A and B invested ₹ 10,000 and ₹ ₹ 12,000 in a business two years ago. After 1 year their net loss was ₹ 880 . And during the 2 nd year their net profit was ₹ 2,530. So the presen

The order and degree of the differential equation \(\left(1+3 \frac{d y}{d x}\right)^{\frac{2}{3}}=4 \frac{d^3 y}{d x^3}\) respectively are:

If the curves \(x=y^2\) and \(x y=k\) meet at right angles, then the value of \(k\) is:

If \(A\) and \(B\) are square matrices of the same order, then \((A+B)(A-B)\) is equal to

If \(A^2-A+I=0\), then \(A^{-1}\) is equal to :

\(\int \log _e x d x\) is equal to:

The mean of the numbers obtained on throwing a die having 1 on three faces, 2 on two faces and 5 on one face is:

The probability distribution of the random variable \(X\) is given by

X	0	1	2	3
P(X)	0.2	k	2k	2k

The variance of the random variable \(X\) is given by:

Read the following passage carefully and answer the given questions.
Cancerous cells just continue to divide giving rise to masses of cells called tumors. Benign tumors normally remain confined to their original location and do not spread to other parts of the body and cause little damage. The malignant tumors, on the other hand are a mass of proliferating cells called neoplastic or tumor cells. Transformation of normal cells into cancerous neoplastic cells may be induced by physical, chemical or biological agents. Ionising radiations like X-rays and gamma rays and non-ionizing radiations like UV cause cancer. Cancer-causing viruses are called oncogenic viruses which have viral oncogenes. The substances to which an immune response is produced are called allergens. The antibodies produced to these are of IgE type. Common examples of allergens are mites in dust, pollens, animal dander, etc. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs provide the sites for interaction of lymphocytes with the antigen, which then proliferate to become effector cells.
The tumors that remain confined to their original location and do not spread to other parts of the body are:

The necessary conditions for total internal reflection are
(A) Light must travel from denser to rarer medium.
(B) The angle of incidence in the denser medium must be less than the critical angle for the two media.
(C) Light must travel from rarer to denser medium.
(D) The angle of incidence in the denser medium must be greater than the critical angle for the two media.
Choose the correct answer from the options given below:

If for the following data :

YEAR (X)	2000	2001	2002	2003	2004	2005	2006
PRODUCTION (iN TONNES) (Y)	40	45	46	42	47	50	46

the equation of the straight line trend is \(y=45.143+1.036(x-2003)\), then the trend value for the year 2004 is

Elements of group-15, 16 and 17 form compounds with hydrogen with general formula MH3, H2M and HX (called hydrogen halides). Stability of these hydrides, along with M-H bond strength and basic nature decreases down the group. Boiling point of these hydrides mainly depends on the strength of their inter molecular forces.
Which of the following is liquid at \(20^{\circ} C\) ?
A. HCl
B. HI
C. HF
D. NH3
E. HBr
Choose the correct answer from the options given below:

Read the paragraph given below and answer the question.
Sutton and Boveri argued that the pairing and separation of a pair of chromosomes would lead to the segregation of a pair of factors they carried. Sutton united the knowledge of chromosomal segregation with Mendelian principles and called it the chromosomal theory of inheritance.The scientist who noted that 'The behaviour of chromosomes was parallel to the behaviour of gene' were: