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Two bodies A and B are charged with equal magnitude of charge but A with positive charge and B with negative. If $$M_A$$ and $$M_B$$ are masses before charging and $$M'_A$$ and $$M'_B$$ are the masses after charging, then $$m_0$$ is some constant mass.
The number of natural numbers $$n\leq 30$$ for which $$\sqrt{n+\sqrt{n+\sqrt{n+\cdots}}}$$ is a natural number is
Elements A, B and C have atomic numbers $$X$$, $$X+1$$ and $$X+2$$, respectively. C is an alkali metal. A reacts with another element Y to form the compound AY. A and Y belong to the same group. AY possesses an
Air has three major components nitrogen, oxygen, and argon. Given that one mole of air at sea level is made up of 78 percent nitrogen, 21 percent oxygen, and 1 percent argon by volume. What is the density of air? Assume that gases behave ideally and the atomic mass of argon is 40 amu.
A conductor of length $$L$$ has a varying cross section with area $$2A$$ at P and $$A$$ at Q as shown in the adjacent figure. If it carries a steady current $$I$$, then
The number of natural numbers $$n\leq30$$ for which $$\sqrt{n+\sqrt{n+\sqrt{n+\cdots}}}$$ is a prime number is
Rhodoferax fermentans is a species of photosynthetic bacteria. From your knowledge about bacteria in general, identify the component that CANNOT be present in this organism.
If atmospheric humidity decreases, transpiration rate
Vessels A and B are made of conducting material. Both contain water. Vessel A floats in B. Vessel B is now heated at a uniform rate, then
The number of squares formed by 5 vertical and 4 horizontal lines, all equispaced, is
If 0.50 mole of a monovalent metal $$M^{+1}$$ halide is mixed with 0.2 mole of a divalent metal $$L^{+2}$$ phosphate, the maximum number of moles of $$M_3PO_4$$ that can be formed is
Every major city in India has a pollution control board to monitor air and water pollution. The following data is from three different localities in Bangalore city from the year 2015.
ppb stands for parts per billion and ppm stands for parts per million. These are different units to express concentration. They are very similar to percentage, which is parts per hundred. Based on the above data, which place will you choose to live in?
A body thrown vertically up reaches a maximum height and returns back. Its acceleration is
The number of integers $$a,b,c$$ for which $$a^2+b^2-8c=3$$ is
Which of the following is NOT produced by the endoplasmic reticulum?
Vaccines prevent infections by pathogens by
Velocity of a particle moving along a straight line varies with time as shown in the adjacent figure. Net forces acting on the particle are $$F_1,F_2,F_3,F_4$$ and $$F_5$$ in the intervals OA, AB, BC, CD and DE respectively. Identify the correct statement.
If set X consists of three elements then the number of elements in the power set of power set of X is
The heat of neutralisation of $$CH_3COOH$$, $$HCOOH$$, $$HCN$$ and $$H_2S$$ are $$-55.2$$, $$-56.07$$, $$-2.8$$ and $$-3.34$$ kJ per equivalent respectively. The increasing order of strength of these acids is
To prevent the formation of oxides, peroxides, and superoxides, alkali metals are sometimes stored in an unreactive atmosphere. Which of the following gases should not be used for lithium
A wooden block W is suspended by using a cord from a heavy steel ball B. The entire system is dropped from a height. Neglecting air resistance, the tension in the cord is
In a $$n$$-sided regular polygon, the radius of the circum-circle is equal in length to the shortest diagonal. The number of values of $$n<60$$ for which this can happen is
Which of the following does NOT contain living cells?
If DNA was made of 6 nucleotides instead of 4, what are the total number of triplet codons possible?
