side it bears a large and blackish compound eye

Which of the following statement is correct with reference to the cockroach eye?
1. Both eyes together consist of about 2000 hexagonal ommatidia
2. Its vision has more sensitivity but less resolution
3. Mosaic vision is not found due to diurnal habit
4. Compound eyes are situated at the vertex region of the head

Which of the following statement is not true with respect to Periplaneta?
(1) The gizzard part of alimentary canal has an outer layer of thick longitudinal muscles and inner thin cuticle forming six highly chitinous plates called teeth
(2) The hindgut is broader than midgut and is differentiated into ileum, colon and rectum
(3) If the head of cockroach is cut off, it will still live for as long as one week
(4) Each Malpighian tubule is lined by glandular and ciliated cells. These are located at the junction between midgut and hindgut

Select the correct match

(1) a(ii), b(iii), c(i)
(2) a(ii), b(i), c(iii)
(3) a(i), b(iii), c(ii)
(4) a(iii), b(i), c(ii)

Given below is a diagrammatic representation of a glandular tissue

Identify the structure labelled as 'A' and choose the correct option with respect to its example.
(1) Gastric gland
(2) Goblet cells
(3) Oxyntic cells
(4) Sebaceous gland

Given below is a diagrammatic representation of alimentary canal of cockroach.
Choose the option which is not correct with respect to the function of labelled structure A, B, C and D

(1) Oesophagus opens into a sac like structure labelled as A used for storing of food.
(2) B helps in grinding of food because it have an outer thick cuticular layer and inner muscular layer.
(3) C is present at the junction of foregut and midgut and secretes digestive juice.
(4) D helps in removal of excretory product from haemolymph.

Which type of junctions in the epithelial tissues facilitate the cells to communicate with each other by connecting the cytoplasm of adjoining cells for rapid transfer of ions or small molecules?
(1) Tight junctions
(2) Adhering junctions
(3) Gap junctions
(4) Desmosomes

Brush bordered cuboidal epithelium is present in
1. Proximal convoluted tubules
2. Small intestine
3. Lining of stomach
4. Smaller ducts of pancreas

Digestive enzymes for digestion of carbohydrates, proteins and lipids are mainly secreted by________of cockroach
(1) Crop
(2) Midgut and Hepatic caecae
(3) Gizzard
(4) Salivary glands

Consider the two statements:
I. If the head of a cockroach is cut off, it will still live for as long as one week.
II. The endocrine hormones can take over the function of neural tissue for short periods.
1. Both I and II are correct and II explains I
2. Both I and II are correct but II does not explain I
3. Only I is correct
4. Both I and II are incorrect

This epithelial tissue is found in ducts of glands and tubular parts of nephrons in kidneys. Its main functions are secretion and absorption. choose the correct option
(1) simple epithelium
(2) Simple cuboidal epithelium
(3) Simple columnar epithelium
(4) Ciliated epithelium

Choose the correct option with respect to the location of this tissue

(1) In ducts of glands
(2) In tubular part of kidney
(3) In the inner surface of hollow organs like bronchioles and fallopian tubes
(4) In the walls of blood vessels and air sacs of lung

Mark the correct statement with respect to cockroach
(1) Haemolymph is composed of colourless
     plasma and erythrocytes
(2) All the spiracles are always open in cockroach 
(3) Haemolymph enters heart through ostia and is
      pumped from posterior to anterior direction
(4) Haemolymph has no role in transportation of 
     nutrients and metabolic wastes

The mushroom gland of cockroach is present in 
(1) $6^{\mathrm{th}}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>7^{\mathrm{th}}$  abdominal segments
(2) $4^{\mathrm{th}}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>6^{\mathrm{th}}$ abdominal segments
(3) $2^{\mathrm{nd}<mspace\; width="1em"></mspace>}-<mspace\; width="1em"></mspace>6^{\mathrm{th}}$ abdominal segments
(4) $9^{\mathrm{th}}<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>{10}^{\mathrm{th}}$ abdominal segments

Choose the incorrect statements with respect to life cycle of
cockroach
(1) They have paurometabolous development
(2) The female produces 9-10 oothecae, each
      containing 14-16 eggs
(3) The eggs are centrolecithal, microlecithal and 
     cleidoic 
(4) The nymphs undergo 13 moultings to reach 
      excep

Sense organs of cockroach include
1. Compound eyes
2. Johnston's organ
3. Osphradium
4. Spiracles

Match the following.

