If $\sin x + \sin^2 x = 1$, then what is the value of $\cos^2 x + \cos^4 x$?

A train traveling at a speed of 36 km/h crosses a telegraph post in 40 seconds. Find the length of the train.

If two straight lines $3x – 2y = 5$ and $2x + ky + 7 = 0$ are perpendicular to each other, then what is the value of $k$?

If the points $(5,5)$, $(10,k)$ and $(-5,1)$ are collinear, then find the value of $k$.

If $\tan \theta + \cot \theta = 5$, then what is the value of $\tan^2 \theta + \cot^2 \theta$?

Find the roots of the equation $x^2 – 7x + 12 = 0$.

The area of a circle is $154\text{ cm}^2$. What will be its circumference?

If $2^x = 8^{y+1}$ and $9^y = 3^{x-9}$, then what are the values of $x$ and $y$ respectively?

The radii of two concentric circles are 5 cm and 3 cm. What will be the length of the chord of the larger circle that touches the smaller circle?

The focal length of a concave mirror is 15 cm. If an object is placed at a distance of 30 cm from the mirror, where will the image be formed?

1 kilowatt-hour (1 kWh) is equal to how many Joules?

What is the main reason why the color of the sky appears blue?

On which part of the human eye is the real image of an object formed?

In which order is an ammeter always connected in an electrical circuit?

Which mirror is used as a rear-view mirror in vehicles?

‘Newton’ is the SI unit of which physical quantity?

When ice melts, what is the effect on its volume?

In the modern periodic table, elements are arranged in the increasing order of what?

Which gas is filled in chips packets to prevent oxidation?

What is the pH value of pure water?

What is the nature of an aqueous solution that turns blue litmus paper to red?

What is the main component of Biogas and CNG?

What is the correct chemical formula of Plaster of Paris (POP)?

Rusting of iron is an example of which type of chemical reaction?

What is used to remove the permanent hardness of water?

If the HCF of two numbers is 12 and their LCM is 72, and one of the numbers is 24, then what is the other number?

Find the value of the discriminant of the equation $x^2 – 5x + 6 = 0$.

The radius of a right circular cylinder is 7 cm and its height is 10 cm. What will be its curved surface area?

If $\tan \theta = \frac{4}{3}$, then what is the value of $\sin \theta + \cos \theta$?

Find the arithmetic mean of the first 10 natural numbers.

What will be the distance of the point $(3, 4)$ from the origin?

If the perimeter and the area of a circle are numerically equal, then what will be the radius of that circle?

If the mode of a frequency distribution is 12 and the mean is 3, then what will be its median?

If a die is thrown once, what is the probability of getting a prime number?

On what factor does the specific resistance (or resistivity) of a conductor depend?

What is measured by the odometer of a vehicle?

What is the least distance of distinct vision for a normal human eye?

Which semiconductor element is primarily used to make solar cells?

Which type of mirror is most suitable for shaving or makeup?

If the mass of an object on Earth is 60 kg, what will be its mass on the Moon?

Sound waves are an example of which type of mechanical waves?

What should be the melting point and resistance of a fuse wire?

In which group are the ‘Halogens’ placed in the modern periodic table?

Which acid is primarily found in vinegar?

What was the name of the toxic gas leaked in the Bhopal Gas Tragedy?

What is the chemical formula of rust?

Bauxite is the main ore of which metal?

Which element is lustrous despite being a non-metal?

Which odorous substance is added to LPG gas cylinders to detect leakage?

Which mandatory metal is always present in an amalgam?

If $x + \frac{1}{x} = 4$, then find the value of $x^3 + \frac{1}{x^3}$.

The side of an equilateral triangle is 6 cm. What will be its area?

If the $n^{\text{th}}$ term of a series is $3n + 1$, then what will be the sum of the first 5 terms of this series?

The length, breadth, and height of a cuboid are 12 cm, 9 cm, and 8 cm respectively. Find the length of its longest diagonal.

If $\log_2 (x + 3) = 4$, then what is the value of $x$?

The ratio of the areas of two similar triangles is $25:49$. What will be the ratio of their corresponding sides?

If $\tan 2A = \cot (A – 18^\circ)$, where $2A$ is an acute angle, then find the value of $A$.

What will be the coordinates of the point on the $x$-axis which is equidistant from the points $(2, -5)$ and $(-2, 9)$?

What is the refractive index of water?

At what temperature do the Celsius and Fahrenheit scales show the same reading?

