101. A, 0, B are three points on a line segment and C is a point not lying on AOB. If ∠AOC = 40° and OX, OY are the internal and external bisectors of ∠AOC respectively, then ∠BOY is
102. If 4x = sec θ and 4/x = tan θ then $$(x^2 - \frac{1}{x^2})$$ is
103. If 2 - cos^2 θ = 3 sin θ cos θ, sin θ ≠ cos θ then tan θ is
104. If sin θ + cos θ = √2 cos (90 - θ), then cot θ is
105. If $$x sin^3 θ + y cos^3 θ = sin θ cos θ$$ and x sin θ = y cos θ, sin θ ≠ 0, cos θ ≠ 0, then $$x^2 + y^2$$ is
106. In the following figure, O is the centre of the circle and XO is perpendicular to OY. If the area of the triangle XOY is 32, then the area of the circle is
107. The side BC of ΔABC is produced to D. If ∠ACD = 108° and ∠B = ∠A/2, then ∠A is
108. Two circles of radii 4 cm and 9 cm respectively touch each other externally at a point and a common tangent touches them at the points P and Q respectively. Then the area of a square with one side PQ, is
109. Two tangents are drawn from a point P to a circle at A and B. 0 is the centre of the circle. If ∠AOP = 60°. then ∠APB is
110. If each interior angle is double of each exterior angle of a regular polygon with n sides, then the value of n is
111. If the length of the side PQ of the rhombus PQRS is 6 cm and ∠PQR = 120°, then the length of QS, in cm, is
112. The angle formed by the hourhand and the minutehand of a clock at 2 : 15 p.m. is
113. Two sides of a triangle are of length 4 cm and 10 cm. If the length of the third side is ‘a cm, then
114. If $$x=(0.08)^2$$, $$y=\frac{1}{(0.08)^2}$$ and $$z=(1-0.08)^2 - 1$$, then out of the following, the true relation is
115. In xy plane, P and Q are two points having coordinates (2, 0) and (5, 4) respectively. Then the numerical value of the area of the circle with radius PQ, is
116. If $$x^4 + \frac{1}{x^4} = 23$$, then the value of $$(x-\frac{1}{x})^2$$ will be
117. The value of $$\sqrt{6+\sqrt{6+\sqrt{6+...}}}$$ is equal to
118. If $$x + \frac{1}{x} = 12 $$, the value of $$x^2 + \frac{1}{x^2}$$ is
119. $$sec^4 θ - sec^2 θ$$ is equal to
120. In ΔABC, AD is the median and AD = 1/2 BC. If ∠BAD = 30°, then measure of ∠ACB is
123. If a + b + 1 = 0, then the value of $$(a^3 + b^3 +1 - 3ab)$$ is
124. In the xy coordinate system, if (a, b) and (a + 3, b + k) are two points on the line defined
by the equation x = 3y - 7, then k = ?
125. The average age of four boys, five years ago was 9 years. On including a new boy, the present average age of all the five is 15 years. The present age of the new boy is
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