Codes
 

If $|\overrightarrow{u_1}+\overrightarrow{u_2}|=|\overrightarrow{u_1}-\overrightarrow{u_2}|<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\left|\overrightarrow{u_2}\right|$ is finite then
1. $\overrightarrow{u_1}$ is parallel to $\overrightarrow{u_2}$
2. $\overrightarrow{u_1}$=$\overrightarrow{u_2}$
3. |$\overrightarrow{u_1}$|=|$\overrightarrow{u_2}$|
4. $\overrightarrow{u_1}$ and $\overrightarrow{u_2}$ are mutually perpendicular

Two forces of magnitude F have a resultant of the same magnitude F. The angle between the two forces is 
1. 45°
2 120°
3. 150°
4. 60°

If two forces of 5 N each are acting along X and Y axes, then the magnitude and direction of resultant is 
1. $5\sqrt{2},\pi /3$
2. $5\sqrt{2},\pi /4$
3. $-5\sqrt{2},\pi /3$
4. $-5\sqrt{2},\pi /4$

If vectors A = cosωt $\hat{i}$ + sinωt $\hat{j}$ and B = (cosωt/2) $\hat{i}$ + (sinωt/2) $\hat{j}$ are functions of time, then the value of t at which they are orthogonal to each other
1. t=$\mathrm{\pi }$/4ω
2. t=$\mathrm{\pi }$/2ω
3. t=$\mathrm{\pi }$/ω
4. t=0 
 

Six vectors \(\overrightarrow a ~\text{through}~\overrightarrow f\) have the directions as indicated in the figure. Which of the following statements may be true?
      
1. \(\overrightarrow b + \overrightarrow c = -\overrightarrow f\)
2. \(\overrightarrow d + \overrightarrow c = \overrightarrow f\)
3. \(\overrightarrow d + \overrightarrow e = \overrightarrow f\)
4. \(\overrightarrow b + \overrightarrow e = \overrightarrow f\)

In the given figure
 

A truck travelling due north with 20m/s turns towards west and travels at the same speed. Then the change in velocity is -
(1)  40 m/s north-west
(2)  $20\sqrt{2}$ m/s north-west
(3)  40 m/s south-west
(4)  $20\sqrt{2}$ m/s south-west

A child pulls a box with a force of \(200~\text{N}\) at an angle of $\mathrm{}$\(60^{\circ}\) above the horizontal. Then the horizontal and vertical components of the force will be:
              
1. \(100~\text{N}, ~175~\text{N}\)
2. \(86.6~\text{N}, ~100~\text{N}\)
3. \(100~\text{N}, ~86.6~\text{N}\)
4. \(100~\text{N}, ~0~\text{N}\)

The displacement x of a particle along a straight line at time t is given by $\mathrm{x}={\mathrm{a}}_0+{\mathrm{a}}_1\mathrm{t}+{\mathrm{a}}_2{\mathrm{t}}^2$. The acceleration of the particle is:
1. \(a_0\)
2. \(a_1\)
3. \(2a_2\)
4. \(a_2\)

The vector \(\overrightarrow b\) which is collinear with the vector \(\overrightarrow a = \left(2, 1, -1\right)\) and satisfies the condition \(\overrightarrow a. \overrightarrow b=3\) is:
1. \(\left(1, \frac{1}{2}, \frac{-1}{2}\right)\)
2. \(\left(\frac{2}{3}, \frac{1}{3}, \frac{-1}{3}\right)\)
3. \(\left(\frac{1}{2}, \frac{1}{4}, \frac{-1}{4}\right)\)
4. \(\left(1, 1, 0\right)\)

Two vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ lie in a plane. Another vector $\overrightarrow{\mathrm{C}}$ lies outside this plane. The resultant $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}+\overrightarrow{\mathrm{C}}$ of these three vectors
(1)  can be zero
(2)  cannot be zero
(3)  lies in the plane of $\overrightarrow{\mathrm{A}}<mspace\; width="1em"></mspace>\&\overrightarrow{\mathrm{B}}$
(4)  lies in the plane of $\overrightarrow{\mathrm{A}}<mspace\; width="1em"></mspace>\&<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$

A set of vectors taken in a given order gives a closed polygon. Then the resultant of these vectors is a 
(1)  scalar quantity
(2)  pseudovector
(3)  unit vector
(4)  null vector

The vector sum of two vectors P and Q is minimum when the angle $\mathrm{\theta }$ between their positive directions, is
(A)  $\frac{\mathrm{\pi }}{4}$
(B)  $\frac{\mathrm{\pi }}{3}$
(C)  $\frac{\mathrm{\pi }}{2}$
(D)  $\mathrm{\pi }$

If the vector sum of two vectors $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ is maximum, then the angle $\mathrm{\theta }$ between two vectors will be:
1.  $0°$
2.  $30°$
3.  $45°$
4.  $60°$

What is the torque of a force $\overrightarrow{\mathrm{F}}=\left(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}+4\hat{\mathrm{k}}<mspace\; width="1em"></mspace>\right)$newton acting at a point $\overrightarrow{\mathrm{r}}=\left(3\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}<mspace\; width="1em"></mspace>\right)$ metre about the origin? (Given: $\overrightarrow{\mathrm{\tau }}<mspace\; width="1em"></mspace>=\overrightarrow{\mathrm{r}<mspace\; width="1em"></mspace>}\times \overrightarrow{\mathrm{F}}$)
1. $6\hat{\mathrm{i}}-6\hat{\mathrm{j}}+12\hat{\mathrm{k}}<mspace\; width="1em"></mspace>$
2. $17\hat{\mathrm{i}}-6\hat{\mathrm{j}}-13\hat{\mathrm{k}}<mspace\; width="1em"></mspace>$
3. $-6\hat{\mathrm{i}}+6\hat{\mathrm{j}}-12\hat{\mathrm{k}}<mspace\; width="1em"></mspace>$
4. $-17\hat{\mathrm{i}}+6\hat{\mathrm{j}}-13\hat{\mathrm{k}}<mspace\; width="1em"></mspace>$

The acceleration of a particle starting from rest varies with time according to relation, $a=\alpha <mspace\; width="1em"></mspace>t+\beta$. The velocity of the particle at time instant \(t\) is: \(\left(\text{Here,}~ a=\frac{dv}{dt}\right)\)
1. $\alpha t^2+\beta t$
2. $\alpha t^2+\frac{\beta t}{2}$
3. $\frac{\alpha t^2}{2}+\beta t$
4. $2\alpha t^2+\beta t$

If \(\left|\overrightarrow {v_1}+\overrightarrow {v_2}\right|= \left|\overrightarrow {v_1}-\overrightarrow {v_2}\right|\) and \(\overrightarrow {v_1}\) and \(\overrightarrow {v_2}\) are non-zero vectors, then:
1. \(\overrightarrow {v_1}\) is parallel to \(\overrightarrow {v_2}\)
2. \(\overrightarrow {v_1} = \overrightarrow {v_2}\)
3.  \(\overrightarrow {v_1}\) and \(\overrightarrow {v_2}\) are mutually perpendicular 
4. \(\left|\overrightarrow {v_1}\right|= \left|\overrightarrow {v_2}\right|\)

If the acceleration \(a(t)= 4t+6\), the velocity of a particle starting from rest is: \(\left(\text{here} ,  a = \frac{d v}{d t}\right)\)
1. \(2t+6\)
2. \(4\)
3. \(0\)
4. \(2t^2+6t\)

A force of $F\left(x\right)=2x^2+3$ N is applied to an object. How much work is done, in Joules, moving the object from x=1 to x=4 meters? $\left(work={\int }_a^{b}F\left(x\right)<mspace\; width="1em"></mspace>dx\right)$
1. $\frac{11}{3}<mspace\; width="1em"></mspace>J$
2. 51 J
3. $\frac{5}{3}<mspace\; width="1em"></mspace>J$
4. $\frac{164}{3}<mspace\; width="1em"></mspace>J$

Given velocity v(t) = $\frac{5}{2}\mathrm{t}+3$. Assume s(t) is measured in meters and t is measured in seconds. If s(0) = 0, the position s(4) at t = 4s is:  $\left(\mathrm{Given},<mspace\; width="1em"></mspace>\mathrm{v}=\frac{\mathrm{ds}}{\mathrm{dt}}\right)$

${\int }_0^Q\frac{q}{C}dq$, where C is a constant, can be expressed as:
1. $\frac{Q^2}{C}$
2. $\frac{-Q^2}{2C}$
3. $\frac{-Q^2}{C}$
4. $\frac{Q^2}{2C}$

The velocity of a rocket, in metres per second, \(t\) seconds after it was launched is modelled by \(v(t)=2\sqrt{t}\). What is the total distance travelled by the rocket during the first four seconds of its launch?
1. \(\frac{16}{3}~\text{m}\)
2. \(32~\text{m}\)
3. \(\frac{32}{3}~\text{m}\)
4. \(16~\text{m}\)

The work done by gravity exerting an acceleration of \(-10\) m/${\mathrm{s}}^2$ for a \(10\) kg block down \(5\) m from its original position with no initial velocity is: \(\left(F_{\text{gravitational}}= \text{mass}\times \text{acceleration and} ~w = \int^{b}_{a}F(x)dx \right)\)
1. \(250\) J
2. \(500\) J
3. \(100\) J
4. \(1000\) J

Water flows into a container of 1000 L at a rate of (180+3t) gal/min for an hour, where t is measured in minutes. Find the amount of water that flows into the pool during the first 20 minutes.
1. 4000 gal
2. 2800 gal
3. 4200 gal
4. 3800 gal

If charge flown through a wire is given by q=3sin(3t), then-current flown through the wire at $\mathrm{t}=\frac{\mathrm{\pi }}{9}$ seconds is: $\left(\mathrm{i}=\frac{\mathrm{dq}}{\mathrm{dt}}\right)$
1. 4.5 Amp
2. 4.5$\sqrt{3}$ Amp
3. $\frac{\sqrt{3}}{2}$ Amp
4. 9 Amp

The position of a particle is given by \(s\left( t\right) = \dfrac{2 t^{2} + 1}{t + 1}\). Then, at \(t= 2\), its velocity is: \(\left(v_{inst}= \dfrac{ds}{dt}\right)\)
1. \(\dfrac{16}{3}\)
2. \(\dfrac{15}{9}\)
3. \(\dfrac{15}{3}\)
4. None of these

If acceleration of a particle is given as a(t) = sin(t)+2t. Then the velocity of the particle will be:
(acceleration $\mathrm{a}=\frac{\mathrm{dv}}{\mathrm{dt}}$)
1. \(-\cos(t)+ \frac{t^2}{2}\)
2. \(-\sin(t)+ t^2\)
3. \(-\cos(t)+ t^2\)
4. None of these

The current in a circuit is defined as $I=\frac{dq}{dt}$. The charge (q) flowing through a circuit, as a function of time (t), is given by $q=5t^2-20t+3$. The minimum charge flows through the circuit at:
1. \(t = 4~\text{s}\)
2. \(t = 2~\text{s}\)
3. \(t = 6~\text{s}\)
4. \(t = 3~\text{s}\)

The angle between the two vectors \(\left(- 2 \hat{i} +3 \hat{j} + \hat{k}\right)\) and \(\left(\hat{i} + 2 \hat{j} - 4 \hat{k}\right)\) is:
1. \(0^{\circ}\)
2. \(90^{\circ}\)
3. \(180^{\circ}\)
4. \(45^{\circ}\)

If $\overrightarrow{\mathrm{a}}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{b}}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{c}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\overrightarrow{0}$; then which of the following statements is incorrect?
(1) $\overrightarrow{\mathrm{a}},<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{b}}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{c}}$ must each be a null vector.
(2) The magnitude of $\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}$ equals the magnitude of $\overrightarrow{\mathrm{c}}$.
(3) The magnitude of ä can never be greater than the sum of the magnitudes of $\overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{c}}$
(4) ä must lie in the plane of $\overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{c}}$.

