JMI 11th Science Entrance Paper 2023 Answer Key

JMI 11th Science PYQ Math 2023

26. A ______ is a proven statement used for proving another statement.

(A) axiom

(B) theorem

(D) algorithm

Answer:

Explanation:

27. If two positive integers a and b are written as $a = x^3y^2$ and $b = xy^3$ ; x, y are prime numbers, then HCF (a, b) is:

(A) $xy$

(B) $xy^2$

(D) $x^2y^2$

Answer:

(B)

xy^2

Explanation:

The Highest Common Factor (HCF) is found by taking the smallest power of each common prime factor.
For

x^3

and

x^1

, it’s

x

.
For

y^2

and

y^3

, it’s

y^2

. Result:

xy^2

28. If $a-b$ , $a$ and $a + b$ are zeroes of the polynomial $x^3 -3x^2 + x +1$ , then the value of $a+b$ is:

(A) $1\pm\sqrt{2}$

(B) $-1 +\sqrt{2}$

(D) $3$

Answer:

1\pm\sqrt{2}

Explanation:

The sum of the roots is

3a = -(-3)/1 = 3

a= 1

The product of all roots is

(1-b)(1)(1+b) = -1

1-b^2 = -1

b= \pm\sqrt2

therefore,

a +b = 1\pm\sqrt2

29. If $3k +7$ , $k + 19$ and $2k +1$ are any three consecutive terms of an A.P., then the value of k is:

(A) 10

(B) 1

(D) -10

Answer:

Explanation:

For three terms in an Arithmetic Progression,

2 * (middle term ) = sum of other two

2(k+19) = (3k +7) + (2k+1)

2k+38 = 5k +8

3k +30

k + 10

30. If $x= 2Sin^2 \theta$ and $y= 2Cos^2 \theta + 1$ , then the value of $x+ y$ is equal to:

(A) 3

(B) 2

(D) 0

Answer:

Explanation:

x + y = 2Sin^2 \theta + 2Cos^2 \theta + 1

.
Factoring out 2 gives

2(Sin^2 \theta + Cos^2 \theta ) + 1

.
Since

(Sin^2 \theta + Cos^2 \theta ) =1

,
the sum is

2(1) + 1 = 3

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JMI 11th Science Entrance Paper 2023 Answer Key

JMI 11th Science PYQ Math 2023

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