A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150 . If the population mean is 56 then the value of \(t\)-test statistic is :

Match List - I with List - II

List - I	List - II
(A) The number of possible matrices of order 3 × 3 with each entry 1 or 0	(I) \(2^4\)
(B) The number of possible matrices of order 2 × 3 with each entry 1 or 0	(II) \(2^9\)
(C) The number of possible matrices of order 2 × 3 with each entry 0, 1, 2	(III) \(2^6\)
(D) The number of possible matrices of order 2 × 2 with each entry 1 or 0	(IV) \(3^6\)

Choose the correct answer from the options given below:

A measurable characteristic of a population is called:

If \(a+b+c=\pi\), then the value of \(\left|\begin{array}{ccc}\sin (a+b+c) & \sin (a+c) & \cos b \\ -\sin b & 0 & \tan a \\ \cos (a+c) & \tan (b+c) & 0\end{array}\right|\) is:

For what value of k, the following system have a unique solution? (where R is set of real numbers)
x + y + z = 1
2x + 3y + 4z = 3
x - y + kz = 5

Let \(A=\{1,2,3\}\), then the possible equivalence relations on \(A\) are :
(A) \(\{(1,1),(2,2),(3,3)\}\)
(B) \(\{(1,1),(2,2),(3,3),(1,2),(2,1)\}\)
(C) \(\{(1,1),(2,2),(3,3),(1,2),(2,1),(1,3)\}\)
(D) \(\{(1,1),(2,2),(3,3),(1,3),(3,1)\}\)
Choose the correct answer from the options given below :

The linear inequalities satisfying the shaded feasible region given in the figure are

(A) \(x \geq 0, \quad y \geq 0, \quad 2 x+y \geq 2\)
(B) \(x \geq 0, \quad y \geq 0, \quad 2 x+y \leq 2\)
(C) \(x \geq 0, \quad y \geq 0, \quad 2 x+y \geq 2, \quad x+2 y \leq 8, \quad x-y \leq 1\)
(D) \(x+2 y \geq 8, \quad x-y \geq 1\)
Choose the correct answer from the options given below:

Choose the correct statements:
A. In uniform electric field E, the net force on electric dipole is zero.
B. The torque on dipole in electric field is \( \tau = PE \cos \theta \), where \( \theta \) is angle between \( \vec{P} \) and \( \vec{E} \).
C. In non uniform Electric field, when dipole moment P is parallel to E, the dipole has a net force in the direction of decreasing field.,
D. The direction of torque is perpendicular to both \( \vec{P} \) and \( \vec{E} \).
E. The net torque is zero if E is not uniform.
Choose the correct answer from the options given below:

\(\int \frac{d x}{\sqrt{5-x}}=\) (where \(C\) is arbitrary constant.)

If \(x=e^y+e^y+\cdots\) to \(\infty, x>0\) then \(\frac{d^2 y}{d x^2}\) is:

A resistance of \( 15\Omega \) is connected in series with an unknown resistance \( R_1 \). This combination is connected to one gap of a meter bridge, while a resistance \( R_2 \) is connected in the other gap. The balance point is at 50 cm. When \( 15\Omega \) is removed, the balance point shifts by 10 cm. The value of \( R_1 \) is

Read the passage carefully and answer
Carbohydrates are essential for both plants and animals. Some common examples of carbohydrates are glucose, fructose, sucrose, glycogen, cellulose and starch. They form a major portion of our food. Honey has been used for a long time as an instant source of energy in Ayurvedic medicine. Carbohydrates are used as storage molecules in both plants and animals. The cell wall of bacteria and plants is made of cellulose. We use cellulose in the form of wood for making furniture and as cotton fiber for clothing. They also provide raw material for textiles, paper, lacquers, and breweries. Carbohydrates are classified as Monosaccharides, Oligosaccharides and Polysaccharides on the basis of their behavior towards hydrolysis.
Monosaccharides cannot be hydrolyzed further to simpler units whereas oligosaccharides can yield 2-10 units of monosaccharides on hydrolysis. Polysaccharides, which are non-sugars yield a large number of monosaccharide units on hydrolysis.
Answer the following questions about carbohydrates:
Animal starch is popularly known as

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: