\(f(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, & -1 \leq x<0 \\\frac{2 x+1}{x-2}, & 0 \leq x \leq 1\end{array}\right.\)
is continuous in the interval \([-1,1]\), then \(p\) is equal to :

Five dice are thrown simultaneously. If the occurrence of an even number in a single dice is considered a success, then the probability of at most 3 successes is:

The image of the point \((3,-2,1)\) in the plane \(3 x-y+4 z=2\) is:

Let \(A=\left[\begin{array}{cc}\frac{1}{3} & 2 \\ 0 & 2 x-3\end{array}\right]\) and \(B=\left[\begin{array}{cc}3 & 6 \\ 0 & -1\end{array}\right]\).
If AB = I (where I is an identity matrix of order 2), then the value of x is:

\(\int x^2 \tan ^{-1} x d x\)=

A machine has been producing steel tubes of mean inner diameter of 2 cm.
A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm.
Test the hypothesis that the machine is working in the proper order at 5% level of significance and answer, which of the following statements are correct?
[Given that \(t_{0.05}=2.262\)]
(A) The value of the test statistic is t = 0.476
(B) The null hypothesis is rejected at \(5 \%\) level of significance.
(C) The null hypothesis is accepted at \(5 \%\) level of significance.
(D) The degree of freedom is 10
Choose the correct answer from the options given below:

Which one of the following statement is incorrect about sinking fund?

If \(f: R \rightarrow R\) be given by \(f(x)=\left(3-x^3\right)^{\frac{1}{3}}\), then \((f \circ f)(x)\) is:

\(\int_1^2 \frac{1}{x(x+1)} d x, x>0\) equals

The solution of the differential equation \(\frac{d y}{d x}=\frac{6}{x^2} ; y(1)=3\) is :

The projection of the vector \(\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}\) on the vector \(2 \hat{i}+6 \hat{j}+3 \hat{k}\) is:

Match List-l with List-ll

List-l (Birth control methods)	List-II (Features)
(A) Diaphragms	(I) Removal of vas deferens
(B) Lactational amenorrhea	(II) Increase phagocytosis of sperms
(C) Vasectomy	(III) Absence of menstrual cycle and ovulation following parturition
(D) IUDs	(IV) Cover the cervix and blocks the entry of sperm

Choose the correct answer from the options given below:

Which of the following does NOT serve as biofertilizer in paddy field?