What is the commercial unit for measuring electrical energy?

Due to which physical phenomenon do liquid drops become spherical?

Which type of lens is used to correct short-sightedness (Myopia)?

The propulsion of a rocket is based on which of Newton’s laws?

The brilliance of a diamond is a result of which phenomenon of light?

In which type of circuit connections are household electrical appliances connected?

What is the acceleration due to gravity ($g$) of an object at the center of the Earth?

Which metal/element is called ‘Strategic Metal’ because it is as strong as steel but half its weight?

Which acid is present in an ant sting?

What is the effect on the weight of iron when it gets rusted?

Which element is known as the ‘Rogue Element’ because its position is not fixed in the periodic table?

Which chemical is widely used to disinfect drinking water?

Which is the lightest metal?

Brass is an alloy of which two metals?

Which allotrope of carbon is a good conductor of electricity?

If $\frac{x}{y} = \frac{4}{5}$, then find the value of $\frac{7x + 3y}{7x – 3y}$.

Find the smallest square number that is completely divisible by each of the numbers 4, 9, and 10.

If $A:B = 2:3$ and $B:C = 4:5$, then what will be the value of $A:B:C$?

The lengths of the diagonals of a rhombus are 16 cm and 12 cm. What will be its area?

If $\sin (A + B) = 1$ and $\cos (A – B) = \frac{\sqrt{3}}{2}$, then find the values of $A$ and $B$.

The ratio of the volumes of two spheres is $64:27$. What will be the ratio of their surface areas?

If the roots of the equation $3x^2 – 12x + k = 0$ are real and equal, then what will be the value of $k$?

What is the total number of natural numbers between $100$ and $200$ that are completely divisible by $3$?

Which device is used to measure the speed of vehicles?

What is the SI unit of electric potential?

Which property of light remains unchanged when it passes from one medium to another?

What is the time period of revolution of a geostationary satellite?

Where should an object be placed in front of a shaving concave mirror to get an erect and magnified image?

According to the law of conservation of energy, what happens to the total energy of the universe?

Which part of the eye helps in adjusting the focal length of the eye lens?

One Horse Power (1 HP) is equal to how many watts?

What is the chemical name and formula of ‘Caustic Soda’?

Elements of which group in the periodic table are called ‘Noble Gases’ or ‘Inert Gases’?

What is the general chemical nature of non-metallic oxides?

Which mixture, containing a $3:1$ ratio of concentrated HCl and concentrated $\text{HNO}_3$, is used to dissolve gold?

How many periods and groups are there in total in the modern periodic table?

Which gas is called the ‘Fuel of the Future’?

What is the chemical formula of Baking Soda?

Besides iron and carbon, stainless steel is an alloy of which two main metals?

What is the IUPAC name of ‘Acetic Acid’ found in vinegar?

If $x^2 + \frac{1}{x^2} = 7$, then find the value of $x + \frac{1}{x}$.

The ratio of two numbers is $3:4$ and their LCM is 120. What will be the sum of those numbers?

If $\tan \theta + \sin \theta = m$ and $\tan \theta – \sin \theta = n$, then $m^2 – n^2$ is equal to what?

The base of an isosceles triangle is 8 cm and one of its equal sides is 5 cm. What will be its area?

What will be the coordinates of the mid-point of the line segment joining the points $(-4, 3)$ and $(4, -3)$?

If $5^{x-1} + 5^{x+1} = 130$, then find the real value of $x$.

If the radius of a circle is increased by 10%, by what percentage will its area increase?

The data $7, 8, 9, 12, x, 15, 17, 20$ are arranged in ascending order. If their median is 14, find the value of $x$.

What is the probability of getting a doublet when two dice are thrown simultaneously?

If the system of equations $kx – y = 2$ and $6x – 2y = 3$ has no solution, then what will be the value of $k$?

The height and slant height of a cone are 12 cm and 13 cm respectively. What will be its volume?

If the 3rd term of an A.P. is 5 and the 7th term is 9, find its first term and common difference.

What is the SI unit of the power of a lens?

The reddish appearance of the sun at sunrise and sunset is due to which phenomenon of light?

What will be the equivalent resistance when three resistors of 1 ohm, 2 ohm, and 3 ohm are connected in series?

The apparent bending of a stick dipped in a bucket of water is due to which phenomenon of light?

An electrical generator converts which form of energy into which form?

What is the frequency of ultrasonic waves?

What will be the effect on the kinetic energy of a body if its momentum is doubled?

