List of top Mathematics Questions asked in CBSE Class XI

Find the equation of the hyperbola satisfying the give conditions: Foci (0, \(±\sqrt{10}\)), passing through (2, 3)
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 (±4, 0), the latus rectum is of length 12.
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 (0, ±13), the conjugate axis is of length 24.
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: Vertices (0, ±3), foci (0, ±5)
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 (±2, 0), foci (±3, 0)
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 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 sum of the following series up to n terms: (i) 5+55+555+…(ii) .6+.66 +. 666+…

The ratio of the A.M. and G.M. of two positive numbers a and b, is m : n. Show that \(a : b =\sqrt{ (m + √m^2 - n^2) }: (m -\sqrt{ √m^2 - n^2)}.\)
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?
Evaluate \(\lim_{x\rightarrow 5}\) f(x), where f(x) = |x|-5
Evaluate \(\lim_{x\rightarrow 0}\) f(x), where { \(\frac{x}{|x|}\), x≠0 0, x=0
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.
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.
Evaluate \(\lim_{x\rightarrow 0}\)f(x), where { |x|/x, x≠0 0, x=0

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn.

Find \(\lim_{x\rightarrow 1}\) f(x) where { x2 -1, x≤1 -x2-1, x>1
Find \(\lim_{x\rightarrow 0}\) f(x) and \(\lim_{x\rightarrow 1}\) f(x) where { 2x+3, x≤0 3 (x+1), x>0
Evaluate the Given limit: \(\lim_{x\rightarrow \frac{\pi}{2}}\frac{tan\,2x}{x}-\frac{\pi}{2}\)

If  \(\frac{ a + bx }{ a - bx }= \frac{b + cx }{ b - cx} =\frac{ c + dx }{ c - dx }(x ≠ 0),\) then show that a, b, c and d are in G.P.

A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.