\(\int(x-1) e^{-x} d x=\)

\(I=\int a^{5 x+3} d x\) is :

A T.V. panel costing Rs 18000 has a useful life of 12 years. If the annual depreciation is Rs 1000, then its scrap value by linear method is :

In binomial distribution with \(n =10\) and \(P =1\), the probability of the event that unequal number 3 of failures and successes occur is:

The differentiation of \(\frac{x^3}{1-x^3}\) w.r.t. \(x^3\) is:

The vector equation of a line passing through the point with position vector \(2 \hat{i}-\hat{j}+\hat{k}\) and parallel to the line joining the points with position vectors \(-\hat{i}+4 \hat{j}+\hat{k}\) and \(\hat{i}+2 \hat{j}+2 \hat{k}\) is:

A box contains 3 white and 2 red balls. If we draw one ball and without replacing the first ball, the probability of drawing red ball in the second draw is:

The chromosomal disorders are caused due to absence, excess or abnormal arrangement of one or more chromosomes. Failure of segregation of chromatids during cell division results in the gain or loss of chromosome(s), called aneuploidy.
Which of the following statements are correct with respect to the humans suffering from the disorder?
(A) One in every 800 live births shows this karyotype
(B) The affected individual has 45 chromosomes.
(C) Non-disjunction of chromosomes at the time of gamete formation causes this disorder.
(D) In this disorder, individual has 45 autosomes
Choose the correct answer from the options given below:

To prepare 250 mL standard solution of M/20 \(\text{NaCl}\), amount of \(\text{NaCl}\) required is :

The equation of the tangent, to the curve \(y=x^2-2 x-3\) which is perpendicular to the line x + 2y + 3 = 0, is:

When a current carrying coil is placed in a uniform external magnetic field with its magnetic moment antiparallel to the external magnetic field, then
(A) its potential energy is minimum
(B) its potential energy is maximum
(C) torque on it is maximum
(D) torque on it is zero
(E) coil is in unstable equilibrium
Choose the correct answer from the options given below:

Match List - I with List - II

List - I (Differential Equations)	List - II (Order and degree)
(A) \(ydx + xlog(y/x)dy - 2xdy = 0\)	(I) Order: 2, degree:1
(B) \(\left(\frac{d^3 y}{d x^3}\right)^2+3 \frac{d^2 y}{d x^2}+2\left(\frac{d y}{d x}\right)^4=y^2\)	(II) Order :1, degree:1
(C) \(\frac{d y}{d x}+\log \left(\frac{d y}{d x}\right)+x=y\)	(III) Order: 3, degree:2
(D) \(\left(\frac{d s}{d t}\right)^4+2 s \frac{d^2 s}{d t^2}=0\)	(IV) Order: 1, degree: Not defined

Choose the correct answer from the options given below:

Match List-l with List-ll

List-l (Matrix A)	List-ll (Determinant of adjA)
(A) \(\left[\begin{array}{cc}2 & 1 \\ -1 & 2\end{array}\right]\)	(I) 3
(B) \(\left[\begin{array}{ll}3 & 4 \\ 3 & 6\end{array}\right]\)	(II) 6
(C) \(\left[\begin{array}{cc}3 & 7 \\ -2 & -4\end{array}\right]\)	(III) 5
(D) \(\left[\begin{array}{ll}4 & 3 \\ 3 & 3\end{array}\right]\)	(IV) 2

Choose the correct answer from the options given below :