The twinkling of stars in the sky is a result of which atmospheric phenomenon?

What is the effect on the value of acceleration due to gravity ($g$) when moving above the surface of the Earth?

At what temperature is the density of water maximum?

Which thermodynamic principle is primarily used in refrigerators or air conditioners?

How is the resistance of a conductor wire related to its area of cross-section (proportional or inversely proportional)?

In which block are the ‘Coinage Metals’ (like Cu, Ag, Au) placed in the modern periodic table?

Which household weak base is used to neutralize the effect of an ant or bee sting?

What is Dry Ice actually in its solid form?

What is the correct chemical formula of Washing Soda?

What is the property of beating metals into thin sheets called?

Which two components are essential in contact with iron for rusting to occur?

In which unit is the purity of gold measured and how many carats is pure gold?

What is the chemical formula of the acid present in vinegar?

What is the chemical name of the rusted iron layer?

Gun metal is an alloy of which metals?

Which element is found in a liquid state at room temperature despite being a non-metal?

If $\log x + \log y = \log (x + y)$, then express $x$ in terms of $y$.

Find the area of a quadrant of a circle whose circumference is 22 cm.

What will be the nature of the roots of the equation $2x^2 – 3x + 5 = 0$?

If the vertices of a triangle are $(0,4)$, $(0,0)$, and $(3,0)$, what will be its perimeter?

A bag contains 3 red and 5 black balls. What will be the probability of drawing a red ball from this bag?

If $\cos \theta = \frac{\sqrt{3}}{2}$, then what is the value of $\csc^2 \theta – \sec^2 \theta$?

The ratio of the volumes of two cubes is $1:27$. What will be the ratio of their edges?

Find the largest number which divides 70 and 125, leaving remainders 5 and 8 respectively.

If $x – 2$ is a factor of the polynomial $x^3 – 3x^2 + kx – 10$, then find the value of $k$.

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is $30^\circ$. Find the height of the tower.

Which type of mirror is used in the headlights of vehicles?

In which type of connection is a fuse wire connected with the live wire in an electrical circuit?

What is the main difference in signs between the Lens Formula and the Mirror Formula?

What is the refractive index of a diamond?

Where is the far point located for a healthy human eye?

The heat ($H$) produced in a conductor when current passes through it is how related to the square of the current ($I$)?

In which medium (solid, liquid, or gas) is the speed of sound the fastest?

Hydraulic brakes work on which physical principle or law?

Which scientist discovered electromagnetic induction?

Which atmospheric layer prevents ultraviolet rays from reaching the Earth?

Which gas is also known as ‘Marsh Gas’?

What is the other name of ‘Aqua Regia’ which dissolves noble metals like gold and platinum?

What is the ability of metals to be drawn into thin wires called?

Which gas is released when baking soda is heated?

What is the common name of the alloy made of copper and zinc?

What is the pH value of a neutral solution?

What are the vertical columns called in the modern periodic table?

What is the chemical name of bauxite?

Which allotrope of carbon is the hardest natural substance?

Which acid is produced in the process of turning milk into curd?

If $\frac{a}{3} = \frac{b}{4} = \frac{c}{7}$, then what will be the value of $\frac{a+b+c}{c}$?

Find the average of the first 5 prime numbers.

If the difference between the circumference and diameter of a circle is 30 cm, what will be the radius of that circle?

Find the value of $\sin 25^\circ \cos 65^\circ + \cos 25^\circ \sin 65^\circ$.

If $2^x \times 8^{\frac{1}{5}} = 2^{\frac{1}{5}}$, then find the value of $x$.

What will be the product of the zeroes of the quadratic equation $x^2 + 7x + 10 = 0$?

The area of an equilateral triangle is $9\sqrt{3}\text{ cm}^2$. What will be the length of each of its sides?

If the distance between the points $(x, 2)$ and $(3, 4)$ is $\sqrt{8}$, what can be the value of $x$?

What is the probability that a number selected at random from numbers $1$ to $50$ is a multiple of 7?

If the mean of $3, 4, 5, 17, x$ is $6$, then find the value of $x$.

Which type of lens is used to correct Presbyopia?

What is the color of the insulation of the live wire used in domestic electrical circuits?

What is the speed of light in a vacuum?

Which device is used to measure electric current?

What is the nature of the image always formed by the side mirrors (convex mirrors) of vehicles?

Kilowatt (kW) is the unit of which physical quantity?

Which type of mirror is used inside a solar cooker to focus sunlight?

What is the central point of a lens called?

What is the SI unit of resistivity?

How does the potential energy of a freely falling body change as it comes down?

What is the full form of LPG?

What is the valency of noble or inert gases?

Which organic acid is found in tomatoes?

What is the chemical name and formula of Bleaching Powder?

Which main metal is added to iron to make stainless steel rustproof?

What are the horizontal rows called in the modern periodic table?

Which non-metal is lustrous in its solid state at room temperature, and which disease is caused by its deficiency?

Temporary hardness of water is primarily due to which salts?

What is the general nature of metallic oxides?

What is the full form of CNG?

What is the chemical formula of Quick Lime?

What is glass actually?

Bronze is an alloy of which two metals?

What is the reaction between an acid and a base to form salt and water called?

Which hydrocarbon gas is the main component of gobar gas?

If $x – \frac{1}{x} = 5$, then find the value of $x^2 + \frac{1}{x^2}$.

The HCF of two numbers is 6 and their product is 720. What will be their LCM?

If $\sin \theta = \cos \theta$ and $\theta$ is an acute angle, then what is the value of $\theta$ in degrees?

The base of a right-angled triangle is 6 cm and its hypotenuse is 10 cm. What will be its area?

Find the distance between the points $(2, 3)$ and $(4, 1)$.

If $3^{x+2} = 81$, then what is the value of $x$?

If each side of a square is increased by 20%, by what percentage will its area increase?

What will be the mean of the first 5 even natural numbers?

What is the probability of drawing an ace from a well-shuffled deck of 52 playing cards?

If the linear equations $2x + 3y = 7$ and $kx + 6y = 14$ have infinitely many solutions, then what will be the value of $k$?

The radius of the base of a right circular cone is 3 cm and its height is 4 cm. What will be its curved surface area?

Find the 10th term of the A.P. $2, 7, 12, \dots$.

What is the magnification power of a plane mirror?

The twinkling of stars is due to which property of light?

If two resistors of 2 ohm and 4 ohm are connected in parallel, what will be the equivalent resistance?

An air bubble inside water behaves like which type of lens?

An electric motor converts which form of energy into which form?

What is the SI unit of the frequency of sound?

Which type of energy does a passenger sitting in a moving train possess?

What are the colors of the topmost and bottom-most bands in a primary rainbow respectively?

What is the approximate value of acceleration due to gravity ($g$) on the surface of the Earth?

What is the freezing point of water on the Celsius and Fahrenheit scales?

Which mirror is used in vehicles to view the trailing traffic?

What will be the effect on the resistance of a wire if its length is doubled?

Elements of which block of the periodic table are called ‘Transition Elements’?

Which natural acid is secreted in our stomach for digesting food?

Which gas is called ‘Laughing Gas’ and what is its chemical formula?

Which gas is released when bleaching powder is left open in the air?

What is the property of metals by virtue of which they can be drawn into thin wires called?

What is the process of coating zinc on iron to protect it from rusting called?

Pure gold is very soft; which metal is added to harden it for making jewelry?

Which mild base is applied to neutralize the effect of an ant sting?

What is the common or commercial name of copper sulfate ($\text{CuSO}_4 \cdot 5\text{H}_2\text{O}$)?

Solder wire is an alloy of which two metals?

Which is the only metal found in a liquid state at room temperature?

If $\log_x 243 = 5$, then find the value of $x$.

The circumference of a circle is 44 cm, what will be its diameter?

If the roots of the quadratic equation $x^2 – kx + 4 = 0$ are real and equal, then what will be the value of $k$?

What will be the distance between the origin $(0,0)$ and the point $(-6, 8)$?

What will be the probability of getting a number greater than 4 when a die is thrown?

If $\sec \theta = \frac{13}{12}$, then find the value of $\sin \theta$.

The ratio of the radii of two spheres is $2:3$. What will be the ratio of their volumes?

What will be the median of the first 5 prime numbers?

If $\alpha$ and $\beta$ are the zeroes of the polynomial $x^2 – 4x + 1$, then what is the value of $\alpha + \beta$?

A kite string is 60 m long and makes an angle of $60^\circ$ with the horizontal. Assuming there is no slack in the string, find the height of the kite.

Why is a concave mirror used for shaving?

Why should the melting point of a fuse wire be low?

What is the relation between the power of a lens and its focal length ($f$) in meters?

What is the approximate refractive index of glass?

