1. This document contains 12 math word problems divided across 5 worksheets. The problems cover topics like derivatives, limits, probability, complex numbers, trigonometry and sequences and series. 2. The document tests a variety of calculus, trigonometry and algebra skills through problems involving derivatives, limits, sums, probabilities, graphs and equations. 3. Many problems ask students to use concepts like derivatives, limits, sequences, series, trigonometric identities and equations to solve word problems step-by-step and demonstrate mathematical reasoning and problem solving abilities.

1. WORK SHEET – 1 ( FOR MANASTHALI) CLASS XI
1. Find the derivative of 𝑒 𝑥
by first principle.
2. Find sum to n terms of series 0.7 + 0.77 + 0.777 + .......
3. 150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on a second
day, 4 more workers dropped out on 3rd
day & so on it took 8 more days to finish the work. Find the number
of days in which the work was completed.
4. If the coefficient of ar – 1
, ar
& ar + 1
in exp of (1 + a)n
are in A.P., prove that n2
– n (4r + 1) + 4r2
– 2 = 0.
5. Using P.M.T. prove that :- (1 + x)n
 1 + nx for all x > -1.
6. Find the value of cos 20o
cos 40o
cos 60o
cos 80o
.
7. Draw the graph of f(x) = [x] & find its domain & range
8. f (x) =
𝑘 cos 𝑥
𝜋−2𝑥
𝑥 <
𝜋
2
3 𝑥 >
𝜋
2
, find k if lim 𝑥 →
𝜋
2
𝑓 𝑥 exists
9. Find the rank of the word “: MOTHER”.
10. Prove that the product of lengths of the perpendiculars drawn from ( 𝑎2 − 𝑏2 , 0) & (− 𝑎2 − 𝑏2 , 0) to
line
𝑥
𝑎
cos 𝜃 +
𝑦
𝑎
sin 𝜃 = 1
WORKSHEET – 2( FOR MANASTHALI) CLASS XI
1. If 4 digit numbers greater than 5000 are formed from the digit 0, 1, 3, 5 & 7. What is the probability of family
a number divisible by 5 when digits can be repeated.
2. Solve :- x2
– (7 – i) x + (18 – i) = 0
3. Find the coefficient of x40
in (1 + 2x + x2
)27
.
4. The first, second & last terms of an A.P. are a, b, c respectively. Prove that the sum of n terms is
𝑎+𝑐 (𝑏+𝑐−2𝑎)
2 (𝑏−𝑎)
.
5. If x = a +
𝑎
𝑟
+
𝑎
𝑟2 +, , , , , , , , , ∞, y = b -
𝑏
𝑟
+
𝑏
𝑟2 + .............. ∞ , z = c -
𝑐
𝑟2 +
𝑐
𝑟4 + .............. ∞, prove
𝑥𝑦
𝑧
=
𝑎𝑏
𝑐
6. If the image of the point (2, 1) with respect to line mirror is (5, 2), find the equation of the mirror.
7. Find the centre & radius of a circle passing through (5, -8), (2, -9) & (2, 1).
8. Evaluate :- lim 𝑥→0
1−cos 𝑥 cos 2𝑥
𝑥2 .
9. Find the derivative of sin 𝑥 by first principle.
10. Prove :-
cos 8𝐴 cos 5𝐴−cos 12𝐴 cos 9𝐴
sin 8𝐴 cos 5𝐴+cos 12𝐴 sin 9𝐴
= tan 4A
11. Find domain & range of f(x) =
𝑥−2
3−𝑥