A circus performer of weight $$W$$ is standing on a wire as shown in the adjacent figure. The tension in the wire is
Number of integers $$n$$ such that the number $$1+n$$ is a divisor of the number $$1+n^2$$ is
When 1 gram of a mixture of aluminium and zinc was treated with HCl, a gas was liberated. At the end of the reaction, the volume of the liberated gas was found to be 524 $$\text{cm}^3$$ under STP conditions. The individual weights of aluminium and zinc in the mixture, respectively, are
Choose that element which is most different from the other three
In the following diagrams O is point object and I is its image formed by a concave mirror. Identify the diagram in which position of image I is nearly correct.
If for $$x,y>0$$ we have $$\frac{1}{x}+\frac{1}{y}=2$$ then the minimum value of $$xy$$ is
Which of these is a mollusc?
What is the mechanism used by the kidneys to remove waste products from the body?
Following diagram shows refraction of parallel beam of light through a spherical surface. Identify the correct ray diagram.
Tenth term in the sequence 12, 18, 20, 28, ... is
An electron pair donor is a Lewis base and an electron pair acceptor is a Lewis acid. Which among the following statements is correct?
Greenhouse gases absorb and trap outgoing infrared radiation from Earth and contribute to global warming. Going only by the condition of permanent dipole moment, in the list of gases given below, how many can be potential greenhouse gases? Water, sulphur dioxide, boron trifluoride, carbon monoxide, carbon dioxide, nitrogen, oxygen, methane, hydrogen sulphide, ammonia.
In the diagram $$M_1$$ and $$M_2$$ are two plane mirrors at right angles to each other. O is a luminous point object. Consider two images formed due to first reflection at $$M_1$$ and $$M_2$$. The area of the triangle formed by the object and two images is
The probability of a point within an equilateral triangle with side 1 unit lying outside its in-circle is
Penicillin cannot be used to treat influenza because
Thin cuboidal strips are made by slicing a potato. They are all made to be exactly 8 cm long and 2 mm wide. Each strip is placed in sugar solutions of different concentration. After soaking it for 5 hours, their lengths are measured again. The following graph shows the results of the experiment. What concentration of sugar solution is isotonic with the contents of the cells of the potato?
A fisherman of height $$h$$ is standing on the bank of a lake. A fish in the water perceives his height as $$h'$$. Then
A triangle has perimeter 316 and its sides are of integer length. The maximum possible area for such a triangle is achieved for
Hennig Brand, one of the many alchemists was in pursuit of the philosopher’s stone. Brand's method is
believed to have consisted of evaporating large quantities of urine to leave a black residue that was then left
for a few months. The residue was then heated with sand, driving off a variety of gases and oils. The final
substance to be driven off, was condensed as a white solid, which he called as “cold fire” as it was luminous
and glowed in the dark and also caught fire on slight warming and producing a large quantity of light. It has also
been called as the “Bearer of light”. Which element is “cold fire”?
When solid KOH is mixed with solid $$NH_4Cl$$, a gas is produced. Which gas is it?
Object A is completely immersed in water. True weight of object A is $$W_A$$. Weight of water with beaker is $$W_B$$. Let B be the buoyant force. $$W_1$$ and $$W_2$$ are scale readings of spring balance and weighing scale respectively.
Number of numbers less than 40 having exactly four divisors is
Antibodies play an important role in defending the body against infections by which of the following mechanisms
The figure shows a food web, where A, B, C, D and other labels represent different species. The direction of the arrows symbolizes the direction of flow of nutrients. An increase in the population of which species is likely to decrease the population of species A
A point object O is kept at origin. When a concave mirror $$M_1$$ placed at $$x=6$$ cm, image is formed at infinity. When $$M_1$$ is replaced by another concave mirror $$M_2$$ at the same position, image is formed at $$x=30$$ cm, then the ratio of the focal length of $$M_1$$ to that of $$M_2$$ is
[image]
The number $$3^8(3^{10}+6^5)+2^3(2^{12}+6^7)$$ is
Melting point of a substance is $$10^\circ\text{C}$$. What does this mean?
The following substances have approximately the same molecular mass. Which is likely to have the highest boiling point?
