Std : X
Date : 18/12/20
DESAI CLASSES
Subject – Algebra
Topic - 1st Preliminary Exam
Test No : 77
Marks: 40
Q1. (A) Choose the correct alternative. [4]
1. From the following quadratic equations has roots 2, -1?
(a) 𝑥2 + 𝑥 + 2 = 0
(b)𝑥2 − 𝑥 − 2 = 0
(c)𝑥2 + 2𝑥 − 2 = 0
(d) 𝑥2 − 2𝑥 + 2 = 0
2. To solve x + y = 3; 3x – 2y – 4 = 0 by determinant method find D
(a) 5
(b) 1
(c) -5
(d) - 1
3. Which number cannot represent a probability?
(a) 2
3
(b)15%
(c)1.5
(d) 0.7
4. For a given A.P., t7 = 13, d = -2, then a =
(a) 10
(b) 15
(c) 20
(d) 25
(B) Solve the following questions :- [4]
1. Two digit numbers are formed using digits 2, 3 and 5 without
repeating a digit. Write the sample space ‘S’
2. If Dx = 36, Dy = 45 and D = 3 are the values of the determinants for
certain simultaneous equations x and y, find x
3. Find the common difference of the A.P. 5, 8, 11, 14,……..
4. Verify whether -1 is the root of quadratic equation 𝑥2 + 4𝑥 − 5 = 0
Q2. (A) Complete the following activities . (any two )
[4]
1. Solve using formula 3𝑚2 + 2𝑚 − 7 = 0. Fill in the blanks
3𝑚2 + 2𝑚 − 7 = 0
Comparing the above equation with 𝑎𝑚2 + 𝑏𝑚 + 𝑐 = 0, we get
a = 3, b= 2, c = -7
𝑏2 − 4𝑎𝑐 =
m=
…[Formula]
m =
or m =
2. In the given figure, the arrow rests on any number after the rotation
of the disc. The probability that it will rest on any number is equal.
Let A be any random number. To find the probability of A, fill in the
boxes
n(S) =
Let A be the event that arrow points at the number
which is a perfect cube
A=
n(A) =
P(A) = 𝑛(𝐴) =
𝑛(𝑆)
3. Complete the following table to draw the graph of the equation
3y – x = 4
x
y
(x, y)
5
0
2
2
(2, 2)
(B) Solve the following questions (Any four) [8]
1. A card is drawn at random from a pack of well shuffled 52 playing cards.
Find the probability that the card drawn is
a) an ace
b) a spade
2. Find the first four terms of an A.P. when a = 8 and d = -5
3. Write the following equation in the form 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0. Also, write
the values of a, b, c for the equation 𝑥2 + 5𝑥 = −(3 − 𝑥)
4. Given A.P. is 12, 16, 20, 24,… Find the 24th term of this progression
5. Find the value of the determinant
2√3
9
2
3√3
Q 3. (A) Complete the following activity : (Any one) [3]
1. Two given A.P.’s are 2, 7, 12, …. and 18, 21, 24,…. If nth term of both the
progressions are equal then find the value of n. complete the following
activity
The first A.P. is 2, 7, 12,….
Here, a = 2, d =
nth term = a + (n – 1)d =
The second A.P. is 18, 21, 24, ….
Here, a = 18, d =
nth term = a + (n – 1)d =
Since, the nth terms of the two A.P.’s are equal
 ____ = 3n + 15
n=
2. Out of 200 students from a school, 135 like Kabaddi and the remaining
students do not like the game. If one student is selected at random
from all the students, fill in the following boxes to find the probability
that the student selected doesn’t like Kabaddi
Total number of students in the school =
n(S) =
Number of students who like Kabaddi = 135
 Number of students who do not like Kabaddi =
Let A be the event that the student selected does not like Kabaddi.
n(A) =
P(A) =
….[Formula]
P(A) =
(B) Solve the following questions : (Any two) [6]
1. Sum of the present ages of Manish and Savita is 31. Manish’s age 3 years
ago was 4 times the age of Savita. Find their present ages.
2. Suyash scored 10 marks more in second test than that in the first. 5 times
the score of the second test is the same as square of the score in the first
test. Find his score in the first test
3. A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition
of the digits is allowed. Find the probability that the number so formed is a
prime number
4. If m times the mth term of an A.P. is equal to the n times the nth term, then
show that (m + n)th term of the A.P. is zero
Q4. Solve the following questions : (Any two) [8]
1. Draw the graphs representing the equations 2x = y + 2 and 4x + 3y = 24 on
the same graph paper. Find the area of the triangle formed by these lines
and the X-axis
2. Sum of areas of two squares is 244cm2and the difference between their
perimeter is 8cm. find the ratio of their diagonals
3. If the 9th term of an A.P. is zero, then show that the 29th term is twice the
19th term
Q5. Solve the following : (Any one)
[3]
1. The co-ordinates of the point of intersection of lines ax + by = 9 and bx +
ay = 5 are (3, -1). Find the values of a and b
2. If 460 is divided by a natural number, quotient is 6 more than five times
the divisor and remainder is 1. Find Quotient and divisor