The value of the function f(x) is given at n distinct values of x and its value is to be interpolated at the point x<sup>⋆</sup>, using all the n points. The estimate is obtained first by the Lagrange polynomial, denoted by $${I_{\text{L}}}$$ and then by the Newton polynomial, denoted by $${I_{\text{N}}}$$. Which one of the following statements is correct?

The value of the function f(x) is given at n distinct values of x and its value is to be interpolated at the point x* using all the n points. The estimate is obtained first by the Lagrange polynomial, denoted by IL, and then by the Newton polynomial, denoted by IN. Which one of the following statements is correct?

A

I_L is always greater than I_N

B

No definite relation exists between I_L and I_N.

C

I_L is always less than I_N

D

I_L and I_N are always equal

The value of the expression:sin²1° + sin²11° + sin²21° + sin²31° + sin²41° + sin²45° + sin²49° + sin²59° + sin²69° + sin²79° + sin²89° is?

A

0

B

$${\text{5}}\frac{1}{2}$$

C

$${\text{4}}\frac{1}{2}$$

D

5

Raw material purchased:
1^st January, 600 units @ Rs. 12 per unit
12^th January, 500 units @ Rs. 14 per unit
21^st January, 300 units @ Rs. 13 per unit
Raw material issued for manufacture:
3^rd January 300 units
5^th January 124 units
15^th January 250 units
16^th January 300 units
Raw material returned to stores from manufacturing department on 14^th January, 50 units. The material is issued on First-in-First out method.
The value of material remaining in store on 21^st January will be:

A

5,775

B

6,100

C

6,350

D

6,600

If a² sec²x - b² tan²x = c², then the value of sec²x + tan²x is equal to (assume b² ≠ a²)

A

$$\frac{{{b^2} - {a^2} + 2{c^2}}}{{{b^2} + {a^2}}}$$

B

$$\frac{{{b^2} + {a^2} - 2{c^2}}}{{{b^2} - {a^2}}}$$

C

$$\frac{{{b^2} - {a^2} - 2{c^2}}}{{{b^2} + {a^2}}}$$

D

$$\frac{{{b^2} - {a^2}}}{{{b^2} + {a^2} + 2{c^2}}}$$

Silicon is doped with arsenic (concentration 10²⁰ atoms.m^-3). At room temperature, the electron and hole mobilities in Si are 0.14 m².v^-1.s^-1 and 0.05 m²v^-1.s^-1 respectively. The conductivity in (?m)^-1, at room temperature for Si doped with As is

A

0.11

B

0.96

C

2.24

D

2.72

If the contents of exchangeable ions (cmol kg^-1) determined in soil are Na⁺ = 5, K⁺ = 5, Ca²⁺ = 10, Mg²⁺ = 2, H⁺ = 1, Al⁺³ = 1, Cl^- = 1.6 and HCO^-₃ =0.4, the CEC of soil is

A

26 cmol (P⁺) kg^-1

B

20 cmol (P⁺) kg^-1

C

24 cmol (P⁺) kg^-1

D

None of these

Given that ( 1² + 2² + 3² + .......... + 10² ) = 385, then the value of ( 2² + 4² + 6² + .......... + 20² ) is equal to = ?

A

770

B

1155

C

1540

D

(385)²

Given that (1² + 2² + 3² + ..... + 20²) = 2870, the value of (2² + 4² + 6² + ... + 40² ) is :

A

2870

B

5740

C

11480

D

28700

In a mine ventilation system, the resistances of two splits A and B are 0.5 Ns²m^-8 and 2 Ns²m^-8 respectively. Combined resistance of two shafts and trunk airways is 0.7 Ns²m^-8. A quantity of 20 m³/s of air passes through split A. The total air quantity passing the mine in m³/s is

A

30

B

27

C

25

D

17

How far is point 'R' from Point 'T'? Statement (I): Point 'R' is 5 metres to the north of point 'M'. Point 'U' is 4 metres to the east of point 'R'. Point 'T' is to the west of point 'R' such that points 'U' 'R' and 'T' form a straight line of metres. Statement (II): Point 'Z' is metres to the south of point 'T'. Point 'U' is metres to the east of point 'T'. Point 'M' is metres to the east of point 'Z'. Point 'R' is metres to the north of point 'M'. Point 'R' lies on the line formed by joining points 'T' and 'U'.

A

Statement (I) and (III) are independently sufficient to answer the question.

B

Statement (I) and (II) are together required to answer the question.

C

Statement (I) alone is sufficient to answer the question while statement (II) is not sufficient to answer the question.

D

Statement (II) alone is sufficient to answer (I) is not sufficient to answer the question.

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