Which lens is used in the spectacles of a person suffering from short-sightedness (Myopia)?

What should be the resistance and melting point of a heater wire?

Why can sound waves not travel in a vacuum?

Pascal is the unit of which physical quantity?

On which principle does a dynamo work?

What is the chemical chemical formula of ozone gas which protects us from the ultraviolet rays of the sun?

LPG cooking gas is primarily a mixture of which two gases?

Which group is called ‘Zero Group’ in the modern periodic table?

Which acid is found in lemons?

Why does lime water turn milky when $\text{CO}_2$ gas is passed through it?

Which rustproof alloy is made by mixing chromium and nickel with iron?

What is the approximate pH value of human blood?

On which law was Mendeleev’s periodic table based?

From which ore is aluminum primarily extracted?

Both diamond and graphite are allotropes of carbon, yet why is graphite soft and diamond extremely hard?

Which acid is found in tamarind?

If $\frac{x}{2} = \frac{y}{3} = \frac{z}{5}$, then what will be the value of $\frac{x+y+z}{y}$?

What will be the sum of the first 10 odd natural numbers?

The radius of a circle is 7 cm. What will be the perimeter of its quadrant?

What is the value of $\tan 45^\circ + \cot 45^\circ$?

If $5^x = 125$, then find the value of $x^2$.

If the product of the roots of the equation $x^2 – 5x + k = 0$ is 6, then find the value of $k$.

The perimeter of an equilateral triangle is 18 cm. What will be its area?

The distance of the point $(x, 4)$ from the origin is 5 units. Find the value of $x$.

A bag contains 5 white and 7 red balls. What is the probability of drawing a white ball at random from the bag?

If the mean of $10, 12, 15, x, 20$ is 15, then what is the value of $x$?

Which type of lens is used to correct long-sightedness (Hypermetropia)?

Which metal is the filament of an electric bulb made of and why?

When a ray of light passes from glass to air, does it bend towards or away from the normal?

Which device is used to measure potential difference?

The focal length of a lens is 50 cm, what will be its power (in Diopters)?

What is the SI unit of work?

Is the focal length of a convex mirror positive or negative?

Which scientist first observed the magnetic effect of electric current?

Ohm’s law shows the relation between which two physical quantities?

When an object is thrown upwards, what is its velocity at the highest point?

Which hydrocarbon gas is the main component of CNG gas?

How many electrons are there in the outermost shell of halogen elements?

Which acid is present in sour milk or curd?

What is formed when chlorine gas is passed over slaked lime [$\text{Ca(OH)}_2$]?

Is the melting point of solder alloy lower or higher compared to pure metals?

According to the modern periodic law, the properties of elements are periodic functions of what?

Nichrome is an alloy of which main metals, used in heater wires?

Permanent hardness in water is primarily due to chloride and sulfate salts of which metals?

What is the pH value of a basic solution?

What is the chemical name and formula of marsh gas?

Which chemical reaction occurs when water is poured on quick lime (endothermic or exothermic)?

What is the chemical name and formula of common salt?

What is the approximate percentage of zinc in brass alloy?

What is the main ore of copper?

What is the property that makes the surface of metals shiny called?

If $x + \frac{1}{x} = 5$, then find the value of $x^4 + \frac{1}{x^4}$.

The LCM of two numbers is 14 times their HCF. If the sum of LCM and HCF is 600 and one number is 280, then what is the other number?

If $\sin (A – B) = \frac{1}{2}$ and $\cos (A + B) = \frac{1}{2}$, then what are the values of $A$ and $B$ in degrees?

The height of an equilateral triangle is $3\sqrt{3}$ cm. What will be its area?

Find the distance between the points $(a, b)$ and $(-a, -b)$.

If $\left(\frac{2}{3}\right)^{x-1} = \left(\frac{27}{8}\right)^{x-3}$, then what is the value of $x$?

The total surface area of a cube is $96\text{ cm}^2$. What will be its volume?

What will be the mean of the squares of the first 10 natural numbers?

What is the probability of having 53 Sundays in a leap year?

For what value of $k$ will the system of equations $2x + 3y = 5$ and $4x + ky = 10$ have infinitely many solutions?

If the surface area of a sphere is $616\text{ cm}^2$, then what will be its radius?

Which term of the A.P. $21, 18, 15, \dots$ is $-81$?

Why is only a concave mirror used in the headlights of vehicles?

If the focal length of a convex lens is 25 cm, what will be its power?

