Four identical cones with base diameter of 10 cm are compactly placed inside a box in uprigh position.What will be the area of sqaure (in cm²) formed by connecting tips the cones ?

How many hollow spheres having inner radius of 1 cm can be completely filled by transferring water from a completely filled hollow sphere having inner diameter of 20 cm ?

The two identical bags and two identical boxes are placed as shown. The top of the stable is at the height of.

The graph shows the cumulative number of deaths during a pandemic. The time intervals shown in the graph are equal. The largest increase in the number of deaths was during the period.

The period of a pendulum is given as T = 2  (l/g)^½ where g = 9.81 m/s² and =3.1416.The period of a pendulum of length 1 m correct to the first place of decimal in seconds.

The sides a, b and c of a ΔABC satisfy the equation (a – 8)² + (b – 15)² + (c – 17)² = 0. Then ΔABC is z :

In the given substraction problem, each letter represents a digit between 0 and 9 :
 

	T	A	S	5
-		R	S	R
	2	T	A	9

 

Three apartments,which are in a row, are occupied by Umar, Ramesh and John. Only one of them is the landlord, whose apartment is at one end. Ramesh's apartment is not next to John's apartment.The apartment on the left is not the landlord's, the one isn the middle is not Ramesh's and the one on the right is not John's.Who is the landlord  ?

At a book–signing session, there are 5 authors who write only single-author books and another 5 who write only in pairs.Every author signs books that are authored or co-authored by him/her. In order to collect signatures of all 10 authors, in th best possible scenario, the minimum number of books that need to be purchased is :

The gross domestic products (GDP) and total populations of four countries A, B, C and D in appropriate units are shown in the accompanying figures



Countries with the highest and the lowest per capita GDP are, respectively.

In a class of 84 students, 29 failed in Science (S), 43 failed in Maths (M) and 17 students passed in both.Which of the following Venn diagrams is the correct depiction of the situation ?

A milk vendor has 50 L of milk and supplies 5 L to every customer. After each transaction he adds 5L of water. What is the percentage of milk contained in a litre of solution purchased by the fifth customer ? 

An expenditure of Rs. 96 was supposed to be shared equally by all the students in a class. Since four students didn't contribute, the remaining students had to contribute an additional amount of Rs. 4 each. how many students contributed ?

While calculating the average of twenty 2-digit numbers, digits of one of the numbers got interchanged because of which the average reduced by 1.8. The difference in the values of the digits of the number that were interchanged is.

Based on the clue given in statements A to D, find the correct 3-digit number.
1. Two of the digits are present in the number 395, but they are not placed correctly.
2. One of the digits is present in the number 718 and is placed correctly.
3. None of the digits is present in the number 148
4. One of the digits is present in the number 835 is placed correctly.

Which of the following plots represents the function y = x ?

1% of the population of a country is suffering from a disease.One person undergoes a diagnostic test which has 98% reliability (i.e., 98% of people who are sick test positive and 98% of the healthy people test negative).If the person is tested positive,the chances that The person is acually having the disease is, approximately :

A man of height 2 m looks at the top of a 40m tall building from some distance. The angle of elevation of his line of sight is 45^o. When he further moves away from the building by a distance x, the angle of elevation becomes 30°. Then x is approximately :

In an 800 m wide river, water flows at a speed of 9 km/h. A man can row a boat in still water with a speed of 15 km/h. If the path of the boat is maintaind perpendicular to the flow of the water, then how long will the man take to cross it ?

On a large flat surface identical circular coins are placed in the most compact arrangement without overlapping with each other. If the number of coins available is unlimited, then the fraction of the surface area that is not covered by the coins is closest to :

For the given reaction [*Co(L)n]²⁺ + [Co(L)n]³⁺ → [*Co(L)n]³⁺ + [Co(L)n]²⁺ the correct statement with respect to the rate of electron transfer process is o-phen = o-phenanthroline; *Co is labelled atom :

Choose the correct order of energy of 2σ_g and 1 _u molecular orbitals for B₂, C₂ and O^g₂ :

The pair in which both actinides show +3 oxidation state only is :

The complex (es) showing activity against cancerous cells is/are :

Consider the nuclear reaction ₉₂X²³⁴ + ß + α → Y + γ + 2ß⁺ Y is :

Correct statement/s among the following with respect to ionization energy (IE) is/are :
a. (IE₁ + IE₂ + IE₃) for indium is more than that of aluminium
b. IE₁ of scandium is higher than that of cobalt
c. IE₁ of gallium is lower than that of selanium
d. IE₁ of nitrogen is greater than that of oxygen

The reason for significantly high solubility of AgClO₄ in benzene than in alkane solvents is :

Correct statement for 'Inductively Coupled Plasma Atmoic Emission Spectroscopy' is :

The number of geometrical isomers of the complex [RhH(C≡CR)₂(PMe₃)₃] is :

I₂ is violet in the solid as well as in gas phase.However in acetone or ethanol,it turns brown.Choose the correct statement (s) for this colour change :
a. Dissociation of I₂ in atomic state
b. Interaction of low-lying σ*-orbital of iodine with lone pair of O (Solvent)
​c. Formation of a charge-transfer complex

The pair of compounds in which both members show LMCT band in their electronic spectra is :

During the binding of O₂ to myoglobin (Consider 'heme' in xy-plane), the molecular orbital of O₂ and atomic orbital of Fe involved in the formation of σ-bond is :

During the binding of O₂ to myoglobin (consider 'heme' in xy-plane), the molecular orbital of O₂ and atomic orbital of Fe involved in the formation of the σ-bond is :

The correct IUPAC name for the following molecule is :

The stereochemical relationship of H_a and H_b in the following molecule is :

The correct order of stability of the carbocations A-C is :

The correct statement for the orientation of the bromine atoms in the most stable conformation of A and B is :

The major product formed in the following reaction is :

The following carboxylic acids undergo decarboxylation upon heating.The ease of decarboxylation is in the order : 

​

The HOMO of -molecular orbitals of methalazide is :

The following transformation involves a series of :

The synthetic equivalent of the given synthon is :

The correct order of the pK_a of the following compounds is :

Muscone is a :

The natural product that gives a signal at ẟ 218 ppm in its ¹³C NMR Spectrum is :

The correct order of carbonyl stretching frequency for the given compounds is :

The expectation value of p² of a particle in a cubic box of side l, having the wave function  

For the d³ electron configuration,the ground state term symbol is :

The total bond order between adjacent carbon atoms of benzene is :

The following is the character table fo the C_2v, point group :


 
There are two functions f₁ and f₂ belonging to A₂ and B₁ representations, respectively. The correct option for the product of two functions f₁ and f₂ and the integral f f₁ f₂ dπ is