List of practice Questions

In two different experiments, an object of mass $5\, kg$ moving with a speed of $25 \,ms ^{-1}$ hits two different walls and comes to rest within
(i) 3 second, 
(ii) 5 seconds, respectively.
Choose the correct option out of the following :

Given below are two statements :
Statement I: In polluted water values of both dissolved oxygen and BOD are very low.
Statement II: Eutrophication results in decrease in the amount of dissolved oxygen.
In the light of the above statements, choose the most appropriate answer from the options given below :

 NCC parade is going at a uniform speed of $9\, km / h$ under a mango tree on which a monkey is sitting at a height of $196\, m$ At any particular instant, the monkey drops a mango A cadet will receive the mango whose distance from the tree at time of drop is : (Given g= 9.8 m/s²)

Which one is an amphoteric oxide:

A baby cools from 50°C to 40°C in 5 min. The surrounding temperature is 20°C. In what further time (in minutes) will it cool to 30°C?

A,B and C are voltmeters of resistance R, \(\frac{3}{2}R\) and 3R respectively. When some potential difference is applied between X and Y, the voltmeters readings are V_A, V_B and V_C respectively. Then:

Write down the structure of picric acid

are radish and carrot the root modification?

What is Acrolein?

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Lithium salts are hydrated.
Reason (R) : Lithium has higher polarising power than other alkali metal group members.
In the light of the above statements, choose the most appropriate answer from the options given below :

The \( \text{Eu}^{2+} \) ion is a strong reducing agent in spite of its ground state electronic configuration (outermost) : [Atomic number of Eu = 63]

Among the following allotropic forms of sulphur, the number of allotropic forms, which will show paramagnetism is __________

If $n \geq 2$ is a positive integer, then the sum of the series ${ }^{n+1} C_{2}+2\left({ }^{2} C_{2}+{ }^{3} C_{2}+{ }^{4} C_{2}+\ldots .+{ }^{n} C_{2}\right)$ is:

Let \(\binom{n}{k}\) denote \(^nC_k\).
If \(A_k = \sum_{i=0}^{9} \binom{9}{i} \binom{12}{12-k+i} + \sum_{i=0}^{8} \binom{8}{i} \binom{13}{13-k+i}\) and \(A_4 - A_3 = 190 p\), then p is equal to ___________.

If \({}^{20}C_r\) is the co-efficient of \(x^r\) in the expansion of \((1+x)^{20\), then the value of \(\sum_{r=0}^{20} r^2 \cdot {}^{20}C_r\) is equal to :}

\(3 \times 7^{22} + 2 \times 10^{22} - 44\) when divided by 18 leaves the remainder _________.

If the coefficient of \( a^7b^8 \) in the expansion of \( (a + 2b + 4ab)^{10} \) is \( K \cdot 2^{16} \), then K is equal to _________.

If the coefficients of $x^7$ in $\left(x^2 + \frac{1}{bx}\right)^{11}$ and $x^{-7}$ in $\left(x - \frac{1}{bx^2}\right)^{11}$, $b \neq 0$, are equal, then the value of b is equal to :

The value of \( 2^{15}C_1 + 2^{15}C_2 - 3^{15}C_3 + \cdots - 15^{15}C_{15} + \binom{14}{1} + \binom{14}{3} + \binom{14}{5} + \cdots + \binom{14}{11} \) is :

The term independent of x in the expansion of [ (x + 1)/(x^{2/3} - x^{1/3} + 1) - (x - 1)/(x - x^{1/2}) ]¹⁰, x ≠ 1, is equal to ________.

Let n C_r denote the binomial coefficient of x^r in the expansion of (1 + x)^n. If ∑_{k=0}^{10} (2² + 3k) n C_k = α 3^{10} + β 2^{10}, α, β ∈ R, then α + β is equal to ________.

A possible value of 'x', for which the ninth term in the expansion of
$\left\{ 3^{\log_3\sqrt{25^{x-1}+7}} + 3^{(-\frac{1}{8})\log_3(5^{x-1}+1)} \right\}^{10}$ in the increasing powers of $3^{(-\frac{1}{8})\log_3(5^{x-1}+1)}$ is equal to 180, is :