Objective Questions

Questions (696)

#	Question	Topic	Actions
101	The 5th term of an AP is 20 and the 12th term is 48. Find the sum of the first …	Arithmetic Progression	View
102	Find the 6th term of an AP if a=7 and d=5.	Arithmetic Progression	View
103	Find the 20th term of an AP 2, 5, 8, ...	Arithmetic Progression	View
104	Sum of first 15 terms of AP 4, 9, 14, ...	Arithmetic Progression	View
105	The quadratic formula is:	MTH 101 Past Questions	View
106	Prove by mathematical induction that 1 + 2 + 3 + ... + n = n(n+1)/2 for all n ≥…	Mathematical Induction	View
107	Prove by induction that 1² + 2² + 3² + ... + n² = n(n+1)(2n+1)/6 for n ≥ 1.	Mathematical Induction	View
108	Prove by induction that 1×2 + 2×3 + ... + n(n+1) = n(n+1)(n+2)/3 for n ≥ 1.	Mathematical Induction	View
109	Prove by induction that 1×3 + 3×5 + 5×7 + ... + (2n-1)(2n+1) = n(2n+1)(2n+3)/3 …	Mathematical Induction	View
110	Prove by induction that log(a) + log(a²) + log(a³) + ... + log(a^n) = n(n+1)/2 …	Mathematical Induction	View
111	Prove by induction that n! > 2^n for n > 4.	Mathematical Induction	View
112	Prove by induction that 1³ + 2³ + 3³ + ... + n³ = (1+2+...+n)² for all n ≥ 1.	Mathematical Induction	View
113	Prove by induction that 1² + 3² + 5² + ... + (2n-1)² = n(2n-1)(2n+1)/3 for n ≥ …	Mathematical Induction	View
114	Prove by induction that 1×2⁰ + 2×2¹ + 3×2² + ... + n×2^{n-1} = (n−1)2^n + 1 for…	Mathematical Induction	View
115	Prove by induction that sum_{i=1}^n i(i+1)(i+2) = n(n+1)(n+2)(n+3)/4 for n ≥ 1.	Mathematical Induction	View
116	Prove by induction that 1² + 2² + 3² + ... + n² = n(n+1)(2n+1)/6 for n≥1 and fi…	Mathematical Induction	View
117	Expand and simplify the coefficients of (2x + 1)^4.	Binomial Expansion	View
118	Expand (1 + √x)^6 and simplify the coefficients.	Binomial Expansion	View
119	In the expansion of (2x^2 + rx + 1)^6, the coefficients of x^2 and x^3 are 27 a…	Binomial Expansion	View
120	Expand √(1 + 3x) up to the term in x^3.	Binomial Expansion	View
121	In the expansion of (1 - x)^(1/4) up to x^7, evaluate 77^(1/4) correct to five …	Binomial Expansion	View
122	Find the term independent of x in the expansion of (x + 1/x)^10.	Binomial Expansion	View
123	If coefficients of x^2 and x^3 are equal in (ax - b)^5, find relation between a…	Binomial Expansion	View
124	Expand (1 - 5x)^(-5) up to term in x and evaluate (0.99)^(-5).	Binomial Expansion	View
125	Expand (2 - x)^2 in ascending powers of x.	Binomial Expansion	View
126	Expand (1 + x)^5 up to x^3.	Binomial Expansion	View
127	The sum of the roots of ax² + bx + c = 0 is:	MTH 101 Past Questions	View
128	If the coefficient of x^k in (1+x)¹⁰ is 84 and n=9, what is k?	MTH 101 Past Questions	View
129	Solve: 3x-7 = ?	MTH 101 Past Questions	View
130	If P(k) = k(k+3)(k-1) is true, then what is P(k+1)?	MTH 101 Past Questions	View
131	Which method is NOT a common method for solving quadratic equations?	MTH 101 Past Questions	View
132	For the equation 2x² + 3x - 2 = 0, the discriminant is:	MTH 101 Past Questions	View
133	If \(\|x - y\| = 0\), then	MTH 101 Past Questions	View
134	If \(n(A) = p\), \(n(B) = q\), \(n(U) = N\), and \(A \cap B = \emptyset\), then…	MTH 101 Past Questions	View
135	If tanθ = 1, find θ (0° < θ < 90°)	MTH 101 Past Questions	View
136	If P(n): 3ⁿ > 2ⁿ for all n ≥ 1, what is the smallest n for which this holds?	MTH 101 Past Questions	View
137	Simplify \(\frac{(\csc y + \cot y)(\csc y - \cot y)}{\csc y}\)	MTH 101 Past Questions	View
138	The binomial coefficient 8C5 equals:	MTH 101 Past Questions	View
139	The number of ways to select 2 courses from 3 maths and 4 physics courses is:	MTH 101 Past Questions	View
140	In a geometric sequence, the first term is 2 and the common ratio is 3. What is…	MTH 101 Past Questions	View
141	If a geometric sequence has a = 6 and r = -2, what is the 4th term?	MTH 101 Past Questions	View
142	Find the geometric mean between 4 and 16.	MTH 101 Past Questions	View
143	Find the 6th term of the geometric sequence: 5, 10, 20,...	MTH 101 Past Questions	View
144	How many permutations are there of 7 objects taken 3 at a time?	MTH 101 Past Questions	View
145	Evaluate 7C3.	MTH 101 Past Questions	View
146	Solve -2 ≤ -3x < 5	MTH 101 Past Questions	View
147	Convert π/4 to degrees	MTH 101 Past Questions	View
148	Find the coefficient of x⁴ in the binomial expansion of (1-2x)⁷	MTH 101 Past Questions	View
149	The product of the roots of the equation ax² + bx + c = 0 is:	MTH 101 Past Questions	View
150	Let A, B, C ⊆ U. Simplify (A ∩ B) ∪ (A ∩ B^c)?	MTH 101 Past Questions	View
151	The inverse of f(x) = x + 1 is:	MTH 101 Past Questions	View
152	Evaluate: 3 + 5 × 6	MTH 101 Past Questions	View
153	What is the expanded form of (x + 2)(2x - 7)?	MTH 101 Past Questions	View
154	Factor: x² - 1	MTH 101 Past Questions	View
155	What is the set of points that are equidistant from a fixed point known as?	Analytical Geometry - The Circle	View
156	The fixed point from which all points on a circle are equidistant is called the?	Analytical Geometry - The Circle	View
