In figure 7.30, side of square ABCD is 7 cm. With centre D and radius DA,sector D - AXC is drawn. Fill in the following boxes properly and find out the area of the shaded region.

In figure 7.30, side of square ABCD is 7 cm. With centre D and ra…

Evaluate the following:
If A = 45°, verify that:
$\cos2\text{A}=2\cos^2\text{A}-1=1-2\sin^2\text{A}$

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Solve the following quadratic equation by factorization.
$2 x^2-2 x+\frac{1}{2}=0$

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Solve the following quadratic equation by factorization.
$2y^2 + 27y + 13 = 0$

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If $\alpha,\beta$ are the zeros of the polynomial $2y^2 + 7y + 5$, write the value of $\alpha+\beta+\alpha\beta.$

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Express the following in terms of trigonometric ratios of angles lying between 0° and 45°.$\cos78^\circ+\sec78^\circ$

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If graph of quadratic polynomial $ax^2 + bx + c$ cuts positive direction of y-axis, then what is the sign of $c$?

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Find the value of discriminant for each of the following equation.
$\sqrt{5} x^2-x-\sqrt{5}=0$

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Which of the following sequences are A.P. ? If they are A.P. find the common difference.
2, 4, 6, 8, . . .

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Find the value of discriminant for of the following quadratic equation:
$3 x^2+2 x+1=0$

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Very-Short and Short-Answer Questions:
If $\sec\theta+\tan\theta=\text{x},$ find the value of $\sec\theta.$

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