If $\overrightarrow{\mathrm{a}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>2\hat{\mathrm{i}}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{b}}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>3\hat{\mathrm{i}}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>2\hat{\mathrm{j}}$, then $\left|\overrightarrow{\mathrm{a}}<mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>\overrightarrow{\mathrm{b}}\right|=?$ 

\(\overrightarrow A\) and \(\overrightarrow {B}\) are two vectors given by \(\overrightarrow {A}= 2\hat i + 3\hat j\) and \(\overrightarrow {B}= \hat i + \hat j\). The component of \(\overrightarrow A\) parallel to \(\overrightarrow B\) is:
1. \(\frac{(2\hat i -\hat j)}{2}\)
2. \(\frac{5}{2}(\hat i - \hat j)\)
3. \(\frac{5}{2}(\hat i + \hat j)\)
4. \(\frac{(3\hat i -2\hat j)}{2}\)

If a vector is inclined at angles \(\alpha ,\beta ,~\text{and}~\gamma\), with \(x\), \(y\), and \(z\)-axis respectively, then the value of \(\sin^{2}\alpha+\sin^{2}\beta+ \sin^{2}\gamma\)${}^{}$
is equal to:
1. \(0\)
2. \(1\)
3. \(2\)
4. \(\frac{1}{2}\)

A vector $\overrightarrow{\mathrm{A}}$, which has magnitude 8.0 is added to a vector $\overrightarrow{\mathrm{B}}$ which lies on the x-axis. The sum of these two vectors lies on the y-axis and has a magnitude twice the magnitude of $\overrightarrow{\mathrm{B}}$. The magnitude of the vector $\overrightarrow{\mathrm{B}}$
1.  8
2.  $\sqrt{2}<mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>8$
3.  $\frac{8}{\sqrt{5}}$
4.  $8\sqrt{5}$

If \(\overrightarrow {A}\) $\mathrm{and}$ \(\overrightarrow{B}\) are two vectors inclined to each other at an angle \(\theta,\) then the component of \(\overrightarrow {A}\)$\stackrel{}{}$ perpendicular to \(\overrightarrow {B}\) and lying in the plane containing \(\overrightarrow {A}\) and$$ \(\overrightarrow {B}\) will be:
1. \(\frac{\overrightarrow {A} \overrightarrow{.B}}{B^{2}} \overrightarrow{B}\)
2. \(\overrightarrow{A}   -   \frac{\overrightarrow{A} \overrightarrow{.B}}{B^{2}} \overrightarrow{B}\)
3. \(\overrightarrow{A} -\overrightarrow{B}\)
4. \(\overrightarrow{A} + \overrightarrow{B}\)$\stackrel{}{}$

If $\overrightarrow{\mathrm{R}}$ is the resultant of two vectors $\overrightarrow{\mathrm{A}}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{B}}$ and $\overrightarrow{\mathrm{R}}$' is the difference in them, and $\left|\overrightarrow{\mathrm{R}}\right|<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\left|\overrightarrow{\mathrm{R}}\text{'}\right|$, then:
(1) $\overrightarrow{\mathrm{A}}<mspace\; width="1em"></mspace>\parallel <mspace\; width="1em"></mspace>\overrightarrow{\mathrm{B}}$
(2) $\overrightarrow{\mathrm{A}}<mspace\; width="1em"></mspace>\perp <mspace\; width="1em"></mspace>\overrightarrow{\mathrm{B}}$
(3) $\overrightarrow{\mathrm{A}}$ is antiparallel to $\overrightarrow{\mathrm{B}}$
(4) $\overrightarrow{\mathrm{A}}$ makes an angle of 120° with $\overrightarrow{\mathrm{B}}$

Two forces of the same magnitude are acting on a body in the East and North directions, respectively. If the body remains in equilibrium, then the third force should be applied in the direction of:
1. North-East
2. North-West
3. South-West
4. South-East

Given are two vectors, \(\overrightarrow{A} =   \left(\right. 2 \hat{i}   -   5 \hat{j}   +   2 \hat{k} \left.\right)\) and \(\overrightarrow{B} =   \left(4 \hat{i}   -   10 \hat{j}   +   c \hat{k} \right).\) What should be the value of \(c\) so that vector \(\overrightarrow A \) and \(\overrightarrow B\) would becomes parallel to each other?
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)

If \(\overrightarrow{A} \times \overrightarrow{B} = \overrightarrow{C} + \overrightarrow{D}\), then which of the following statement is correct?

