SAT (Stage-2) Mock Test - 43

This is the correct option. Temporary or permanent damage to body parts causes physical diseases. Invasion of the body by other organisms causes infectious diseases. Inadequate diet causes deficiency diseases.

This option is correct. Application of nitrogenous manure to a plant causes vigorous vegetative growth.

The depth of water and the amount of dissolved salts in the water classify the aquatic ecosystem. Different zones defined by depth and distance from shore are: Littoral zone, limnetic zone, profundal zone and benthic zone.

This is the correct option. People living in urban areas are not direct stakeholders in the management or conservation of forests.

Water, temperature and nature of soil are responsible for the biodiversity of a region. This is the reason why tropical rainforests show maximum biodiversity.

Check by the options.
For n = 3,

p(x) = x + 3
p(-x) = -x + 3
p(x) + p(-x) = x + 3 + (-x) + 3 = 6

A zero polynomial is an additive identity where all the coefficients including constant are zero. Now the graph of a zero polynomial is x-axis and we define zero of a polynomial as the value of x for which it becomes zero. Therefore, the zero of a zero polynomial is whole x-axis, i.e. it includes all real numbers.

The LCM is the product of the prime factors raised to the highest power that appears in the factor of the said numbers.
Now, the highest power of a is 3, which occurs in the prime factorisation of q.
The highest power of b is 2, which occurs in the prime factorisation of p.
Hence, the LCM is a³b².

You have to put the values x = 2 and y = -3 to find if both the equations in the given options hold good. This is found to be correct in option 4 only.

x - y = 2 and x + y = 4
Solving the two simultaneous equations, we get x = 3 and y = 1.
So, a = 3 and b = 1

A quadratic equation will have no real roots when b² - 4ac < 0. This is true in option 1 where b² - 4ac = -0.97. In rest of the options, it is either 0 or greater than 0.

2x² + 7x - 4 = 0
2x² - 8x + x + 4 = 0
2x(x - 4) - 1(x - 4) = 0
(2x - 1)(x - 4) = 0
x = (1/2) and 4.
One of the zeros of the polynomial 2x² + 7x - 4 is (1/2).

Given:
p^th term = a ⇒ t₁ + (p - 1)d = a … (1)
q^th term = b ⇒ t₁ + (q - 1)d = b ... (2)
r^th term = b ⇒ t₁ + (r - 1)d = c … (3)
The given expression is: a(q - r) + b(r - p) + c(p - q)
This is equivalent to: q(a - c) + r(b - a) + p(c - b)
Putting the values of a, b and c in terms of t₁ and d in the given expression, we get
q[(p - 1)d - (r - 1)d] + r[(q - 1)d - (p - 1)d] + p[(r - 1)d - (q - 1)d]
= q[pd - d - rd + d] + r[qd - d - pd + d] + p[rd - d - qd + d]
= qpd - qrd + rqd - prd + prd - qpd = 0
a(q - r) + b(r - p) + c(p - q) = 0
Thus, answer option (2) is correct.