2. WORK SHEET – 3 ( FOR MANASTHALI) CLASS XI
1. Let R1 be a relation on R : (a, b)  R1 1 + ab > 0 a, b  R Show that
a. (a, 0)  R1 for all a  R
b. (a, b)  R1 ⇒ (b, a)  R1 for all a, b  R
2. Find domain & range of f(x) =
𝑥2
𝑥−4
3. If 10 sin4
 + 15 cos 4
 = 6, find the value of 27 cosec 6
 + 8 sec6
 .
4. Evaluate :- lim 𝑥 →2 𝑓(𝑥)if f(x) =
𝑥 − [𝑥] 𝑥 < 2
4 𝑥 = 2
𝑥 − 5 𝑥 > 2
5. Prove that
𝑑
𝑑𝑥
𝑖𝑛 𝑥−𝑥 cos 𝑥
𝑥 sin 𝑥+cos 𝑥
=
𝑥2
(𝑥 sin 𝑥+cos 𝑥)2
6. The letters of word SOCIETY are placed at random in a row. What is the probability that three vowels come
together?
7. Find the probability of getting an even numbers on first die or a total of in a single throw of two dice.
8. An arc is in form of semi ellipse. It is sin wide & 2m high at centre. Find the height of arch at a point 1.5 m
from one end.
9. If a is the A.M. of b & c and two G.M. are G1 & G2, prove G1
3
+ G3
2 = 2abc
10. Find sum of 24 terms of AP if it is known that a1 + a5 + a10 + a15 + a20 + a24 = 225.
WORK SHEET – 4( FOR MANASTHALI) CLASS XI
1. If the first term of an A.P. is z & sum of first 5 terms is equal to ¼ of sum of rent 5 terms. Find S30 .
2. Prove that :-
tan 3𝑥
tan 𝑥
never lies between
1
3
& 3.
3. Prove that :- sin2
72 – sin2
60 =
5− 1
8
.
4. Find real value of x & y:- (x4
+ 2xi) – ( 3x2
+ iy) = (3 – 5i) + (1 + 2iy) .
5. Solve :-
5𝑥
4
+
3𝑥
8
>
39
8
,
2𝑥−1
12
−
𝑥−1
3
<
3𝑥+1
4
6. The letter of word “RANDOM” are written in all possible orders in dictionary. Find the rank of word “
RANDOM”.
7. Prove by PMI that :-
𝑥5
5
+
𝑥3
3
+
7𝑛
15
is a natural number for all n  N .
8. Using concept of slope, prove that the line joining the mid points of the two sides of a triangle is 11 to third
side.
9. Evaluate :- lim 𝑥 →2
𝑥2− 4
3𝑥−2− + 2
10. Prove that :- lim 𝑥 →
𝜋
4
𝑡𝑎𝑛 3 𝑥−tan 𝑥
cos (𝑥+
𝜋
4
)
= -4
11. Find the derivative of cos3
x by first principle.
12. Three dice are thrown together. Find the probability of getting a total of at least 6.

3. WORKSHEET – 5( FOR MANASTHALI) CLASS XI
1. f(x) =
5𝑥
𝑥 − 2𝑥2 𝑥 ≠ 0
0 = 0
does lim 𝑥 →0 𝑓(𝑥) exist ?
2. if a1, a2, a3 ....... an are in A.P. where ai > 0. Show that
1
𝑎1+ 𝑎2
+
1
𝑎2+ 𝑎3
+ … . +
1
𝑎 𝑛−1+ 𝑎 𝑛
=
𝑥− 1
𝑎1+ 𝑎 𝑛
.
3. the natural number are grouped as follows : (1), (2, 3), (4, 5, 6), (7, 8, 9, 10) ....... find the first term of nth
group.
4. If z1 , z2 are complex numbers :-
𝑧1− 3𝑧2
3− 𝑧1 𝑧2
= 1 & 𝑧2 ≠ 1, then find 𝑧1 .
5. Find all non zero complex numbers z satisfying 𝑧 = iz2
.
6. If 𝑛 𝑐𝑟 : 𝑛 𝑐𝑟+2 = 1 : 2 : 3 find n & r.
7. Find the derivative of tan 𝑥 by first principle.
8. Solve :- sin 3x + cos 2 x = 0
9. In a triangle ABC. If a cos A = b cos B, then prove that either triangle is isosceles or right angled.
10. Prove :- 3 cosec 20o
– sec 20o
= 4.
11. Find the least value of n for which 1 + 3 + 32
+ ............. to n terms is greater than 7000.
12. Find the derivative of
a. sin
𝑥2
3
− 1 b. log (sec x + tan x) c.
1
𝑎2− 𝑥2
.