Introduction

Q. Value of $sin37°.cos53°$ is

1. 9/25
2. 12/25
3. 16/25
4. 3/5

Q.

The earth takes $24\mathrm{h}$ to rotate once about its axis. How much time does the sun take to shift by $1°$ when viewed from the earth?

Q. Temperature can be expressed as a derived quantity in terms of any of the following

1. Length and mass
2. Mass and time
3. Length, mass and time
4. None of these

Q.

What are the 4 main factors that affect the size of a wave?

Q.

$\overrightarrow{A}$ is a vector with magnitude $A$, then the unit vector $\hat{A}$ in the direction of $\overrightarrow{A}$ is

1. $A\overrightarrow{A}$

2. $\overrightarrow{A}.\overrightarrow{A}$

3. $\overrightarrow{A}\times \overrightarrow{A}$

4. $\raisebox{1ex}{$\overrightarrow{A}$}\!\left/ \!\raisebox{-1ex}{$A$}\right.$

Q. One kelvin is equal to

1. $\frac{1}{273.16}$ part of the thermodynamic temperature of triple point of water.
2. $\frac{1}{273.13}$ part of the thermodynamic temperature of triple point of water.
3. $\frac{1}{273.14}$ part of the thermodynamic temperature of triple point of water.
4. $\frac{1}{273.15}$ part of the thermodynamic temperature of triple point of water.

Q. The slope of line that passes through points $(3,5)\text{and}(6,10)$ is

1. $\frac{3}{5}$
2. $\frac{4}{5}$
3. $\frac{5}{4}$
4. $\frac{5}{3}$

Q. Determine the angle (in radians) subtended at the center of a circle of radius $3cm$ by arc of length of $6cm$ and $3\pi cm$ respectively.

1. $2$ and $\pi$
2. $\pi$ and $2\pi$
3. $3$ and $2$
4. $2\pi$ and $\pi$

Q. The equation of the line making ${37}^{\circ }$ with $x-axis$ and passing through $(2,-4)$ is
[Hint:- $\tan {37}^{\circ }=\frac{3}{4}$]

1. $4y+3x+22=0$
2. $3y-4x+22=0$
3. $4y-3x+22=0$
4. $4y-3x-22=0$

Q. Choose the correct option:
i. $y=4a$, is a linear function.
ii. $y=a{x}^2-bx+c,(a=0)$, is a linear function with positive slope.
iii. $y=x$, is an identity function.
iv. $y=3x^2-1$, is a quadratic function.

1. iii and iv
2. i and ii
3. i, ii and iii
4. ii and iv

Q. Choose the incorrect option.

1. Use of solidus (/) is recommended only for indicating a division of one letter unit symbol by another unit symbol. Not more than one solidus is used.
2. A prefix is never used alone. It is always attached to a unit symbol and written or fixed before the unit symbol.
3. The use of a combination of unit and the symbols for unit is avoided when the physical quantity is expressed by combining two or more units.
4. The use of double prefixes is allowed when single prefix is available.

Q. Choose the correct option based on the prallelogram $ABCD$.

1. $\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{BC}\ne \overrightarrow{AD}+\overrightarrow{DC}$
2. $\overrightarrow{AC}\ne \overrightarrow{AB}+\overrightarrow{BC}\ne \overrightarrow{AD}+\overrightarrow{DC}$
3. $\overrightarrow{AC}\ne \overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AD}+\overrightarrow{DC}$
4. $\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{BC}=\overrightarrow{AD}+\overrightarrow{DC}$

Q. If $a+b+c=6$ and $ab+bc+ca=16$, find the value of $a^2+b^2+c^2$.

1. 4
2. 6
3. 10
4. 36

Q. Angstrom is the unit of

1. mass
2. length
3. weight
4. current

Q. Gravitational force between two objects having masses $m_1$ and $m_2$ is given by $F=G\frac{m_1.m_2}{r^2}\text{N}$, where $G$ is constant . Choose the incorrect option.

