10th Board Sample Question Paper

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Sample Questions :
Q1

Find the [HCF × LCM] for the numbers 105 and 120.

Q2

Find the number of solutions of the following pair of linear equations:

x + 2y − 8 = 0

2x + 4y = 16


Q3

If, a, and 2 are three consecutive terms of an A.P., then find the value of a.

Q4


Two coins are tossed simultaneously. Find the probability of getting exactly one head.

Q5

In figure 1, ΔABC is circumscribing a circle. Find the length of BC.

Q6
If the diameter of a semicircular protractor is 14 cm, then find its perimeter.

Q7
If 1 is a zero of the polynomial p(x) = ax2 − 3(a − 1) x − 1, then find the value of a.


Q8
In ΔLMN, ∠L = 50° and ∠N = 60°. If ΔLMN ∼ ΔPQR, then find ∠Q.


Q9
If sec2θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.

Q10
Find the discriminant of the quadratic equation

Q11

Find all the zeroes of the polynomial 2x3 + x2 − 6x − 3, if two of its zeroes are and.


Q12
If , then evaluate

OR

Find the value of tan 60°, geometrically.

Q13
If the points A (4, 3) and B (x, 5) are on the circle with the centre O (2, 3), find the value of x.

Q14

Which term of the A.P. 3, 15, 27, 39… will be 120 more than its 21st term?

Q15

In Figure 2, ΔABD is a right triangle, right-angled at A and AC ⊥ BD. Prove that AB2 = BC . BD.

Sample paper of 10th class