Does the resistance of a conductor wire decrease or increase when its thickness (area of cross-section) increases?

The formation of a rainbow is a combined result of which three main phenomena of light?

In Fleming’s left-hand rule, what does the thumb represent the direction of?

What is the audible range of frequency for the human ear?

If the velocity of an object is tripled, how many times will its kinetic energy become?

By which method do sun rays reach the Earth?

Which scientist gave the Universal Law of Gravitation?

What is the unit of latent heat?

The image of a person standing in front of a plane mirror is formed at the same distance behind the mirror as the object is in front of it. Is this statement true or false?

Kilowatt-hour (kWh) is the unit of which physical quantity?

Which is the most electronegative element in the periodic table?

Which type of medicine (Antacid) is used for treating indigestion?

Which gas is primarily responsible for the depletion of the ozone layer?

What is the chemical name and formula of limestone?

How many carats of gold are generally used for making ornaments?

Why is applying oil or grease effective in preventing the rusting of iron?

Which plastic material insulation is coated on electric wires to prevent electric shock?

What is the common name of methanoic acid present in an ant sting?

What is the chemical formula of Blue Vitriol?

What is the percentage of silver in German Silver alloy?

Which is the only non-metal found in a liquid state at room temperature?

If $\log (x+y) = \log x + \log y$, then what is the value of $y$ in terms of $x$?

What will be the effect on the area of a circle if its diameter is doubled?

If the roots of the quadratic equation $ax^2 + bx + c = 0$ are not real, will the value of discriminant ($D$) be less than or greater than zero?

What will be the length of the line segment joining the points $(4, 5)$ and $(7, 9)$?

A card is drawn from a pack of 52 playing cards. What will be the probability of it being a black queen?

If $\sin \theta = \frac{3}{5}$, then find the value of $\tan \theta$.

The ratio of the radii of two cylinders is $2:3$ and the ratio of their heights is $5:3$. What will be the ratio of their volumes?

What will be the median of $1, 2, 10, 18, 5, 9$?

If $x – 1$ is a factor of the polynomial $2x^2 + kx$, then find the value of $k$.

A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of $30^\circ$ with it. If the distance from the foot to the top is 8 m, what was the total height of the tree?

Which mirror is used in a search light?

Why is a fuse wire always connected in series in a circuit?

Where should an object be placed in front of a convex lens to get a real and equal-sized image?

What is the unit of refractive index?

How is the eye defect called Cataract treated?

Name any two household appliances based on the heating effect of electric current.

What is the echo produced due to the reflection of sound waves called?

What is the property of thickness or resistance to flow of a liquid called?

An electric generator works on which principle of energy conversion?

The white appearance of clouds is due to which phenomenon of light?

Which gas is primarily included in natural gas?

Why are noble gases chemically inert?

Which acid is found in oranges and lemons?

Which weak acid is formed when carbon dioxide gas dissolves in water?

What is the alloy of copper and tin ($\text{Cu} + \text{Sn}$) called?

Below what pH value of rainwater is it called ‘Acid Rain’?

Up to which element was Newlands’ Law of Octaves properly applicable?

Which is the main ore of iron from which its industrial extraction takes place?

Diamond is a bad conductor of electricity while graphite is a good conductor; what is the main structural reason for this?

Which natural acid is found in apples?

If $a:b = 3:4$ and $b:c = 8:9$, then what will be the value of $a:c$?

What will be the average of the first 10 natural numbers?

The perimeter of a semi-circle is 36 cm. What will be its radius?

What is the value of $\sin^2 30^\circ + \cos^2 30^\circ$?

If $a^x = b$, $b^y = c$ and $c^z = a$, then what will be the value of $xyz$?

Find the roots of the quadratic equation $x^2 – 3x – 10 = 0$.

The hypotenuse of an isosceles right-angled triangle is $8\sqrt{2}$ cm. What will be the length of its other sides?

In which quadrant is the point $(3, -4)$ located?

What will be the probability of getting an even number when a die is thrown once?

If the mean of $6, 7, x, 8, y, 14$ is 9, then find the value of $x + y$.

Which type of lens is used to correct Astigmatism?

What is the frequency and voltage of the alternating current (AC) supplied to our homes?

The refractive index of glass is maximum for which color of light?

What is the SI unit of resistance?

What is the focal length of a plane mirror?

What is the SI unit of power?

Which metal wires are used to interconnect solar cells in a solar panel?

