List of top Questions asked in CBSE Class XI

IQ of a person is given by the formula \(IQ = \frac{MA}{CA}×100, \) Where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it.The resulting mixture is to be more than 4% but less than 6% boric acid.If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

A solution is to be kept between 68°F and 77°F. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by \(F = \frac{9}{5}C + 32\,\, ?\)

Solve the inequalities and represent the solution graphically on number line: 5(2x –7) – 3(2x+3) ≤ 0, 2x+19 ≤ 6x+47.

Solve the following inequalities and represent the solution graphically on number line: 3x –7 > 2(x-6), 6-x > 11-2x.

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{x^2cos(\frac{\pi}{4})}{sin\,x}\)

Find the range of each of the following functions.
(i) f(x) = 2 - 3x, x ∈ R, x> 0.
(ii) f(x) = x²+ 2, x, is a real number.
(iii) f(x) = x, x is a real number

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (4x+5sinx)(3x+7cosx)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (ax²+ sin x)(p+qcos x)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): (x²+1) cosx

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): x⁴(5sinx - 3cosx)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{a+b\,sin\,x}{c+d\,cos\,x}\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{sec\,x-1}{sec\,x+1}\)

Expand using Binomial Theorem \(( 1+ \frac{X}{2} - \frac{2}{X})^4, X≠0\)

Find an approximation of (0.99)5 using the first three terms of its expansion

Find the value of \(( a^2 + \sqrt{a^2-1})^4 + ( a^2 - \sqrt{a^2-1})^4\)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): 4\(\sqrt x\) -2

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers): \(\frac{a}{x^4}-\frac{b}{x^2}\) + cosx

Find the derivative of
(i) 2x - \(\frac{3}{4}\)
(ii)(5x³+3x-1)(x-1)
(iii) x-3(5+3x) (iv)x⁵(3-6x-9)
(v) x-4(3-4x-5) (vi)\(\frac{2}{x+1}-\frac{x^2}{3x-1}\)

Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (-1, -1) are the vertices of a right angled triangle.

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, -4) and B (8, 0).

Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).

If f(x)={|x|+1, x <0 0, x=0 |x|-1, x>0}
For what value (s) of a does lim x\(\rightarrow\)af(x) exist?

Find the derivative of the following functions (it is to be understood that \(a, \,b,\, c,\, d,\, p,\, q,\, r\) and \(s\) are fixed non-zero constants and \(m\) and \(n\) are integers), \((x+a)\).