In a class text, to the question, find out 23% of 200, two students answered in following ways: Student A: 23% of 200 = 23% of (100 + 100) = 23 + 23 = (20 + 20) + (3 + 3) = 46 Student B: 23% of 200 = 200 × $\frac{23}{100}$ = 2 × 23 = 46 Which of the following statements is the most appropriate in the given context? 1. Since student B has used the standard algorithm, teacher gives full marks to student B and zero to student A 2. Teacher gives full marks to both the students as they have attempted the question using their own algorithms. Both formal and informal algorithms are integral to solving problems in mathematics. 3. Teacher gives zero marks to student A and directs him to redo the question using the algorithm taught in the Class 4. Teacher accepts both the responses but directed student A to refrain from using informal algorithm

Simplify the value of $$\frac{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} \times {\text{0}}{\text{.3}} - {\text{3}} \times 0.9 \times {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}}}}{{{\text{0}}{\text{.9}} \times {\text{0}}{\text{.9 + 0}}{\text{.2}} \times {\text{0}}{\text{.2 + 0}}{\text{.3}} \times {\text{0}}{\text{.3}} - 0.9 \times {\text{0}}{\text{.2}} - {\text{0}}{\text{.2}} \times {\text{0}}{\text{.3}} - 0.3 \times 0.9}} = ?$$

A

1.4

B

0.054

C

0.8

D

1.0

In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted. - If the first question is answered wrong, the student gets zero marks. - If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question. - If both the questions are answered correctly, the student gets the sum of the marks of the two questions. The following table shows the probability of correctly answering a question and the marks of the question respectively. question Probability of answering correctly marks QuesA 0.8 10 QuesB 0.5 20 Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)?

A

First QuesB and then QuesA. Expected marks 14

B

First QuesB and then QuesA. Expected marks 22

C

First QuesA and then QuesB. Expected marks 14.

D

First QuesA and then QuesB. Expected marks 16.

Consider the differential equation $$\frac{{{{\text{d}}^2}{\text{y}}\left( {\text{t}} \right)}}{{{\text{d}}{{\text{t}}^2}}} + 2\frac{{{\text{dy}}\left( {\text{t}} \right)}}{{{\text{dt}}}} + {\text{y}}\left( {\text{t}} \right) = \delta \left( {\text{t}} \right)$$ with $${\left. {{\text{y}}\left( {\text{t}} \right)} \right|_{{\text{t}} = 0}} = - 2$$ and $${\left. {\frac{{{\text{dy}}}}{{{\text{dt}}}}} \right|_{{\text{t}} = 0}} = 0.$$
The numerical value of $${\left. {\frac{{{\text{dy}}}}{{{\text{dt}}}}} \right|_{{\text{t}} = 0}}$$ is

A

-2

B

-1

C

0

D

1

The error in $${\left. {\frac{{\text{d}}}{{{\text{dx}}}}{\text{f}}\left( {\text{x}} \right)} \right|_{{\text{x}} = {{\text{x}}_0}}}$$ for a continuous function estimated with h = 0.03 using the central difference formula $${\left. {\frac{{\text{d}}}{{{\text{dx}}}}{\text{f}}\left( {\text{x}} \right)} \right|_{{\text{x}} = {{\text{x}}_0}}} = \frac{{{\text{f}}\left( {{{\text{x}}_0} + {\text{h}}} \right) - {\text{f}}\left( {{{\text{x}}_0} - {\text{h}}} \right)}}{{2{\text{h}}}},$$ is 2 × 10^-3. The values of x₀ and f(x₀) are 19.78 and 500.01, respectively. The corresponding error in the central difference estimate for h = 0.02 is approximately

A

1.3 × 10^-4

B

3.0 × 10^-4

C

4.5 × 10^-4

D

9.0 × 10^-4

To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?

A

30,000

B

2,70,000

C

3,90,000

D

4,20,000

The rate of the heterogenous catalytic reaction A(g) + B(g) → C(g) is given by $$ - {{\text{r}}_{\text{A}}} = \frac{{{\text{k}}.{{\text{K}}_{\text{A}}}.{{\text{p}}_{\text{A}}}.{{\text{P}}_{\text{B}}}}}{{1 + {{\text{K}}_{\text{A}}}.{{\text{P}}_{\text{A}}} + {{\text{K}}_{\text{C}}}.{{\text{p}}_{\text{C}}}}},$$ where K_A and K_C are the adsorption equilibrium constants. The rate controlling step for this reaction is

A

Absorption of A

B

Surface reaction between absorbed A and absorbed B

C

Surface reaction between absorbed A and B in the gas phase

D

Surface reaction between A in the gas phase and absorbed B

Consider a system governed by the following equations:
$$\frac{{{\text{d}}{{\text{x}}_1}\left( {\text{t}} \right)}}{{{\text{dt}}}} = {{\text{x}}_2}\left( {\text{t}} \right) - {{\text{x}}_1}\left( {\text{t}} \right);\,\frac{{{\text{d}}{{\text{x}}_2}\left( {\text{t}} \right)}}{{{\text{dt}}}} = {{\text{x}}_1}\left( {\text{t}} \right) - {{\text{x}}_2}\left( {\text{t}} \right)$$
The initial conditions are such that $${{\text{x}}_1}\left( 0 \right)

A

[

A. $${{\text{x}}_{1{\text{f}}}}

B. $${{\text{x}}_{2{\text{f}}}}

B

$${{\text{x}}_{1{\text{f}}}} = {{\text{x}}_{2{\text{f}}}}

C

$${{\text{x}}_{1{\text{f}}}} = {{\text{x}}_{2{\text{f}}}} = \infty $$

Let $$\nabla \cdot \left( {{\text{f}}\overrightarrow {\text{v}} } \right) = {{\text{x}}^2}{\text{y}} + {{\text{y}}^2}{\text{z}} + {{\text{z}}^2}{\text{x}},$$ where f and v are scalar and vector fields respectively. If $$\overrightarrow {\text{v}} = {\text{y}}\overrightarrow {\text{i}} + {\text{z}}\overrightarrow {\text{j}} + {\text{x}}\overrightarrow {\text{k}} ,$$ then $$\overrightarrow {\text{v}} \cdot \nabla {\text{f}}$$ is

A

x²y + y²z + z²x

B

2xy + 2yz + 2zx

C

x + y + z

D

0

Among 80 students, 24 passed in Chemistry, 35 passed in Physics and 29 passed in Mathematics, 8 students did not appear for the examination. If 2 students have passed in all the three subjects, 2 students have passed in Physics and Chemistry both but not in Mathematics, 2 students have passed in Chemistry and Mathematics both but not in Physics, and 8 students have passed in Physics and Mathematics both but not in Chemistry, then how many students have passed in Mathematics only?

A

19

B

18

C

20

D

17

If {x} is a continuous, real valued random variable defined over the interval (-$$\infty $$, +$$\infty $$) and its occurrence is defined by the density function given as:
$${\text{f}}\left( {\text{x}} \right) = \frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}$$ where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral $$\int_{ - \infty }^{\text{a}} {\frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}{\text{dx}}} $$

A

1

B

0.5

C

$$\pi $$

D

$$\frac{\pi }{2}$$

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