What is the bouncing back of light into the same medium after striking a smooth surface called?

What should be the resistance of an ideal ammeter?

What is the product of the mass and velocity of a body called?

Which gas is found in the highest amount in biogas?

What is the number of protons present in the nucleus of an atom of an element called?

Why is baking soda used to get relief from a bee sting?

What is the chemical formula of Gypsum?

What is the alloy of copper, zinc, and nickel ($\text{Cu} + \text{Zn} + \text{Ni}$) called?

In Mendeleev’s periodic table, elements were arranged in the increasing order of what?

Quick Silver is another name for which metal?

What is the chemical formula of alum, which is used in water purification?

What is the pH value of an acidic solution?

Natural rubber is a polymer of which substance?

Why is nitrogen gas filled in chips packets?

What is the chemical name of Washing Soda?

Which metal is mixed in stainless steel to provide shine and rust-resistance?

Zinc Blende is the main ore of which metal?

What is that chemical process called in which a substance combines with oxygen?

If $x – \frac{1}{x} = 3$, then find the value of $x^3 – \frac{1}{x^3}$.

The ratio of two numbers is $5:6$. If their HCF is 4, then what will be their LCM?

What will be the value of $\sin^2 45^\circ + \cos^2 45^\circ + \tan^2 45^\circ$?

The equal sides of an isosceles triangle are 10 cm and the angle between them is $90^\circ$. Find the area of the triangle.

If the point $(x, y)$ is equidistant from the points $(a+b, b-a)$ and $(a-b, a+b)$, then what is the relation between $x$ and $y$?

If $4^x – 4^{x-1} = 24$, then find the value of $(2x)^x$.

If the radius of a cylinder is doubled and its height is halved, what will be the ratio of its new volume to its old volume?

What is the formula to find the mean of the first $n$ natural numbers?

What will be the probability of getting at least one Head when two coins are tossed simultaneously?

For what value of $m$ will the pair of equations $3x + my = m$ and $2x + (m-1)y = 1$ have no solution?

The radius of a hemisphere is 7 cm. What will be its total surface area?

Find the 11th term of the A.P. $-5, -\frac{5}{2}, 0, \frac{5}{2}, \dots$.

Which mirror is used to focus sunlight in a solar furnace?

The power of a convex lens is $+4\text{ D}$, what will be its focal length?

Out of two wires of equal length and same material, which one will have less resistance: the thicker one or the thinner one?

When white light passes through a glass prism, which color undergoes the maximum deviation?

What is the main function of ‘Split Rings’ (or Commutator) in an electric motor?

Which type of waves (like ultrasonic waves) are used to measure the depth of the sea (in SONAR)?

If the mass of a moving object is halved and its velocity is doubled, what will be the effect on its kinetic energy?

The formation of a ‘Mirage’ in deserts is a result of which phenomenon of light?

The value of acceleration due to gravity on the Moon is what fraction of that on the Earth ($g$)?

What is the value of Absolute Zero Temperature on the Celsius scale?

Which mirror is used by dentists to see a magnified image of patients’ teeth?

What is the ratio of the potential difference $V$ across a conductor to the current $I$ flowing through it called?

Which are the lightest gas and the lightest noble gas in the periodic table respectively?

Which acid accumulates when we get cramps in our leg or body muscles due to excessive physical work?

Which gas is primarily used in fire extinguishers to put out fires?

What is the common name of Calcium Sulfate Hemihydrate ($\text{CaSO}_4 \cdot \frac{1}{2}\text{H}_2\text{O}$)?

What is the percentage of pure gold in 18 carat gold?

What is the English name for the process of coating zinc on iron objects (called Yashadlepan in Hindi)?

Give an example of a thermosetting plastic used in making electrical switches?

Which acid is present in a bee sting that causes severe pain and burning sensation?

What is the chemical formula of Green Vitriol?

Which is the main metal in ‘Gun Metal’, an alloy made by mixing copper, zinc, and tin ($\text{Cu} + \text{Zn} + \text{Sn}$)?

Which element remains in liquid form at room temperature despite being a non-metal?

If $\log a + \log b + \log c = 0$, then what is the value of $abc$?

By what percentage will the area of a circle decrease if its radius is reduced by 50%?

If the roots of the quadratic equation $x^2 – 2x + (k+4) = 0$ are real, then what will be the value of $k$?

In what ratio does the $y$-axis divide the line segment joining the points $(2, -3)$ and $(5, 6)$?

