Class 11th

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to…………….

Let p, q, r be three logical statements. Consider the compound statements

  $S_1:\left(\left(\sim p\right)\vee q\right)\vee \left(\left(\sim p\right)\vee r\right)and$  

  $S_2:p\to \left(q\vee r\right)$  

 Then, which of the following is NOT true?

Let AB and PQ be two vertical poles, 160m apart from each other. Let C be the middle points of B and Q, which are feet of these two poles. Let $\frac{\pi }{8}$  and q be the angles of elevation from C to P and A, respectively. If the height of pole PQ is twice the height of pole AB, then tan²q is equal to

If the tangents drawn at the points O(0, 0) and $P\left(1+\sqrt[]{5},2\right)$  on the circle x² + y² – 2x – 4y = 0 intersect at the point Q, then the area of the triangle OPQ is equal to

Let the eccentricity of the hyperbola $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1be\sqrt[]{\frac{5}{2}}$ and length of its latus rectum be $6\sqrt[]{2},ify=2x+c$  is a tangent to the hyperbola H, then the value of c² is equal to

The number of real solutions of x⁷ + 5x³ + 3x + 1 = 0 is equal to……….

Let A₁, A₂, A₃,…. be an increasing geometric progression of positive real numbers. If A₁A₃A₅A₇ = $\frac{1}{1296}$  and A₂ + A₄ = $\frac{7}{36},$  then, the value of A₆ + A₈ + A₁₀ is equal to

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

If  then the value of 16a is equal to

From the base of a pole of height 20 meter, the angle of elevation of the top of tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is: