Mathematics Standard (30/2/3) 2025

If for any event E, P(E) + P(E') = q, then the value of q² - 3  is :

If sin θ = cos θ (0° < θ < 90°),  then the value of  sec θ . sin θ is : 

If an arc of a circle of diameter 10 cm subtends an angle of 144° at the centre of the circle, then the length of the arc is : 

If a^b = 32, where 'a' and 'b' are positive integers, then the value of b^ab is:

If one zero of the polynomial q(x) = (p² + 4)x² + 65x + 4p is reciprocal of the other, then the value of 'p' is:
 : 

The equation of a line parallel to the y-axis and at a distance of 5 units to the right of y-axis is : 

The sum of the exponents of prime factors in the prime factorisation of 4004 is : 

The points ( 5, 0), (5, 0) and (0, 4) are the vertices of a triangle which is a/an : 

The 10^th term of the AP

5, 19/4, 9/2, 17/4, ... is

(a) In the given figure, PS/SQ = PT/TR and ∠PST = ∠PRQ. Prove that △PQR is an isosceles triangle.
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OR

(b) In the given figure,  ABE ≅ ACD. Prove that  ADE ~ ABC.

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(a) Prove that : $\sqrt{se{c}^2 \theta +\cos e{c}^2 \theta }$ = tan θ + cot θ

OR

(b) If cosec θ = x + $\frac{1}{4x}$, prove that cosec θ + cot θ = 2x or $\frac{1}{2x}$.

Find the sum of all 3-digit natural numbers which are divisible by 11.

Find the Mean and Mode of the following data : 

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(a) The numerator of a fraction is 3 less than its denominator. If 2 is added to both numerator and denominator, then the sum of the new fraction and the original fraction is $1\frac{9}{20}$. Find the original fraction. 

OR 

(b) A train travelling at a uniform speed for 360 km would have taken 48 minutes less to travel the same distance if its speed were  5 km/h more. Find the original speed of the train.