U-tube contains some amount of mercury. Immiscible liquid X is poured in the left arm and immiscible liquid Y is poured in the right arm. Length of liquid X is 8 cm, length of liquid Y is 10 cm and upper levels of X and Y are equal. If density of Y is $$3.36\text{ g cm}^{-3}$$ and density of mercury is $$13.6\text{ g cm}^{-3}$$, then density of X is
Let the number of rectangles formed by 6 horizontal and 4 vertical lines be $$n$$ and those formed by 5 vertical and 5 horizontal lines be $$m$$, then we have
In a human cell undergoing meiosis, what are the total number of cellular DNA molecules present during Prophase I
During gaseous exchange in the alveoli, what happens to nitrogen?
The effective resistance between A and D in the circuit shown in the adjacent figure is
If ABCD is a rhombus and $$\angle ABC=60^\circ$$ then
Identify the overall change in the following set of reactions.
1. Carbon dioxide $$\rightarrow$$ carbonic acid $$H_2CO_3$$.
2. Ethanol (alcohol) → Ethanal (aldehyde)
3. Ethanal (aldehyde) → Ethanol (alcohol)
4. Sulphuric acid to sulphur trioxide $$SO_3$$.
Choose the correct option which best describes these conversions.
An element with atomic number 44 is below which element in the periodic table?
Three bulbs $$B_1,B_2$$ and $$B_3$$ having rated powers 100 W, 60 W and 60 W at 250 V are connected in a circuit as shown in the adjacent figure. If $$W_1,W_2$$ and $$W_3$$ are the output powers of the bulbs respectively, then
If $$a,b>0$$ then
Which of the following is true about ATP
Which of the following statements is true regarding communication in neurons
Rod AB of radius $$2r$$ is joined with rod BC of radius $$r$$. They are of same material and of same length. The combination carries a current $$I$$. Choose the correct statement.
The statement “a is not less than 4” is correctly represented by
A chemist mixes two ideal liquids A and B to form a homogeneous mixture. The densities of the liquids are 2.0 g/mL for A and 3 g/mL for B. When she drops a small object into the mixture, she finds that the object becomes suspended in the liquid. If the mixture is made of 40 percent A and 60 percent B by volume, what is the density of the object?
How many different compounds can have the formula $$C_3H_4$$?
In the figure shown, the current carrying loop is fixed, whereas the current carrying straight conductor is free to move. Then straight wire will, ignoring gravity
Two friends A and B watched a car from the top of their buildings. Angle of depression for A was 10 degrees more than angle of depression for B, then
How many times would a red blood cell pass through the heart during one complete cycle?
A gene has two alleles P dominant and p recessive. The homozygous recessive combination leads to death in the embryo stage. If two individuals with genotype Pp are mated, out of the offspring that survive to adulthood, what is the probability of the genotype being Pp?
A convex mirror of focal length $$f$$ produces an image of size equal to $$\frac{1}{n}$$ times the size of the object. Then the object distance is
Total surface area of a sphere S with radius $$\sqrt2+\sqrt3$$ cm is
There are many elements in the periodic table that are named after the country, where they were first made or
obtained. For example, the Latin name for copper was coined by the Romans because their chief source of
copper was from the Island of Cyprus. However, there is one country in the world which was named after an
element (the Latin name). A long time ago, it was believed that this country had mountains full of a valuable
element, however all expeditions to find these mountains failed. But the name stuck on. The element in
question is used for many applications today, and many of its compounds are used as catalysts. The ions of this
metal have very good anti-microbial property and finds application in water purification. The element is
All of these species have the same number of valence electrons as nitrate ion, except
The angle between the hour arm and the minute arm of a clock at 2.10 a.m. is
A craft teacher reshapes the wax from a cylinder of candle with section diameter 6 cm and height 6 cm into a sphere. The radius of this sphere will be
Plants absorb nitrates from the soil, which are most essential to produce
The dry mass, mass excluding water, of a seed in the process of germination
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