1. $m_1$ is an independent variable.
2. $m_2$ is an independent variable.
3. $r$ is a dependent variable.
4. None of these

Q.

The adjacent sides of a parallelogram are $a=\hat{i}+2\hat{j}$ and $b=2\hat{i}+\hat{j}$, where $\hat{i}$ and $\hat{j}$ are the usual unit vectors along the positive directions of $x$ and $y$-axes respectively. Then the angle between the diagonals is?

1. $30°\&150°$

2. $45°\&135°$

3. $60°\&120°$

4. $90°\&90°$

Q. In a right angled triangle having hypotenuse 2 units.
If $\theta$ is included angle and $\sin \theta =\frac{1}{2}.$
Find the value of Adjacent side wrt included Angle $\theta$

1. $\sqrt{2}$
2. $\sqrt{3}$
3. $\sqrt{5}$
4. $\sqrt{8}$

Q. For a given quadratic expression $2x^2+5x-9=0$, find the product of the roots.

1. $2.5$
2. $4.5$
3. $-2.5$
4. $-4.5$

Q. If a particle moves with velocity $v\left(t\right)=(2t^2-t)m/s$, then find the velocity (in $m/s$) of particle at $t=3s$.

1. $5m/s$
2. $10m/s$
3. $20m/s$
4. $15m/s$

Q. The time period of a body in $SHM$ is represented by $T_o=P^a{\rho }^b{S}^c$, where $P$ is pressure, $\rho$ is density and $S$ is surface tension. The value of $a,b$ and $c$ respectively for the relation to be dimensionally correct is

1. $-\frac{3}{2},\frac{1}{2},1$
2. $-1,-2,3$
3. $\frac{1}{2},-\frac{3}{2},-\frac{1}{2}$
4. $1,2,\frac{1}{3}$

Q. Calculate $sin{15}^o.cos{15}^o$.

1. $\frac{1}{4}$
2. $\frac{3}{2}$
3. $\frac{3}{4}$
4. $\frac{\sqrt{3}}{2}$

Q.

Name radiation that can be detected by a thermopile.

Q. If $y=x^2+2x-3$, y-x graph is

1. 
2. 
3. 
4. 

Q. Unit vector perpendicular to $x-y$ plane is

1. $\hat{i},-\hat{i}$
2. $\hat{j},-\hat{j}$
3. $\hat{k},-\hat{k}$
4. $\text{All of the above}$

Q. The density of a material in CGS system of units is $4{\text{g/cm}}^3$. In a system of units in which unit of length is $10\text{cm}$ and unit of mass is $100\text{g}$, the value of density of material will be

1. $40\text{unit}$
2. $4\text{unit}$
3. $0.4\text{unit}$
4. $0.04\text{unit}$

Q. Find the nature of roots for the equation $x^2+x+12=0$

1. Integers
2. Negative integers
3. Whole numbers
4. Complex

Q. A point $P$ having the coordinate $(2,3)$. Find the position vector of $P$ ?

1. $\overrightarrow{P}=2\hat{i}+3\hat{ȷ}$
2. $\overrightarrow{P}=3\hat{i}+3\hat{ȷ}$
3. $\overrightarrow{P}=2\hat{i}+2\hat{ȷ}$
4. $\overrightarrow{P}=3\hat{i}+2\hat{ȷ}$

Q. If Rakesh travels from $A$ to $B$ and Ramesh travels from $A$ to $B$ and then to $C$ along a straight line path. Who has the highest displacement?

1. Rakesh
2. Ramesh
3. Both have same displacement
4. More information is needed

Q. If a particle moves with velocity $v\left(t\right)=2t^2-tm/s$, then find the velocity ($m/s$) of particle at $t=3s$.

Q. If $f\left(x\right)=x^2+32x-12$. What is the value of $f\left(4\right)$?