Which of the following statements are correct?
(A) In the sinking fund a fixed amount at regular intervals is deposited.
(B) Sinking fund is a long-term account which can be closed any time.
(C) In a saving account, any amount, any time can be deposited.
(D) Sinking fund can be used only for the purpose it was created.
Choose the correct answer from the options given below :

On which of the following components, the pattern and behavior of the data in any time series is based?
(A). Secular trend component
(B). Seasonal component
(C). Cyclical component
(D). Regular component
Choose the correct answer from the options given below :

The maximum value of \(Z=2 x+3 y\) subject to the constraints \(x \geq 0, y \geq 0, x+y \leq 10,3 x+4 y \leq 36\) is:

Match List-I with List-II (where \(c\) is an arbitrary constant)

List-I	List-II
(A) \(\int \tan x d x\)	(I) \(\log |\sec x+\tan x|+c\)
(B) \(\int \cot x d x\)	(II) \(\log |\sec x|+c\)
(C) \(\int \sec x d x\)	(III) \(\log |\sin x|+c\)
(D) \(\int \operatorname{cosec} x d x\)	(IV) \(\log |\operatorname{cosec} x-\cot x|+c\)

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Consider the following L.P.P minimize \(z=x-7 y+190\) subject to \(x+y \leq 8, x+y \geq 4, x \leq 5, y \leq 5\) and \(x, y \geq 0\). Then which of the following is/are true?
(A) It's feasible region is unbounded
(B) It's feasible region is bounded
(C) It's feasible region has 5 corner polnts
(D) It's feasible region has 6 corner polnts
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If \(A\) and \(B\) are independent events and \(P(A)=\frac{1}{2}, P(B)=\frac{1}{3}\) then
Match List-I with List-II

List-I	List-II
(A) \(P(A \cap B)\)	(I) \(\frac{1}{2}\)
(B) \(P(\bar{A}) P(B)+P(A) P(\bar{B})\)	(II) \(\frac{1}{3}\)
(C) \(P(A \mid B)+P(B \mid A)\)	(III) \(\frac{1}{6}\)
(D) \(P(\overline{A \cap B})\)	(IV) \(\frac{5}{6}\)

Choose the correct answer from the options given below :

Derivative of \(2 x^2\) with respect to \(5 x^4\) is:

Read the passage carefully and answer the questions
Nearly all the transition elements display typical metallic properties such as high tensile strength, ductility, malleability, high thermal and electrical conductivity and metallic lustre. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. They have high enthalpies of atomization. lons of the same charge in a given series show progressive decrease in radius with increasing atomic number. However, the variation within a series is quite small. The filling of 4f before 5d orbital results in a regular decrease in atomic radii called Lanthanoid contraction which essentially compensates for the expected increase in atomic size with increasing atomic number The net result of the lanthanoid contraction is that the second and the third d series exhibit similar radii (e.g., Zr 160 pm, Hf 159 pm) and have very similar physical and chemical properties. There is an increase in ionisation enthalpy along each series of the transition elements from left to right. The first ionisation enthalpy, in general, increases, but the magnitude of the increase in the second and third ionisation enthalpies for the successive elements, is much higher along a series. One of the notable features of a transition elements is the great variety of oxidation states these may show in their compounds.
In the first transition series of elements (Sc to Zn), which element show least enthalpy of atomization?

Assuming the same rate of change continues for the following data :

Year(X)	2019	2020	2021	2022	2023
Profit in Percentage (y)	38	40	65	72	69

The equation of the straight line trend using the least square method is :

The density of a nucleus of mass number A is proportional to :

Darwin's finches and Australian marsupials are an example of:

The area (in sq. units) of the region bounded by the curve \(y=x^5\), the \(x\)-axis and the ordinates \(x=-1\) and \(x=1\) is equal to:

Read the passage carefully and answer the following questions
Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms. They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O-H bond along with the reactions involving the complete - COOH group.
The reagent which doesn't react with both acetone and benzaldehyde is :