Maths-

General

Easy

Question

A set of (2n + 1) elements is given. The no. of subsets of the set which contain atmost n elements -

2_ⁿ
2n+1
2n –1
22n

The correct answer is: 22n

No. of subsets
= ²ⁿ⁺¹C₀+ ²ⁿ⁺¹C₁+ ²ⁿ⁺¹C₂ +...........+ ²ⁿ⁺¹C_n= N
(let) We have 2N = ²ⁿ⁺¹C₀ + ²ⁿ⁺¹C₁ .................²ⁿ⁺¹C_{2n +1}
2N = 2^{2n + 1}
N = 2²ⁿ

An organic compound A upon reacting with NH₃ gives B. On heating B gives C. C in presence of KOH reacts with Br₂ to given CH₃CH₂NH₂ . A is :

chemistry-General

General

Maths-

If r, s, t are prime numbers and p, q are the positive integers such that the LCM of p, q is $r squared s to the power of 4 t squared$ , then the number of ordered pair (p, q) is-

Be careful about selecting the r s and t for this particular problem. Because number ways for each selection of r, s and t there are 3 cases. Because there are two values given

p, q . Hence to calculate the total number of ways is to multiply the number of ways for r, number of ways for s and number of ways for t. So, in this way to solve this particular type of problem.

If r, s, t are prime numbers and p, q are the positive integers such that the LCM of p, q is $r squared s to the power of 4 t squared$ , then the number of ordered pair (p, q) is-

Maths-General

Be careful about selecting the r s and t for this particular problem. Because number ways for each selection of r, s and t there are 3 cases. Because there are two values given

p, q . Hence to calculate the total number of ways is to multiply the number of ways for r, number of ways for s and number of ways for t. So, in this way to solve this particular type of problem.

General

Maths-

A rectangle has sides of (2m – 1) & (2n – 1) units as shown in the figure composed of squares having edge length one unit then no. of rectangles which have odd unit length –

Maths-General

General

chemistry-

Observe the esterification mechanisms for primary and tertiary alcohols
Type-1:

Type-2:
Mechanism:

In the above reaction (P) and (Q) are respectively :

chemistry-General

General

physics-

Two identical samples of a gas are allowed to expand (i) isothermally (ii) adiabatically work done is

physics-General

General

physics-

A thermodynamic system is taken from state A to B along ACB and is brought back to Along BDA as Shown in the P $\to$ V diagram. The net work done during the complete cycle is given by the area.

physics-General

General

physics-

An ideal gas is taken V path ACBA as Shown in figure, The net work done in the whole cycle is

physics-General

General

physics-

In the Cyclic Process shown is the figure, the work done by the gas in one cycle

physics-General

General

physics-

A Cyclic process is Shown in the P $\to$ T diagram. Which of the curve show the same process on a V $\to$ T diagram?

physics-General

General

physics-

The M.I of a disc of mass M and radius R about an axis passing through the centre O and perpendicular to the plane of dise is $\frac{{M R}^{2}}{2}$ If one quarter of the disc is removed the new moment of inertia of disc will be....

physics-General

General

physics-

Work done in the given P $rightwards arrow$ V diagram in the cyclic process is

physics-General

General

physics-

In the following indicators diagram, the net amount of work done will be

physics-General

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A set of (2n + 1) elements is given. The no. of subsets of the set which contain atmost n elements -

2n 2n+1 2n –1 22n

The correct answer is: 22n

No. of subsets= 2n+1C0 + 2n+1C1 + 2n+1C2 +...........+ 2n+1Cn = N(let) We have 2N = 2n+1C0 + 2n+1C1 .................2n+1C2n +12N = 22n + 1N = 22n

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2_ⁿ
2n+1
2n –1
22n

No. of subsets
= ²ⁿ⁺¹C₀+ ²ⁿ⁺¹C₁+ ²ⁿ⁺¹C₂ +...........+ ²ⁿ⁺¹C_n= N
(let) We have 2N = ²ⁿ⁺¹C₀ + ²ⁿ⁺¹C₁ .................²ⁿ⁺¹C_{2n +1}
2N = 2^{2n + 1}
N = 2²ⁿ

An organic compound A upon reacting with NH₃ gives B. On heating B gives C. C in presence of KOH reacts with Br₂ to given CH₃CH₂NH₂ . A is :

An organic compound A upon reacting with NH₃ gives B. On heating B gives C. C in presence of KOH reacts with Br₂ to given CH₃CH₂NH₂ . A is :

If r, s, t are prime numbers and p, q are the positive integers such that the LCM of p, q is $r squared s to the power of 4 t squared$ , then the number of ordered pair (p, q) is-

If r, s, t are prime numbers and p, q are the positive integers such that the LCM of p, q is $r squared s to the power of 4 t squared$ , then the number of ordered pair (p, q) is-

Observe the esterification mechanisms for primary and tertiary alcohols
Type-1:

Type-2:
Mechanism:

In the above reaction (P) and (Q) are respectively :

Observe the esterification mechanisms for primary and tertiary alcohols
Type-1:

Type-2:
Mechanism:

In the above reaction (P) and (Q) are respectively :

A thermodynamic system is taken from state A to B along ACB and is brought back to Along BDA as Shown in the P $\to$ V diagram. The net work done during the complete cycle is given by the area.

A thermodynamic system is taken from state A to B along ACB and is brought back to Along BDA as Shown in the P $\to$ V diagram. The net work done during the complete cycle is given by the area.

A Cyclic process is Shown in the P $\to$ T diagram. Which of the curve show the same process on a V $\to$ T diagram?

A Cyclic process is Shown in the P $\to$ T diagram. Which of the curve show the same process on a V $\to$ T diagram?

The M.I of a disc of mass M and radius R about an axis passing through the centre O and perpendicular to the plane of dise is $\frac{{M R}^{2}}{2}$ If one quarter of the disc is removed the new moment of inertia of disc will be....

The M.I of a disc of mass M and radius R about an axis passing through the centre O and perpendicular to the plane of dise is $\frac{{M R}^{2}}{2}$ If one quarter of the disc is removed the new moment of inertia of disc will be....

Work done in the given P $rightwards arrow$ V diagram in the cyclic process is

Work done in the given P $rightwards arrow$ V diagram in the cyclic process is