List of practice Questions

If a, b, c, d are in G.P, prove that \( (a^n+ b^n), (b^n+c^n), (c^n+d^n) \)dn) are in G.P.
If a and b are the roots of x2 – 3x + p = 0 and c, d are roots of x2 – 12x + q = 0,where a, b, c, d form a G.P. Prove that (q+p) : (q-p) = 17:15.
Evaluate \(\lim_{x\rightarrow 0}\) f(x), where { \(\frac{x}{|x|}\), x≠0 0, x=0
Evaluate \(\lim_{x\rightarrow 5}\) f(x), where f(x) = |x|-5
Suppose f(x) ={ a+bx, x\(<\)1 4, x=1 b-ax x\(>\)1 and if lim x \(\rightarrow\)1 f(x) = f(1), what are possible values of a and b?
The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that \(a : b =\sqrt{ (m + √m^2 - n^2) }: (m -\sqrt{ √m^2 - n^2)}.\)

Find the sum of the following series up to n terms: (i) 5+55+555+…(ii) .6+.66 +. 666+…

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola \(5y^ 2 - 9x^ 2 = 36\)
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola \(49y^ 2 - 16x ^2 = 784\)
Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)
Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±5), foci (0, ±8)
Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5)
Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.
Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±13), the conjugate axis is of length 24.
Find the equation of the hyperbola satisfying the give conditions: Foci (\(± 3\sqrt5, 0\)), the latus rectum is of length 8.
Find the equation of the hyperbola satisfying the give conditions: Foci (±4, 0), the latus rectum is of length 12.
Find the equation of the hyperbola satisfying the give conditions: Vertices (±7, 0), \(e = \frac{4}{3}\)
Find the equation of the hyperbola satisfying the give conditions: Foci (0, \(±\sqrt{10}\)), passing through (2, 3)
Find the 20th term of the series 2×4+4×6+6×8+ ... + n terms.
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?
Match List I (Painting) with List II (State) and choose the correct option:
\[ \begin{array}{|l|l|} \hline \textbf{LIST I} & \textbf{LIST II} \\ \hline A.\ \text{Warli Painting} & I.\ \text{Bihar} \\ B.\ \text{Gond} & II.\ \text{Odisha} \\ C.\ \text{Pata Chitra} & III.\ \text{Maharashtra} \\ D.\ \text{Mithila} & IV.\ \text{Madhya Pradesh} \\ \hline \end{array} \]
Match List I (Personalities) with List II (Known as) and choose the correct option:
\[ \begin{array}{|l|l|} \hline \textbf{LIST I} & \textbf{LIST II} \\ \hline A.\ \text{J.C. Kumarappa} & I.\ \text{Milkman of India} \\ B.\ \text{Chaudhary Charan Singh} & II.\ \text{Founder of Indian Statistical Institute} \\ C.\ \text{Verghese Kurien} & III.\ \text{Author of Economy of Permanence} \\ D.\ \text{P.C. Mahalanobis} & IV.\ \text{Founder of Bharatiya Lok Dal} \\ \hline \end{array} \]

Match List I with List II and choose the correct answer:  \[ \begin{array}{|l|l|} \hline \textbf{LIST I} & \textbf{LIST II} \\ \hline A.\ \text{Adventures of Tom Sawyer} & I.\ \text{Khaled Hosseini} \\ B.\ \text{Paradise Lost} & II.\ \text{Charles Dickens} \\ C.\ \text{Oliver Twist} & III.\ \text{Mark Twain} \\ D.\ \text{The Kite Runner} & IV.\ \text{John Milton} \\ \hline \end{array} \]

What is the unit digit of $(234)^{100} + (234)^{101}$?

Sum of three consecutive odd numbers is always divisible by: 
A) 2 
B) 3 
C) 5 
D) 6