If A is a skew-symmetric matrix of order n, then

A motorcycle has a scrap value of Rs. 22,500 after 15 years of its purchase.
If the annual depreciation charge is Rs. 8,500, then the original cost by linear method is :

\(\int \frac{1}{(x+1)(x+2)} d x=\)

The following data shows the percentage of rural and urban Indian households who have a high speed internet connection.

Year(x)	Rural Household \((y \%)\)	Urban Household\((y \%)\)
2020	2	6
2021	3	7
2022	3	9
2023	4	15
2024	5	20

Based on the above data, which of the following statements are correct?
(A) A straight line trend by the method of least squares for rural Indians \(y_t=3.4+0.7(x-2022)\)
(B) A straight line trend by the method of least squares for urban Indians is \(y_t=11.4+4.3(x-2022)\)
(C) The forecast for the year 2025 for urban group using the trend equation is \(22.2 \%\)
(D) The forecast for the year 2025 for rural group using the trend equation is \(5.5 \%\)
Choose the correct answer from the options given below :

If \(f(x)=\frac{1}{1-x}\), then for x > 1, f(x) is:

The inverse of the matrix \(\left[\begin{array}{lll}4 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 6\end{array}\right]\) is

Which of the following are NOT correct regarding the equation of tangent and normal to the curve \(y=\frac{x-11}{(x-2)(x-3)}\) at the point, where it cuts the \(x\)-aris?
(A) The point of contact is \((11,0)\).
(B) The equation of tangent is \(x-72 y-11=0\).
(C) The equation of normal is \(7 2 x + y - 1 1 = 0\).
(D) The slope of the tangent at the given point of contact is \(\frac{1}{88}\).
Choose the correct answer from the options given below:

Read the passage carefully and answer the questions based on the passage:
Pollen pistil interaction involves all events from the landing of pollen grains on the stigma until the pollen tube enters the embryo sac (when the pollen is compatible). When a pollen tube grows through the style and enters into the ovules, it finally discharges two male gametes in one of the synergids. Syngamy and triple fusion are two fusion events occur in angiosperms. Thus, angiosperms exhibit double fertilization. The products of these fusions are the diploid zygote and triploid primary endosperm nucleus. Zygote develops into embryo and primary endosperm cell forms the endosperm tissue. The developing embryo passes through different stages before maturation.
The coconut water from tender coconut, a good source of nutrition is nothing but:

Arrange the de-Broglie wavelengths associated with the following in decreasing order: (Given: \( h = 6.6 \times 10^{-34} \, \text{J-s} \))
(A) an electron (mass \( 9 \times 10^{-31} \, \text{kg} \)) in the hydrogen atom moving with speed \( 3 \times 10^6 \, \text{m/s} \)
(B) a bullet (mass 0.04 kg) travelling at speed \( 10^3 \, \text{m/s} \)
(C) a ball (mass 0.06 kg) moving with speed 1.0 m/s
(D) a dust particle (mass \( 1.0 \times 10^{-9} \, \text{kg} \)) drifting with speed 3.3 m/s
Choose the correct answer from the options given below:

Let \(A =\left[a_{i j}\right]_{n \times n}\) be a matrix. Then
Match List-I with List-II

List-I	List-II
(A) \(A^T=A\)	(I) A is a singular matrix
(B) \(A^T=-A\)	(II) A is a non-singular matrix
(C) \(|A|=0\)	(III)  A is a skew symmetric matrix
(D) \(|A| \neq 0\)	(IV) \(A\) is a symmetric matrix

Choose the correct answer from the options given below:

Identify the product C in the following sequence of reactions :
\(\text{CH}_3 - \text{CH(OH)} - \text{CH}_3 \xrightarrow{\text{Cu, 573 K}} \text{A} \xrightarrow{\text{CH}_3\text{MgBr}} \text{B} \xrightarrow{\text{H}_3\text{O}^+} \text{C}\)

If 4 individuals in a laboratory population of 40 fruitflies died during a specific time interval of one week. What will be the death rate of the population during that period?

The value of k for which the function \(f(x)=\left\{\begin{array}{ll}\frac{x^2+3 x-10}{x-2} & x \neq 2 \\ k & x=2\end{array}\right.\) is continuous at x = 2 is: