The equation of motion of a missile is x = 3t, y = - 4t, z = t where time 't' is in seconds and the distance is measured in kilometres.
At what distance will the rocket be from the point (0, 0, 0) in 5 seconds?

The value of \(\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)\) at \(x=\frac{1}{5}\) is

Consider the following data

Year(X)	2010	2011	2012	2013	2014
Profit (Rs. in thousands) (y)	10	12	14	16	13

The equation of straight line trend by method of least square for the above data is given by

The following data shows the percentage of rural and urban Indian households who have a high speed internet connection.

Year(x)	Rural Household \((y \%)\)	Urban Household\((y \%)\)
2020	2	6
2021	3	7
2022	3	9
2023	4	15
2024	5	20

Based on the above data, which of the following statements are correct?
(A) A straight line trend by the method of least squares for rural Indians \(y_t=3.4+0.7(x-2022)\)
(B) A straight line trend by the method of least squares for urban Indians is \(y_t=11.4+4.3(x-2022)\)
(C) The forecast for the year 2025 for urban group using the trend equation is \(22.2 \%\)
(D) The forecast for the year 2025 for rural group using the trend equation is \(5.5 \%\)
Choose the correct answer from the options given below :

Mr. Vishnu has an initial investment of Rs. 80,000 in an investment plan. After 3 years, it has grown to Rs. \(1,00,000\), then his rate of return is

Let * be a binary operation defined on \(Q ^{+}\)(the set of positive rational numbers) by the rule \(a * b=\frac{a b}{7}\) for all \(a, b \in Q ^{+}\). Then inverse of \(2 * 7\) is:

If \(x=a \cos \alpha+b \sin \alpha\) and \(y=a \sin \alpha-b \cos \alpha\), then \(\left(x \frac{d y}{d x}-y^2 \frac{d^2 y}{d x^2}\right)\) is equal to :

The area of the region bounded by the circle \(x^2+y^2=1\) is ___________ sq. units.

Light of wavelength 300 nm is used in an experiment on photoelectric effect with lithium having a work function of 2.7 eV. The maximum kinetic energy of ejected photo-electrons will be

Match List-I with List-II
Let A and B be two events such that \(P(A)=0.2, P(B)=0.4, P(B \mid A)=0.5\)

List-I	List-II
(A) \(P(A \cap B)\)	(I) 0.5
(B) \(P(A \mid B)\)	(II) 0.8
(C) \(P(A \cup B)\)	(III) 0.25
(D) \(P\left(A^{\prime}\right)\)	(IV) 0.1

Choose the correct answer from the options given below:

Zygote or embryos upto 8 blastomeres can be transferred into the fallopian tube for further development. The procedure is known as:

Magnetic moment of first series of transition metal complexes is determined by........

The area (in square units) of the region enclosed between the lines \(x+y=2, x=0, x=3\) and \(x\) - axis is equal to