Show that: ( n 2 - n ) is an even number for any n ∈ N .

To show: ( n 2 - n ) is an even number for any n ∈ N . Here, ( n 2 - n ) can be written as n ( n - 1 ) i.e it is a product of n and n - 1 which are two consecutive integers. We know that for two consecutive integers one is even and one is odd. Example: 1 , 2 are two consecutive integers where 1 is odd and 2 is even. Then, the product is 1 × 2 = 2 i.e even. Therefore, the product of n and n - 1 is an even number.

Prove that: tan A - sin A tan A + sin A = sec A - 1 sec A + 1 .

To prove: tan A - sin A tan A + sin A = sec A - 1 sec A + 1 proof: L . H . S = tan A - sin A tan A + sin A = sin A cos A - sin A sin A cos A + sin A = sin A - sin A cos A cos A sin A + sin A cos A cos A = sin A [ 1 - cos A ] sin A [ 1 + cos A ] = 1 - cos A 1 + cos A = 1 - 1 sec A 1 + 1 Sec A = sec A - 1 sec A + 1 = R . H . S ∴ tan A - sin A tan A + sin A = sec A - 1 sec A + 1 Thus. it is proved.

E M B I B E

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 6

EASY

10th CBSE

IMPORTANT

Earn 100

Give an example of sure event. What is the probability of such event.

Important Questions on Model Test Paper

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 7

If

\tan 2 θ = \cot (θ + 6 °)

, where

2 θ

and

(θ + 6 °)

are acute angles, then find the numerical value of

θ

(without degree symbol).

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 8

Show that:

(n^{2} - n)

is an even number for any

n \in N

.

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 9

Prove that:

\frac{\tan A - \sin A}{\tan A + \sin A} = \frac{\sec A - 1}{\sec A + 1}

.

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 10

If

α

and

β

are the zeroes of polynomial

x^{2} - 5 x + k

, such that

α - β = 1

, then find the value of

k

.

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 11

Show that the quadratic equation:

x^{2} - ax - 1 = 0

, always has real roots for

' a'

to be real.

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 12

In figure, a square $OABC$ is inscribed in a quadrant $OPBQ$ of a circle. If $OA = 20 cm$ , then the area of the shaded region is $a c m^{2}$ . Find the value of $a$ .

Question Image

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 13

In a seminar, the number of participants in Hindi, English and Mathematics are

60, 84

and

108

respectively. Find the minimum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject.

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 16 - Model Test Paper>SECTION>Q 13

Find the largest positive integer that will divide