If a body $A$ of mass $M$ is thrown with velocity $V$ at an angle of $30$ degrees to the horizontal and another body $\text{B}$ of the same mass is thrown with the same speed at an angle of $60$ degrees to the horizontal, the ratio of the horizontal range of $A$ to $B$ will be: A) $1: 3$ B) $1: 1$ C) $1: \sqrt{3}$ D) $\sqrt{3}: 1$

If ( (a - b) : (a + b) = 1 : 11 ), find the ratio ( (5a + 4b + 15) : (5a - 4b + 3) ).

A body of density $d_{1}$ is counterpoised by $\mathrm{Mg}$ of weights of density $d_{2}$ in air of density $d$. Then the true mass of the body is:

• $M$
• $M\left(1-\frac{d}{d_{2}}\right)$
• $M\left(1-\frac{d}{d_{1}}\right)$
• $\frac{M\left(\frac{1-d}{d_{2}}\right)}{\left(\frac{1-d}{d_{1}}\right)}$

When a raindrop rolls down a glass window pane, will the force of friction come into play?

If the coordinates of two points $A$ and $B$ are $(3,4)$ and $(5,-2)$ respectively, then the coordinates of any point $P$, if $PA=PB$ and area of $\triangle PAB=10, are:

A $(7,5),(1,0)$ B $(7,2),(1,0)$ C $(7,2),(-1,0)$ D $(2,7),(1,0)$

The diagonal of a gift box, which is cuboidal in shape, is of length 10$\sqrt{5}$ cm and the sum of its length, breadth, and depth is 38 cm.

What is the minimum area of gift paper required to wrap the box?

A $500$ cm$^{2}$ B $944$ cm$^{2}$ C $1444$ cm$^{2}$ D $1944$ cm$^{2}$ E $472$ cm$^{2}$

The ionization enthalpies of lithium and sodium are 520 kJ/mole and 495 kJ/mole respectively. The energies required to convert all the atoms present in 7 mg of lithium vapours and 23 mg of sodium vapours to their respective gaseous cations are:

1. 52 J, 49.5 J

2. 520 J, 495 J

3. 49.5 J, 52 J

4. 495 J, 520 J

Jaydeep purchased 25 kg of rice at the rate of Rs 16.80 per kg and 35 kg of rice at the rate of Rs 25.50 per kg. He mixed the two and sold the mixture. Approximately, at what price per kg did he sell the mixture to make a 25 percent profit?

Rs. 16.80 * 25 + Rs. 25.50 * 35 = Rs. 420 + Rs. 892.50 = Rs. 1312.50 Total cost price = Rs. 1312.50 Profit = 25% of Rs. 1312.50 = Rs. 328.125 Selling price = Rs. 1312.50 + Rs. 328.125 = Rs. 1640.625

Therefore, he needs to sell the mixture at approximately Rs. 26.50 per kg to make a 25% profit.

If $x^{2} - 1 = -b^{2} - 2bx$ and $x^{2} - 1 = -a^{2} - 2ax$ have exactly one root in common then:

A $a=b+2$ B $a=b^{2}+2$ C $a+b+2=0$ D $a-b+2=0$

Extending the same logic you've seen in the video so far, find out the sum of the first 10 natural numbers. (You can use $S_{10}=1+2+3+\ldots+10$ and proceed)

A $10 \times 11$
B $\frac{(10 \times 11)}{2}$
C $\frac{(10 \times 2)}{11}$
D None of these

In the figure, there are angles and they are , and A) 3, ∠ABC, ∠DBC, ∠ABD B) 3, ∠BDA, ∠ABC, ∠BCD C) 3, ∠CAB, ∠BDA, ∠BCD D) 3, ∠ACB, ∠BDA, ∠BCD

An image that cannot be obtained on a screen is called a ________ image.

Option 1) Real Option 2) Mirror Option 3) Wrong Option 4) Virtual

During galvanisation, iron metal is given a thin coating of one of the following metals. This metal is:

(a) chromium, (b) tin, (c) zinc, or (d) copper.

Which among the following is true about the Sepoy Mutiny?

Option 1: The British hurt the religious sentiments of the Indian soldiers. Option 2: Cow fat was used as artillery grease. Option 3: Pig fat was used as artillery grease. Option 4: All of the above.

A bottle kept on a table started leaking when two holes were made at the same level. This is because:

• The liquid inside the bottle is exerting equal pressure in all directions at the same level

• The liquid inside is not exerting any pressure on the bottle

• The liquid is exerting unequal pressure in all directions at the same level

• Can't be said

A sample has 0.1 moles of $\mathrm{H}{2}$ gas. If $3.011 \times 10^{23}$ molecules are added to it, what is the final number of moles of $\mathrm{H}{2}$ in the sample?

$\mathrm{C}^{-4}$ is unstable because it would be very difficult for 6 protons to hold 10 electrons.
A. True
B. False

Which of the electrodes is at a higher potential in a voltaic cell using copper and zinc rods as electrodes and dilute $\mathrm{H}{2}\mathrm{SO}{4}$ as an electrolyte?

A. Copper
B. Zinc
C. Both are at the same potential
D. It depends on the concentration of $\mathrm{H}{2}\mathrm{SO}{4}$

If a + b + c = 0, then the quadratic equation 3ax^2 + 2bx + c = 0 has:

• at least one root in (0,1)
• one root in (2,3) and the other in (-2,-1)
• Imaginary roots
• None of these

A rod of length $L$ and uniform cross-sectional area has varying thermal conductivity which changes linearly from $2 K$ at end $B$ to $K$ at the other end $A. The ends $A$ and $B$ of the rod are maintained at constant temperatures of $100^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$, respectively. At steady state, the graph of temperature $T=T(x)$ where $x$ is the distance from end $A$ will be.