List of practice Questions

If $\lim_{n\rightarrow \infty}$($\sqrt{n^2-n-1}$ + nα+β)=0 then 8(α + β) is equal to

Only fruits are pasta. All noodles are pasta. Examine the following statements:
I. No fruits are noodles.
II. All pasta are noodles.
III. All fruits are noodles.
Choose the most appropriate answer.

If $t = \sqrt{x} + 4$, then $\left.\frac{dx}{dt}\right|_{t=4}$ is

At 3:40, the hour hand and the minute hand of a clock form an angle of:

Let f: ℝ → ℝ be defined as
$f(x) = \left\{ \begin{array}{ll} [e^x] & x < 0 \\ [a e^x + [x-1]] & 0 \leq x < 1 \\ [b + [\sin(\pi x)]] & 1 \leq x < 2 \\ [[e^{-x}] - c] & x \geq 2 \\ \end{array} \right.$
Where a, b, c ∈ ℝ and [t] denotes greatest integer less than or equal to t.
Then, which of the following statements is true?

When the supply curve S_x is backward bending and the demand curve Dx is downward sloping as shown in the figure, there are two equilibria M and N, respectively. Which of the following statements is CORRECT?

A fish swimming in water body when taken out from the water body is covered with a film of water of weight 36 g. When it is subjected to cooking at 100 °C, then the internal energy for vaporization in kJ mol^–1 is ________. [nearest integer]
[Assume steam to be an ideal gas. Given Δ_vapH^Θ for water at 373 K and 1 bar is 41.1 kJ mol^–1; R = 8.31 J K^–1 mol^–1]

If surrounding air is kept at 20 °C and body cools from 80 °C to 70 °C in 5 minutes, then the temperature of the body after 15 minutes will be

Some White are Blue. Some Blue are Green. Some Green are Red. Some Red are Yellow. Some Red are Blue. Some Red are White. Some Yellow are White. Some Yellow are Blue. All Green are White. All Blue are Red.
If the above statements are true, which of the following follow(s) ?
I. No Yellow is Green.
II. Of the Red which are White, some are also Yellow.
III. Of the Red that are Green, some are also Blue.
IV. Some White are Green.
Choose the most appropriate answer.

The sum of all real value of $x$ for which $\frac{3x^2-9x+17}{x^2+3x+10}=\frac {5x^2-7x+19}{3x^2+5x+12}$ is equal to________.

In the given reaction,

(where Et is –C₂H₅)
The number of chiral carbon(s) in product A is ______.

If
$\sum_{k=1}^{10} \frac{k}{k^4 + k^2 + 1} = \frac{m}{n}$
where m and n are co-prime, then m + n is equal to

The longest wavelength of light that can be used for the ionisation of lithium atom (Li) in its ground state is $x × 10^{–8}\ m$. The value of $x$ is ______. (Nearest Integer)
(Given : Energy of the electron in the first shell of the hydrogen atom is $2.2 \times 10^{–18} J$;
$h = 6.63 × 10^{–34}Js$ and $c = 3 × 10^8 ms^{–1}$)

Arrange the given words in the sequence in which they occur in the dictionary and then choose the correct sequence.
1. Preach
2. Praise
3. Precinct
4. Precept

Let P be a fixed 3×3 matrix with entries in $\R$. Which of the following maps from $M_3(\R)$ to $M_3(\R)$ is/are linear?

The number of paramagnetic species among the following is ____B₂,Li₂,C₂,C^-_2,O₂^2--,O₂⁺ and He₂⁺

C(s)+O₂(g)→CO₂(g)+400 kJ
C(s)+$\frac{1}{2}$ O₂(g)→CO(s)+100 kJ
When coal of purity 60% is allowed to burn in presence of insufficient oxygen, 60% of carbon is converted into ‘CO’ and the remaining is converted into ‘CO₂’. The heat generated when 0.6 kg of coal is burnt is _______.

Assertion: Fertile plain regions are densely populated.
Reason: Fertile soil is useful for agriculture.

20 mL of 0.02 M hypo solution is used for the titration of 10 mL of copper sulphate solution, in the presence of excess of KI using starch as an indicator. The molarity of $Cu^{2+}$ is found to be ________ × $10^{–2} M$. [nearest integer]

The number of 4-digit integers in the closed interval $[2022,4482]$ formed by using the digits $0,2,3,4,6,7$ is ___

Given below are two statements and four conclusions drawn based on the statements.
Statement 1: Some soaps are clean.
Statement 2: All clean objects are wet.
Conclusion I: Some clean objects are soaps.
Conclusion II: No clean object is a soap.
Conclusion III: Some wet objects are soaps.
Conclusion IV: All wet objects are soaps.
Which one of the following options can be logically inferred?

Given below are two statements and four conclusions drawn based on the statements.
Statement 1: Some bottles are cups.
Statement 2: All cups are knives.
Conclusion I: Some bottles are knives.
Conclusion II: Some knives are cups.
Conclusion III: All cups are bottles.
Conclusion IV: All knives are cups.
Which one of the following options can be logically inferred?

It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010 ?

An ore body defined by a 300m x 300m area is shown in the figure in which the drill hole locations on equally spaced square grid are marked (numbers 1-16). The average thickness of the ore body at the 4 interior points is 10.8m, at the 4 corners is 11.0m and at the remaining 8 boundary locations is 10.5m, respectively. The corresponding average grades are 1.5, 1.9 and 1.8wt%, respectively. Calculate the average grade (in wt%) of the full ore body using the Included Area Method. (Round off to two decimal places).

Let P₁ be a parabola with vertex (3, 2) and focus (4, 4) and P₂ be its mirror image with respect to the line x + 2y = 6. Then the directrix of P₂ is x + 2y = _______.