If $\left|\overrightarrow{\mathrm{A}}<mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>\overrightarrow{\mathrm{B}}\right|<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\sqrt{3}\overrightarrow{\mathrm{A}}.<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{B}}$, then the value of $\left|\overrightarrow{\mathrm{A}}<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\overrightarrow{\mathrm{B}}\right|$ is:-
1.  ${\left({\mathrm{A}}^2<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>{\mathrm{B}}^2<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\frac{\mathrm{AB}}{\sqrt{3}}\right)}^{1/2}$
2.  A + B
3.  ${\left({\mathrm{A}}^2<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>{\mathrm{B}}^2<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\sqrt{3}\mathrm{AB}\right)}^{1/2}$
4.  ${\left({\mathrm{A}}^2<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>{\mathrm{B}}^2<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>\mathrm{AB}\right)}^{1/2}$

The volume flow rate of water flowing out of a tubewell is given by \(Q = \left( 3 t^{2}- 4 t +1\right)~\text{m}^3/\text{sec}  \). What volume of water will flow out of the tubewell in the third second if the volume flow rate is defined as \(Q=\frac{dV}{dt}\)?
1. \(10\) ${\mathrm{m}}^3$
2. \(17\) ${\mathrm{m}}^3$
3. \(36\) ${\mathrm{m}}^3$
4. \(34\) ${\mathrm{m}}^3$

The position of a particle in a rectangular co-ordinate system is \((3, 2, 5)\). Then its position vector will be:
1. \(5\hat i + 6\hat j + 2\hat k\)
2. \(3\hat i + 2\hat j + 5\hat k\)
3. \(5\hat i + 3\hat j + 2\hat k\)
4. None of these

If \(\overrightarrow {A}= 2\hat i + 4\hat j- 5\hat k,\) then the direction cosines of the vector are:
(direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three \(+\)ve coordinate axes.)
1. \(\frac{2}{\sqrt{45}}, \frac{4}{\sqrt{45}}~\text{and}~\frac{-5}{\sqrt{45}}\)
2. \(\frac{1}{\sqrt{45}}, \frac{2}{\sqrt{45}}~\text{and}~\frac{3}{\sqrt{45}}\)
3. \(\frac{4}{\sqrt{45}}, 0~\text{and}~\frac{4}{\sqrt{45}}\)
4. \(\frac{3}{\sqrt{45}}, \frac{2}{\sqrt{45}}~\text{and}~\frac{5}{\sqrt{45}}\)

Which of the following is a scalar quantity
1. Displacement
2. Electric field
3. Acceleration
4. Work

There are two force vectors, one of \(5~\text{N}\) and the other of \(12~\text{N}\). At what angle should the two vectors be added to get the resultant vector of \(17~\text{N}, 7~\text{N},\) and \(13~\text{N}\) respectively:
1. \(0^{\circ}, 180^{\circ}~\text{and}~90^{\circ}\)
2. \(0^{\circ}, 90^{\circ}~\text{and}~180^{\circ}\)
3. \(0^{\circ}, 90^{\circ}~\text{and}~90^{\circ}\)
4. \(180^{\circ}, 0^{\circ}~\text{and}~90^{\circ}\)

If vectors $\hat{\mathrm{i}}-3\hat{\mathrm{j}}+5\hat{\mathrm{k}}$ and $\hat{\mathrm{i}}-3\hat{\mathrm{j}}-\mathrm{\alpha }\hat{\mathrm{k}}$ are equal vectors, then the value of $\mathrm{\alpha }$ is:
1. -5
2. 2
3. -3
4. 4

A plane is revolving around the earth with a speed of 100 km/hr at a constant height from the surface of the earth. The change in the velocity as it travels half-circle is:
1. 200 km/hr
2. 150 km/hr
3. $100\sqrt{2}$ km/hr
4. 0

Current in a circuit is given by $i<mspace\; width="1em"></mspace>=3t^2+2t$. Find charge that crosses a cross-section from time t=0 to t=2 sec.
1. 12 C
2. 10 C
3. 8 C
4. 2 C

Which of the following is not possible?
1. sin \(\theta\) = \(3\over5\)
2. sec \(\theta\) = \(100\)
3. cosec \(\theta\) = \(0.14\)
4. None of the above