If \(\left[\begin{array}{cc}x-y & t \\ 2 x-y & w\end{array}\right]=\left[\begin{array}{cc}-1 & 2 \\ 0 & 1\end{array}\right]\), then \(2 x+y+3 t+w\) is equal to

Match List - I with List - II

List - I (Time series component)	List - II (Example)
(A) Secular Variation	(I) Pandemic
(B) Seasonal Variation	(II) Recession in business
(C) Cyclic Variation	(III) Monthly sale of woolen clothes
(D) Irregular Variation	(IV) Data regarding National income

Choose the correct answer from the options given below:

A problem in mathematics is given to three students whose chances of solving it are \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\) respectively. The probability that the problem is solved is

A pair of dice is thrown, getting a total of 7 is considered a success. Then the probability of success in a single throw is:

Match List-I with List-II

List-I	List-II
(A) Angle between \(\hat{i}-2 \hat{j}+3 \hat{k}\) and \(2 \hat{i}+\hat{j}\)	(I) \(\cos ^{-1}\left(\frac{2}{\sqrt{18}}\right)\)
(B) Angle between \(\hat{i}+\hat{j}+2 \hat{k}\) and \(2 \hat{i}+2 \hat{j}+4 \hat{k}\)	(II) 0
(C) Angle between \(2 \hat{i}-\hat{j}+\hat{k}\) and \(\hat{i}+\hat{j}+\hat{k}\)	(III) \(90^{\circ}\)
(D) Angle between \(\hat{i}+\hat{j}-\hat{k}\) and \(\hat{i}+\hat{j}+\hat{k}\)	(IV) \(\cos ^{-1}\left(\frac{1}{3}\right)\)

Choose the correct answer from the options given below:

If \(x=a \sin ^2 \theta, y=a \cos ^2 \theta\) then \(\frac{d y}{d x}\) =

The maximum value of the \(f(x)=\frac{1}{4 x^2+2 x+1}\) is :

The increasing order of stability is :
(A) \(\left[ Cu \left( NH _3\right)_4\right]^{2+}\)
(B) \(\left[ Cu \left( CN _4\right]^{2-}\right.\)
(C) \(\left[ Cu (e n)_2\right]^{2+}\)
(D) \(\left[ Cu \left( H _2 O \right)_4\right]^{2+}\)
Choose the correct answer from the options given below :

Which of the following reagents can bring about the given conversion?
3-Nitrobromobenzene to 3-Nitrobenzoic acid

Identify the correct statements among the following.
(A) The number of electrons (\( n_e \)) is more than the number of holes (\( n_h \)) in intrinsic conductors.
(B) Semiconductors are elements (Si, Ge) type as well as compounds (GaAs, CdS).
(C) The number of charge carriers can be changed by 'doping' of a suitable impurity in pure semiconductors.
(D) Holes are essentially electron vacancies in a valence band.
Choose the correct answer from the options given below:

Read the given paragraph and answer the question:
Humans have 23 pairs of chromosomes. 22 pairs are exactly same in both males and females; these are the autosomes. A pair of X-chromosome are present in the female, whereas the presence of an X and Y chromosome are determinant of the male characteristic.
A number of disorders in human beings have been found to be associated with the inheritance of changed or altered genes or chromosomes. Broadly, genetic disorder may be grouped into two categories-Mendelian disorders and Chromosomal disorders.
What is the probability of having a daughter to a couple expecting their first child?

The nuclear force is:

If a person rides his motorbike \(x km\) at 30 km per hour, he has to spend ₹ 3 per kilometer on petrol; if he rides \(y km\) at a faster speed of 40 km per hour, the petrol cost increases to ₹ 4 per kilometer. If he has ₹ 100 to spend on petrol and wishes to find the maximum distance he can travel within one hour, then linear programming problem (LPP) formulation is: