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Model Paper 2 Maths - Model Paper 2

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 73 questions in this chapter.

Question types

Model Paper 2 question types

73 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

73
Questions
4
Question groups
5
Question types
Sample Questions

Model Paper 2 questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 2M.C.Q (1 Marks)1 Mark
$\tan ^{-1}\left(\frac{x}{y}\right)-\tan ^{-1}\left(\frac{x-y}{x+y}\right)=$ _________.
  • A
    $\frac{\pi}{3}$
  • B
    $\frac{\pi}{2}$
  • C
    $\frac{3 \pi}{4}$
  • D
    $\frac{\pi}{4}$
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Q 5M.C.Q (1 Marks)1 Mark
$\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)-\operatorname{cosec}^{-1}(-\sqrt{2})=$ _________.
  • A
    $\frac{\pi}{6}$
  • B
    $\frac{3 \pi}{4}$
  • C
    $\frac{\pi}{2}$
  • D
    $\frac{\pi}{3}$
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Q 62 Marks2 Marks
Find the area of the region in the first quadrant enclosed by X -axis, line $x=\sqrt{3} y$ and the circle $x^2+y^2=4$.
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Q 72 Marks2 Marks
Ten eggs are drawn successively will replacement from a lot containing $10 \%$ defective eggs. Find the probability that there is at least one defective egg.
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Q 82 Marks2 Marks
Abag contains 4 red and 4 black balls. Another bag contains 2 red and 6 black balls. One of two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.
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Q 92 Marks2 Marks
Find the equation of the plane which contains the line of intersection of the planes $\vec{r} \cdot(\hat{i}+2 \hat{j}+3 \hat{k})-4=0, \quad \vec{r} \cdot(2 \hat{i}+\hat{j}-\hat{k})+5=0$ and which is perpendicular to the plane $\vec{r} \cdot(5 \hat{i}+3 \hat{j}-6 \hat{k})+8=0$.
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Q 102 Marks2 Marks
Show that the point $A (1,-2,-8), B (5,0,-2)$ and $C (11,3,7)$ are collinear and find the ration in which B divides AC .
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Q 113 Marks3 Marks
Prove that if a plane has the intercepts $a, b, c$ and is at a distance of $p$ units from the origin, then $\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=\frac{1}{p^2}$.
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Q 133 Marks3 Marks
Solve the following linear programming problem graphically.
Minimise $Z=-3 x+4 y$
$\begin{array}{ll}\text { Subject to } & x+2 y \leq 8, \\ & 3 x+2 y \leq 12, \\ & x \geq 0, y \geq 0\end{array}$
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Q 143 Marks3 Marks
A line makes angles $\alpha, \beta, \gamma$ and $\delta$ with the diagonals of a cube. Prove that $\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma+\cos ^2 \delta=\frac{4}{3}$.
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Q 164 Marks4 Marks
A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is $\tan ^{-1}(0.5)$. Water is poured into it at a constant rate 5 cubic meter per minute. Find the rate at which the level of water rising at the instant when the depth of water in the tank is 10 meter.
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Q 174 Marks4 Marks
The population of a village increase continuously at the rate proportional to the number of its inhabitants present at any time. If the population of the village was 20,000 in 1999 and 25,000 in the year 2004, what will be the population of the village in 2009?
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Q 184 Marks4 Marks
Solve the differential equation $y e^{\frac{x}{y}} d x=\left(x e^{\frac{x}{y}}+y^2\right) d y(y \neq 0)$.
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