For the system \(\left[\begin{array}{cc}2 & -3 \\ -4 & 6\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}5 \\ -10\end{array}\right]\), which of the following statements are correct?
(A) The system has no solution.
(B) The system is consistent.
(C) It has infinitely many solutions.
(D) It has a unique solution.
Choose the correct answer from the options given below :

Ajesh purchased a printer ₹ 15,000 . The printer is estimated to have a scrap value of ₹ 3,000 after a span of 6 years. Then the book value of the printer at the end of 3 years will be :-

If matrix \(A=\left[\begin{array}{ll}3 & x \\ y & 0\end{array}\right]\) and \(A^{\prime}=A\), then :

The number of all possible matrices of order \(2 \times 3\) with each entry 0 or 1 is

An automobile dealer wishes to buy four luxury cars of different brands with some down payment and balance in equal monthly instalments for 10 years
The bank charges \(9 \%\) interest per annum compounded monthly
Given \(\frac{0.0075(1.0075)^{120}}{(1.0075)^{120}-1}=0.01266\)

Luxury Car	Price of the Car (in Rs.)	Down payment (in Rs.)
P	25,00,000	5,00,000
Q	35,00,000	12,00,000
R	45,00,000	15,00,000
S	42,00,000	15,00,000

Match List I with List II

List-I (Luxury Car)	List-II (EMI (in Rs.))
(A) P	(i) 34,182
(B) Q	(ii) 37,980
(C) R	(iii) 29,118
(D) S	(iv) 25,320

Choose the correct answer from the options given below :

If a fair coin is tossed 10 times the probability of atleast 6 heads is:

Let \(\Delta=\left|\begin{array}{ccc}1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1\end{array}\right|\) then \(\Delta\) lies in the interval :

At some instant, the current in the circuit shown below is 1 A, and it is decreasing at a rate of \( 10^2 \text{ A/s} \). The value of the potential difference \( (V_P - V_Q) \) at that instant is:

Read the following passage carefully and answer the given questions.
Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes). B. thuringiensis forms protein crystals during a particular phase of their growth. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (a-1-antitrypsin) used to treat emphysema. In 1997, the first transgenic cow, Rosie, produced human protein-enriched milk (2.4 grams per litre). The milk contained the human alpha-lactalbumin and was nutritionally a more balanced product for human babies than natural cow-milk. A nematode Meloidegyne incognitia infects the roots of tobacco plants and causes a great reduction in yield. A novel strategy was adopted to prevent this infestation which was based on the process of RNA interference (RNAi). This method involves silencing of a specific mRNA due to a complementary dsRNA molecule that binds to and prevents translation of the mRNA (silencing). Biopiracy is the term used to refer to the use of bio-resources by multinational companies and other organisations without proper authorisation from the countries and people concerned without compensatory payment. ELISA is based on the principle of antigen-antibody interaction. Infection by pathogen can be detected by the presence of antigens (proteins, glycoproteins, etc.) or by detecting the antibodies synthesised against the pathogen.
Biopiracy is the term used to refer:

In Young's Double Slit experiment, the intensities of two coherent monochromatic waves are I and 4I. The ratio of intensity at maxima to minima will be :

Which of the following inequalities are NOT correct?
(A) If \(a>1, b>1\), then \(\log _b a+\log _a b \leq 2\)
(B) For any real number \(x,\left(9^x+9^{1-x}\right) \geq 9\)
(C) If \(a, b, c\) are non-zero real numbers of the same sign, then \(\left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\right) \leq 3\)
(D) If \(a, b, c\) are three distinct real numbers, then \((a+b)(b+c)(c+a) \geq 8 a b c\)
Choose the correct answer from the options given below:

A unit vector perpendicular to the vectors \(\hat{i}-\hat{j}\) and \(\hat{i}+\hat{j}\) is

Among the following compounds, which will not undergo oxidation reaction?