157	Which component of a circle is described as the line that marks out the circle …	Analytical Geometry - The Circle	View
158	A line that touches a circle at two distinct points is known as a?	Analytical Geometry - The Circle	View
159	What is a chord that passes through the centre of a circle called?	Analytical Geometry - The Circle	View
160	What is the name for a line from the centre of a circle to any point on the cir…	Analytical Geometry - The Circle	View
161	A portion of the circumference is called an?	Analytical Geometry - The Circle	View
162	A region bounded by an arc and a chord is called a?	Analytical Geometry - The Circle	View
163	What is the standard equation of a circle with centre (a, b) and radius r?	Analytical Geometry - The Circle	View
164	What does the equation of a circle become if its centre is at the origin (0,0)?	Analytical Geometry - The Circle	View
165	Find the equation of the circle with centre (-3,2) and radius 4.	Analytical Geometry - The Circle	View
166	What is the equation of a circle with radius 6 units and centre at the origin?	Analytical Geometry - The Circle	View
167	Find the centre and radius of the circle with equation x² + y² + 3x - 2y + 2 = …	Analytical Geometry - The Circle	View
168	In the general equation of a circle x² + y² + 2gx + 2fy + c = 0, what are the c…	Analytical Geometry - The Circle	View
169	In the general equation of a circle x² + y² + 2gx + 2fy + c = 0, what is the fo…	Analytical Geometry - The Circle	View
170	Which of the following equations does NOT represent a circle?	Analytical Geometry - The Circle	View
171	A quadratic equation in x and y represents a circle if which of the following c…	Analytical Geometry - The Circle	View
172	Find the centre of the circle 4x² + 4y² - 12x - 20y + 9 = 0 after it has been s…	Analytical Geometry - The Circle	View
173	Find the radius of the circle 4x² + 4y² - 12x - 20y + 9 = 0.	Analytical Geometry - The Circle	View
174	What is the equation of a circle passing through the ends of a diameter with en…	Analytical Geometry - The Circle	View
175	The ends of a diameter of a circle are (5,4) and (-3,6). What is the equation o…	Analytical Geometry - The Circle	View
176	What is a tangent to a circle?	Analytical Geometry - The Circle	View
177	The point where a tangent touches a circle is called the?	Analytical Geometry - The Circle	View
178	What is the formula for the equation of the tangent to the circle x² + y² = a² …	Analytical Geometry - The Circle	View
179	Find the equation of the tangent to the circle x² + y² = 10 at the point (4, -2…	Analytical Geometry - The Circle	View
180	What is the formula for the equation of a tangent to the general circle x² + y²…	Analytical Geometry - The Circle	View
181	A normal to a circle at a given point is a line that is?	Analytical Geometry - The Circle	View
182	What is the formula for the equation of the normal to the circle x² + y² + 2gx …	Analytical Geometry - The Circle	View
183	What does TP represent in the context of the length of a tangent from an extern…	Analytical Geometry - The Circle	View
184	What is the formula for the length of the tangent (TP) from an external point P…	Analytical Geometry - The Circle	View
185	Find the length of the tangent drawn from the point (-2,3) to the circle x² + y…	Analytical Geometry - The Circle	View
186	Parametric equations of a circle express the coordinates of points on the circl…	Analytical Geometry - The Circle	View
187	Given a circle with centre (a, b) and radius r, what are its parametric equatio…	Analytical Geometry - The Circle	View
188	Given a circle with centre (3, -2) and radius 4, what is its parametric equatio…	Analytical Geometry - The Circle	View
189	Given the parametric equations x - 9 = 3 cos θ and y + 14 = 3 sin θ, what is th…	Analytical Geometry - The Circle	View
190	Given the parametric equations x - 9 = 3 cos θ and y + 14 = 3 sin θ, what is th…	Analytical Geometry - The Circle	View
191	What is the rationalized form of 2/(√3 + 5)?	MTH 101 Past Questions	View
192	log₅ (1/25) equals:	MTH 101 Past Questions	View
193	Which of the following is a necessary condition for a geometric series to have …	MTH 101 Past Questions	View
194	Find the sum of the first 46 terms of the geometric progression 1/2, 1/4, 1/8, …	Geometric Progression	View
195	Find the sum of the first 22 terms of the geometric progression 2, 4, 8, ...…	Geometric Progression	View
196	A GP has first term 5 and common ratio 2. Find the sum of the first 10 terms.	Geometric Progression	View
197	Find the 15th term of the GP 3, 6, 12, ...	Geometric Progression	View
198	If 60 students: 35 like Tea, 30 like Coffee, 10 like both. How many like only T…	Set Theory	View
199	In a set U = {1..15}, A = {1,3,5,7,9}, B = {5,6,7,8,9}, find (A ∪ B) − (A ∩ B).	Set Theory	View
200	If 40 students: 18 like Football, 22 like Basketball, 10 like both, how many li…	Set Theory	View

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