Correct Answer: C. 4.7

Explanation

To find the next number in the series, look at the difference between consecutive numbers:

• 2.3 - 1.5 = 0.8

• 3.1 - 2.3 = 0.8

• 3.9 - 3.1 = 0.8

The pattern is adding 0.8 to each term.

To find the next term:

• 3.9 + 0.8 = 4.7

Therefore, the correct answer is C. 4.7.

Correct Answer: D. medical doctor

Correct Answer: D. 179^oC

Explanation

\(\alpha = \frac{L_2 - L_1}{L_1(\theta_2 - \theta_1)}\)

L\(_2\) - L\(_1\) = \(\alpha L_1 (\theta_2 - \theta_1)\)

\(\theta_2 = \frac{0.007}{2.3 \times 10^{-5} \times 1.8}\) + 10

= 179°C

Correct Answer: C. lawlessness

Correct Answer: c) 5/7

Explanation

To solve \frac{1}{4} of \frac{20}{7}:

\frac{1}{4} \times \frac{20}{7} = \frac{1 \times 20}{4 \times 7} = \frac{20}{28}

Now, simplify the fraction by dividing both the numerator and the denominator by 4:

\frac{20 \div 4}{28 \div 4} = \frac{5}{7}

The correct answer is c) 5/7.

Correct Answer: C) for gaseous exchange

Explanation

Lenticels are small pores found on the surface of stems and roots that allow gases to enter and exit the plant. The function of lenticels is called gaseous exchange, and it helps the plant to obtain the carbon dioxide it needs for photosynthesis and release the oxygen it produces. This process is essential for the plant's survival. Option A is incorrect because lenticels do not receive excess water in the plant. Instead, they allow gases to enter and exit the plant. Option B is also incorrect because lenticels do not absorb water from the atmosphere. They only allow gases to enter and exit the plant. Option D is also incorrect because lenticels do not absorb light. In summary, the function of lenticels is to allow for gaseous exchange, which is important for the survival of the plant. It helps the plant obtain the carbon dioxide it needs for photosynthesis and release the oxygen it produces.

Correct Answer: D. streams of electrons

Explanation

Cathode rays are streams of electrons observed in vacuum tubes.

Correct Answer: D. political party

Correct Answer: D. Economic difficulties

Explanation

(a) \(\begin{vmatrix} 5 & 2 & -3 \\ -1 & k & 6 \\ 3 & 9 & (k + 2) \end{vmatrix} = - 207\)

\(5[(k)(k + 2) - 54] - 2[(-1)(k + 2) - 18] - 3[-9 - 3k] = - 207\)

\(5k^{2} + 10k - 270 + 2k + 4 + 36 + 27 + 9k = - 207\)

\(5k^{2} + 21k - 203 + 207 = 0\)

\(5k^{2} + 21k + 4 = 0\)

\(5k^{2} + 20k + k + 4 = 0\)

\(5k(k + 4) + 1(k + 4) = 0\)

\((5k + 1)(k + 4) = 0\)

\(k = -\frac{1}{5}; k = -4\)

(b) Equation of curve:

\(x(y^{2} + 1) - y(x^{2} + 1) + 4 = 0\)

(i) Differentiating, we have

\(x(2y\frac{\mathrm d y}{\mathrm d x}) + y^{2} + 1 - y(2x) - (x^{2} + 1)\frac{\mathrm d y}{\mathrm d x} = 0\)

\(\frac{\mathrm d y}{\mathrm d x}(2xy) - \frac{\mathrm d y}{\mathrm d x}(x^{2} + 1) + y^{2} + 1 - 2xy = 0\)

\(\frac{\mathrm d y}{\mathrm d x}(2xy - x^{2} - 1) = 2xy - y^{2} - 1\)

The gradient of the curve at (x, y)

\(\frac{\mathrm d y}{\mathrm d x} = \frac{2xy - y^{2} - 1}{2xy - x^{2} - 1}\)

(ii) Gradient of the tangent at (-1, -3) is

\(\frac{\mathrm d y}{\mathrm d x} = \frac{2(-1)(-3) - (-3)^{2} - 1}{2(-1)(-3) - (-1)^{2} - 1}\)

\(\frac{\mathrm d y}{\mathrm d x} = \frac{-4}{4} = -1\)

Equation : \(\frac{y - (-3)}{x - (-1)} = -1\)

\(y + 3 = - x - 1\)

\(y = - x -4\)