91. If the zeroes of a quadratic polynomial are equal, then:
(a) c and b have opposite signs
(b) c and a have opposite signs
(c) c and b have same signs
(d) c and a have same signs
Answer:
(d) c and a have same signs
Explanation:
For real and equal roots, the discriminant . This implies . Since is always positive (or 0), the product must also be positive. For to be positive, and must have the same sign.
92. The pair of equations and graphically represent lines which are:
(a) Parallel
(b) Intersecting at (n, -m)
(c) Coincident
(d) Intersecting at (-m, n)
Answer:
(d) Intersecting at (-m, n)
Explanation:
The equation $x = -m$ is a vertical line, and $y = n$ is a horizontal line. They intersect precisely at the Cartesian coordinate point $(-m, n)$.
93. If $\sec\theta + \tan\theta = x$, then $\sec\theta – \tan\theta$ will be
(a) $x$
(b) $x^2$
(c) $\frac{2}{x}$
(d) $\frac{1}{x}$
Answer:
(d) $\frac{1}{x}$
Explanation:
We know the trigonometric identity $\sec^2\theta – \tan^2\theta = 1$. This can be factored as $(\sec\theta – \tan\theta)(\sec\theta + \tan\theta) = 1$. Substituting $x$ for the second term gives $(\sec\theta – \tan\theta) \cdot x = 1$, hence $\sec\theta – \tan\theta = \frac{1}{x}$.
94. Perimeter of a sector of a circle whose central angle is $90^\circ$ and radius 7cm is:
(a) 35cm
(b) 11cm
(c) 22cm
(d) 25cm
Answer:
(d) 25cm
Explanation:
The length of the arc is $L = \frac{\theta}{360} \times 2\pi r = \frac{90}{360} \times 2 \times \frac{22}{7} \times 7 = 11 \text{ cm}$. The perimeter of the sector includes the arc and two radii: $P = L + 2r = 11 + 2(7) = 11 + 14 = 25 \text{ cm}$.
95. Extreme values of a given data
(a) affect the median
(b) do not affect the median
(c) nothing can be said
(d) none of these
Answer:
(b) do not affect the median
Explanation:
The median is the middle value of a sorted dataset. It is structurally resistant to outliers or extreme values, unlike the mean, which is heavily affected by them.