What will be the probability of getting a sum of 10 on the numbers appearing when two dice are thrown together?

If $\sin \theta + \cos \theta = \sqrt{2} \cos \theta$, then what is the value of $\theta$?

The radius of the base and the height of a cone and a cylinder are equal. What will be the ratio of their volumes?

What will be the median of the first 9 prime numbers?

If the zeroes $\alpha$ and $\beta$ of the polynomial $x^2 – p(x+1) – c$ are such that $(\alpha + 1)(\beta + 1) = 0$, then find the value of $c$.

From a point on the ground, which is 40 m away from the foot of a tower, the angle of elevation of the top of the tower is $60^\circ$. Find the height of the tower.

In the dispersion of white light by a glass prism, the speed of which color of light is the least inside the prism?

Which safety device is installed in houses to prevent damage caused by short circuits or overloading?

Where should an object be placed in front of a convex lens to get its real, inverted, and highly magnified image?

How is the refractive index of a medium related to the speed of light (proportional or inversely proportional)?

What is that eye defect called in which a person cannot see horizontal and vertical lines clearly at the same time?

The unit of electrical energy is ‘Joule’, but what is the unit of electric power?

To hear an echo, what should be the minimum distance (in meters) between the listener and the reflecting surface?

What is the SI unit of the coefficient of viscosity?

Michael Faraday formulated the laws of electromagnetic induction; these laws are the basis of which device (like a generator)?

Which invisible rays emanating from the sun’s photosphere make us feel hot?

Which hydrocarbon gas is primarily present in Coal Gas?

Why can atoms of noble gases exist independently?

Which acid is found in vinegar and pickles?

Which gas is dissolved under high pressure in cold drinks or soda water?

The alloy of copper and zinc is called brass, then what is the alloy of copper and tin called?

Which substance do farmers spray in fields to reduce the acidity of the soil?

Give an example of Dobereiner’s ‘Triads Rule’.

Hematite ($\text{Fe}_2\text{O}_3$) is the main ore of which metal?

Fullerene is an allotrope of carbon with a football-like structure. How many carbon atoms does it contain?

What is the name of the natural acid found in milk?

If $x:y = 3:5$, then what will be the value of $(5x + 3y) : (5x – 3y)$?

Which formula is used to find the sum of the first 20 natural numbers?

The ratio of the circumference of a circle to its diameter is always equal to what?

What will be the value of $\sec^2 60^\circ – \tan^2 60^\circ$?

If $3^x = 9^y$ and $8^{y+1} = 2^{x+2}$, then find the values of $x$ and $y$.

What will be the roots of the quadratic equation $2x^2 – 5x – 3 = 0$?

The volume of a right circular cylinder is $448\pi\text{ cm}^3$ and its height is 7 cm. What will be its radius?

What will be the perpendicular distance of the point $(4, -6)$ from the $x$-axis?

A card is drawn from a pack of 52 playing cards. What is the probability of it being a red card?

If the arithmetic mean of $x, x+2, x+4, x+6, x+8$ is 11, then find the value of $x$.

Is the main biological reason for Myopia the elongation or shortening of the eyeball?

The fuse wire used in our homes is always made of which alloy (like tin and lead)?

When a ray of light passes from glass to water, does it bend towards or away from the normal (if the refractive index of glass is greater than water)?

A galvanometer is used to detect the presence of what in a circuit?

The focal length of a concave lens is 20 cm. What will be its power along with the sign?

What is the commercial unit of energy, commonly referred to as a ‘Unit’?

Is the focal length of a concave mirror always positive or negative?

An electric generator works on the principle of magnetic induction discovered by which scientist?

What is the inverse of resistance called and what is its unit?

When a body undergoes uniform circular motion, its speed remains constant, but what changes continuously?

Butane gas is the main component of LPG, what is its chemical formula?

Elements of which group in the periodic table are called ‘Alkali Metals’?

Which acid is primarily found in abundance in citrus fruits?

Why does the milky color disappear when an excess of $\text{CO}_2$ gas is passed through lime water (which water-soluble salt is formed)?

Solder alloy is a mixture of which two metals?

In the modern periodic table, what does the number of shells in the electronic configuration of elements represent (period or group)?

The alloy ‘Nichrome’ used in heater wires is a mixture of which metals?

Which sodium salt (like washing soda) is used to remove the permanent hardness of water?

What is the chemical name and formula of Lime Water?

What is that chemical process called in which a substance loses oxygen or gains hydrogen?