Class 10 Maths Important Questions With Answers

1

If  f ( x ) =
2x + 3 , g ( x ) = 1 – x²
then the values of x that satisfy the equation   g o f ( x ) = 0 are

(a)    2,
-2            ( b )   1, -2           ( c )   0 , 3              ( d )  -1 ,
-2

2

Which one of the following is the solution of the
equation 

sec² x – 2 tan x = 4 ?  

(a)     π
/ 2           ( b )    π / 3           ( c )   –
π / 4           ( d )    π
/ 6

3

If the argument of the complex number    is π /
2 then the value of a is

………………………….

4

Which of the following statements is not true ?

(a)  2ⁿ > n for all positive
integers  n.

(b)
For every positive integer n , 8ⁿ  – 5ⁿ  is divisible by 3.

(c)  1²
+ 2² +3²+ … + n²  >   for all
natural numbers n.

(d)  n (n
+ 1) (n + 5) is  not a
multiple of 3 where n is a positive integer.

5

From 7 consonants and 5 vowels, how many words (
with or without meaning ) can be formed consisting of 3 different  consonants and 2 different vowels?

(a) 350
(b) 42,000          (c) 4,200            (d) 21, 000

6

If in a sequence the first term is a₁ =
-3 and the n^th term is  a_n
= 1 – 2 a_n-1 , what is the fourth term of the sequence ?

(a)  27           (b)  – 21               (c)  31                (d)   – 25

7

If the mean of the data   9, x, 5, x, 12, 10, 18, 4, 7, 18, 21 is
known to be 10, what is the value of x ?

(a)  6               (b)  2                  (c)  3                 (d) 1

8

The length of latus rectum of the ellipse  36x² + 4y² =
144  is

(a)  4/9           (b)  4/3                (c) 8/3              (d)  36

9

If R₁ and R₂ are two equivalence relations on a
non‐empty set A, then

(a) R₁ U R₂
is an equivalence relation on A

(b) R₁ ∩ R₂ is an equivalence relation on A

(c) R₁– R₂ is an equivalence
relation on A

(d) None of these

10

If  w is a
complex cube root of unity and A
=   , then A⁹⁸
is equal to

(a) w I            (b) w²                             (c) A²
                       (d) A itself

11

If   y = 1 +  + ….  to
infinity where  x > 1
then   dy / dx is

(a)                 (b)                 (c)              (d)  

12

If a man of height 6 ft walks at a uniform speed of 9 ft / sec  from a lamp
of height  15 ft then the length
of his shadow is increasing at the rate of

(a ) 6 ft /
sec      (b)   12
ft / sec           (c)  10 ft / sec          (d) 15 ft / sec.

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13

  is

 (a)  – ( 2 + cot x ) ^-1  + c              (b)   – ( 2 + cot x ) ^-2  + c

(c)  ( 2 + cot x ) ^-1  + c               (d)  -2 ( 2 + cot x ) ^-1   + c

14

The value of         is

(a)    π /2
(b)    3 π / 4
(c)   5 π/4          (d)    5 π /2

15

The area of the region bounded by the curve y = 2x − x² and the line y = x is

(a)  6 sq.
units         (b)  ½
sq. units    (c)  1/6  sq. units     (d)
1/3  sq. units

16

The solution of the differential equation    is 

(a)   y =  ( x- 1 ) e^x  + c
(b)   xy  = ( x -1 ) e^x +
c

(c)   xy   =  (
x+ 1 ) e ^–x  + c    ( d )
y =  ( x – 1 ) e ^–x   + c

17

If a space vector makes angles 150° and 60°  with
the positive direction of X and Y axes then the  angle made by the vector with the positive
direction of Z‐axis is

(a)   60^o             (b)   120^o          (c)   30^o              (d)   90^o

18

The equation of the plane passing through the origin and containing
the lines whose direction cosines are proportional to 1, 2, 2 and 2, 1,−3 is

(a)  8x  – 7 y + 3z  = 0           ( b )   8x
+7y  +3z  = 0

(c)  4x  – 7y – 3z + 2  = 0
(d )  6x  + 7y – 3z = 0

19

The maximum value of z = 10x + 6y subject to
constraints x≥ 0, y ≥ 0,

x + y ≤ 12,  2x + y ≤ 20 is

(a)  100              (b)   104            (c)   72                ( d )   120

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20

Suppose that
five good pens and two defective ones have been mixed up. To find
the defective ones, the pens are tested one-by-one, at random and without
replacement. What is the probability that both the defective fuses are found
in the first two tests?

(a)  1/
21            (b)  5/ 7              (c)  10 / 21             d)  3/ 7