Q (3) Prove that 

\small (\cos x + \cos y)^{2} + (\sin x - \sin y)^{2} = 4 \cos^{2}\left ( \frac{x+y}{2} \right )

Q(4)  Prove that 

\small (\cos x-\cos y)^{2} + (\sin x - \sin y)^{2} = 4\sin^{2}\left ( \frac{x-y}{2} \right )

Q(5)  Prove that 

\small \sin x + \sin 3x + \sin 5x + \sin 7x = 4\cos x\cos2x \sin4x

Q (6)  Prove that 

\small \frac{(\sin 7x + \sin 5x) + (\sin9x + \sin 3x)}{(\cos7x + \cos5x) + (\cos9x + \cos3x)} = \tan6x

Q(7)   Prove that 

\small \sin3x + \sin2x - \sin x = 4\sin x \cos\frac{x}{2}\cos\frac{3x}{2}

Find    \small \sin\frac{x}{2} , \cos\frac{x}{2} , and \tan\frac{x}{2}    in 

Q (8)   

\small \tan x = - \frac{4}{3}        , x in quadrant  II

 Find     \small \sin\frac{x}{2} , \cos\frac{x}{2} , and \tan\frac{x}{2}   in


Q (9)

\small \cos x = -\frac{1}{3}   , x in quadrant III

    Find    \small \sin\frac{x}{2} , \cos\frac{x}{2} , and \tan\frac{x}{2}     in


Q (10)

\small \sin x = \frac{1}{4}   ,x in quadrant II

Q4. Fill up the blanks with the words given:

herbivore, plant, milk, sugarcane, carnivore

(a) Tiger is a _______________ because it eats only meat.

(b) Deer eats only plant products and so, is called ______________.

(c) Parrot eats only _______________ products.

(d) The ________________ that we drink, which comes from cows, buffaloes and goats is an animal product.

(e) We get sugar from ________________.

Q.4 Write down all the subsets of the following sets

(i) {a}

Q.4 Write down all the subsets of the following sets:

(ii) {a, b}

Q.4 Write down all the subsets of the following sets:

(iii) {1,2,3}

Q.4 Write down all the subsets of the following sets:

(iv) \phi

Q.5 How many elements has P(A), if A = \phi?

Q.6 Write the following as intervals :

(i) {x : x \inR, – 4 < x \leq 6}

(ii) {x : x \in R, – 12 <x <–10}

(iii) {x : x \in R, 0 \leq x < 7}

(iv) {x : x \in R, 3 \leq  x \leq  4}

Q 15)
f(x)\left\{\begin{matrix} 2x & if &x<0 \\ 0& if &0\leq x\leq 1 \\ 4x&if & x>1 \end{matrix}\right.

Among the following edible fishes, which one is a marine fish having rich source of omega-3 fatty acids?

Option: 1

Mystus


Option: 2

Mangur


Option: 3

Mrigala


Option: 4

Mackerel


Match the corresponding entries of column 1 with column 2 [where m is the magnification produced by the mirror]

Column 1

Column 2

(A)    m = -2

(a) Convex mirror

(B)    \text{m} = - \frac{1} {2}

(b) Concave mirror

(C)    m = +2

(c) Real image

(D)    \text{m} = + \frac{1} {2}

(d) Virtual image

Option: 1

\rightarrow b and c; B \rightarrow b and c; C \rightarrow b and d; D \rightarrow a and d


Option: 2

\rightarrow a and c; B \rightarrow a and d; C \rightarrow a and b; D \rightarrow c and d


Option: 3

\rightarrow a and d; B \rightarrow b and c; C \rightarrow b and d; D \rightarrow b and c


Option: 4

\rightarrow c and d; B \rightarrow b and d; C \rightarrow b and c; D \rightarrow a and d


If the velocity of a particle is \upsilon = \text{At} + \text{Bt}^2, where A and B are constants, then the distance travelled by it between 1s and 2s is:

Option: 1

\frac{3} {2}\text{A} + 4\text{B}


Option: 2

3\text{A} + 7\text{B}


Option: 3

\frac{3} {2}\text{A} + \frac{7} {3}\text{B}


Option: 4

\frac{\text{A}} {2} + \frac{\text{B}} {\text{3}}


Taylor conducted the experiments to prove semiconservative mode of chromosome replication on

Option: 1

Vinca rosea


Option: 2

Vicia faba


Option: 3

Drosophila melanogaster


Option: 4

E. coli


Which of the following pairs of ions are isoelectronic and isostructural ?

Option: 1

CO_3^{2-}, SO_3^{2-}


Option: 2

ClO_3^{-}, CO_3^{2-}


Option: 3

SO_3^{2-}, NO_3^{-}


Option: 4

ClO_3^{-}, SO_3^{2-}


For its action, nitrogenase requires:

Option: 1

Light


Option: 2

Mn2+


Option: 3

Super oxygen radicals


Option: 4

High input of energy


Water containing cavities in vascular bundles are found in :

Option: 1

Sunflower


Option: 2

Maize


Option: 3

Cycas


Option: 4

Pinus


Perisperm differs from endosperm in:

Option: 1

its formation by fusion of secondary nucleus with several sperms


Option: 2

being a haploid tissue


Option: 3

having no reserve food


Option: 4

being a diploid tissue


A pregnant female delivers a baby who suffers from stunted growth, mental retardation, low intelligence quotient and abnormal skin.

This is the result of:

Option: 1

Over secretion of pars distalis


Option: 2

Deficiency of iodine in diet


Option: 3

Low secretion of growth hormone


Option: 4

Cancer of the thyroid gland


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